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A heuristic expert system for forest fire guidance in Greece
Journal of Environmental Management (2002) 65, 327±336 doi:10.1006/jema.2002.0592, available online at http://www.idealibrary.com on
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A heuristic expert system for forest ®re guidance in Greece Lazaros S. Iliadis²Anastasios K. Papastavrou* ³ Panagiotis D. Lefakis§ ²
Assistant Professor of Forest Informatics, Dimokriteio University of Thrace Professor of Forest Policy, and § Lecturer of Forest Informatics, Aristoteleio University of Thessaloniki ³
Received 29 September 1999; accepted 8 February 2001
Forests and forestlands are common inheritance for all Greeks and a piece of the national wealth that must be handed over to the next generations in the best possible condition. After 1974, Greece faces a severe forest ®re problem and forest ®re forecasting is the process that will enable the Greek ministry of Agriculture to reduce the destruction. This paper describes the basic design principles of an Expert System that performs forest ®re forecasting (for the following ®re season) and classi®cation of the prefectures of Greece into forest ®re risk zones. The Expert system handles uncertainty and uses heuristics in order to produce scenarios based on the presence or absence of various qualitative factors. The initial research focused on the construction of a mathematical model which attempted to describe the annual number of forest ®res and burnt area in Greece based on historical data. However this has proven to be impossible using regression analysis and time series. A closer analysis of the ®re data revealed that two qualitative factors dramatically affect the number of forest ®res and the hectares of burnt areas annually. The ®rst is political stability and national elections and the other is drought cycles. Heuristics were constructed that use political stability and drought cycles, to provide forest ®re guidance. Fuzzy logic was applied to produce a fuzzy expected interval for each prefecture of Greece. A fuzzy expected interval is a narrow interval of values that best describes the situation in the country or a part of the country for a certain time period. A successful classi®cation of the prefectures of Greece in forest ®re risk zones was done by the system, by comparing the fuzzy expected intervals to each other. The system was tested for the years 1994 and 1995. The testing has clearly shown that the system can predict accurately, the number of forest ®res for each prefecture for the following year. The average accuracy was as high as 8525% for 1995 and 8089% for 1994. This makes the Expert System a very important tool for forest ®re prevention planning. # 2002 Elsevier Science Ltd. All rights reserved.
Keywords: forest ®re risk forecasting, forest ®re risk classi®cation, expert system, heuristics, fuzzy logic.
Introduction Firstly, it is essential to brie¯y describe the forest ®re problem of Greece. The Greek mainland covers an area of 13 200 000 Ha. The term `forestlands' is used to describe, collectively, all the land categories such as `forests', `partly forested and brushlands' and `pastures'. Forestlands cover approximately 2/3 of the total area (Dimitrakopoulos, 1994). Greece has the most severe forest ®re problem among the EU countries, not only according to the * Corresponding author. Email: omega@net®les.gr 0301-4797/02/$ ± see front matter
number of ®res that break out every year, but also, according to the average burnt area per ®re. It has been estimated that almost 394 Ha are burnt per ®re in Greece, 2847 Ha in Spain, 1974 Ha in Italy and 1529 Ha in Portugal (Dimitrakopoulos, 1994). Greece faces an environmental disaster each summer, caused by forest ®res. It is neither a problem related to climatic conditions nor vegetation, but rather a problem of political will, related to the existing forest policy and forest laws (Papastavrou, 1992). The constitution of 1975 introduced, for the ®rst time, laws that protect forestlands in the country. According to article 117, paragraph 3 `forestlands' # 2002 Elsevier Science Ltd. All rights reserved.
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(public or private) remain characterized as forestlands after their destruction and it is compulsory for them to be reforested. It is forbidden for those burnt forestlands to be used for any other purposes (Papastavrou, 1992). On the other hand, Act Number 1734, which was introduced in 26/10/1987, gives authorities the right to rename the burned forests as `pastures' and in this way it indirectly encourages the destruction of the forests. This Act has been called `The arsonist Law' (Papastavrou, 1992). Other more recent acts also indirectly encourage this practice. In other words, the legal `status' motivates people to burn down the forests (Papastavrou, 1992). There seems to be two main factors that affect forest ®res in Greece. The ®rst is political. Every time National elections are held, the number of forest ®res and the total burnt areas, increase signi®cantly. This is due to the fact that individuals, during an election period, promise to legalize all the illegal buildings that have been built inside forest areas, or to change the legal characterization of `forestlands'. This is done due to the lack of cadastral survey. There is a special Act 998/79 which de®nes that every Greek citizen should own at least 4000 square meters of land, in order to build a house near the sea. Many people who do not own exactly 4000 square meters burn down the nearby forests in order to change the boundaries of their property. This is possible, since there is no cadastral survey. There is also the problem of administration within the Forestry Department both at election time and during periods of political unrest. The in¯uence of the political factor to the problem of forest ®res in Greece, has been shown for the ®rst time by Kailidhs (1990), and it was discussed recently in a scienti®c conference regarding ®re-protection (Dimitrakopoulos, 1997). It should be mentioned that all the National elections so far, have been held inside the forest ®re seasons, from March to October. The second important factor is drought. It has been estimated by forest scientists Markalas and Pantelis (1996), that drought cycles follow a periodicity of 3±5 years in Greece. Statistics show that 29% of the forest ®res in the country are caused by arson but the real percentage is believed to be as high as 42% since about 50% of the forest ®res that are classi®ed as unknown, are probably due to arson. Greece's neighboring countries do not face such a severe forest ®re problem, because they already have a cadastral survey and their forest ®res are not caused by arson due to property or land-use problems. Greece is the only European country that does not have a cadastral survey.
It is obvious that the pattern of land-use keeps changing in Greece, in a fast rate. The increasing demand for goods and services, effectively de®nes the way of land-use (Papastavrou, 1992). Greece's forest ®re problem is so complex, that only an Expert System that takes into consideration the in¯uence of the human factor, can penetrate the problem and provide reliable guidance in the direction of forest ®re management. Expert Systems solve problems by heuristic or approximate methods. Such methods are used in the cases for which algorithmic solutions can not be applied. A heuristic is essentially a rule of thumb which encodes a piece of knowledge about how to solve problems in some domain. Such methods are approximate in the sense that they do not require perfect data and the solutions derived, may be proposed with varying degrees of certainty (Jackson, 1993). This is exactly how this Expert System operates. The system produces a forest ®re forecasting for each prefecture of Greece (for the following ®re season). Each forecast has a degree of certainty assigned to it. The system also evaluates imprecise data in order to classify the prefectures or the forest ®re departments of Greece in forest ®re risk zones. It has been proven by the testing of the system, that both operations of the system, function with remarkable accuracy. It is the ®rst time (internationally) that such a system has been constructed, due to the speci®c nature of Greece's problem. Most of the existing computer programs, for forest ®re management, make use of the meteorological conditions and the types of vegetation for a certain area of interest. On the other hand, human factor is the most important factor affecting forest ®res in Greece and it can only be modeled by the use of heuristics, inside the knowledge base of an Expert System.
The development of Greece's forest ®re problem in the last three decades During the decade 1955±1964, the average number of forest ®res was 6378 with a standard deviation of 1935. The minimum was 303 ®res and the maximum 883. Between 1965 and 1974 the mean remained almost stable 6548 ®res, while the standard deviation was a little higher 217. For those 20 years the number of forest ®res remained stable at approximately 640 forest ®res per year. During the decade 1975±1984 the average number
Forest ®re guidance in Greece
of forest ®res per year, increased from 640 to 1018 also, there was a signi®cant change in the standard deviation. After 1985 the number of forest ®res keeps on rising and in 1993 there were 2711 forest ®re breakouts. Naturally there has been no change in the climate conditions or in the existing vegetation of Greece. The only way to explain this significant change in the number of forest ®res and in the burnt area after 1974, is the legislative framework. Data for the last 42 years was gathered in order to perform regression analysis. These data included the number of ®re breakouts and the areas burnt. A time series was formed out, of the number of ®res for each year and a time series of the total areas burnt. Using regression analysis, the number of ®res in the ®rst four years 1955±1958 can be described by a cubic function with coef®cients b0ÿ2289, b1 4523, b2ÿ2001, b3 266. It should be mentioned that R2 is equal to 1 in this case. This means that 100% of the cases can be described by this curve. The situation for the years 1959±1964 can be described by a quadratic function with coef®cients b0 ÿ2620, b1 855 711, b2 ÿ53 661 with R2 079. This means that 79% of the cases for the period 1959±1964 can be described by this curve. Therefore, regression analysis satisfactory describes the number of forest ®res over the period 1955±1964. Regression analysis fails completely for the decade 1975±1984 and there is no curve that describes the number of forest ®res. Various types of regression were tried to ®nd a description of the period; (logistics, logarithmic, inverse, quadratic, cubic, power, S, exp, growth) but the best ®t is that of the cubuc with R2 0449 and coef®cients b0 41183, b1 30081, b3 2292, b2 ÿ45238. Regression analysis also fails for the following decade 1985±1994, when the average climbs to 1547 forest ®res per year. The situation can be described as `out of control' and the curve that ®ts best is a cubic with R2 0267. This means that the best curve describes only 267% of the cases. Table 1 shows the number of forest ®res in Greece and area burnt for each year from 1970 to 1985. Also indicated are the years when elections and drought occurred. Larger numbers of ®res and greater areas burnt tend to occur in years when elections are held and/or drought occurs. The years 1974, 1977, 1981, 1985, 1988, 1992 are characterized as dry years (Markalas and Pantelis, 1996). The in¯uence of political stability and drought in the total burnt area is also obvious in Figure 1. The years with the most burnt areas, 1988, 1985, 1981,
Table 1.
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Fire data for Greece from 1970 till 1995
Year
Number of forest ®res
Burned area in thousands of square meters
1970 1971 1972 1973 1974
558 525 378 610 768
1975 1976 1977
768 590 1253
1978 1979 1980 1981
828 1076 1207 1159
1982 1983 1984 1985
1045 968 1284 1442
1986 1987 1988
1082 1266 1898
1989
1284
1990
1322
1991 1992
1036 1921
1993
2711
1994 1995
1546 1171
91 889 103 627 85 810 195 000 318 688 Election and Drought Year 209 553 83 887 537 632 Election and Drought Year 200 025 211 803 329 653 814 173 Election and Drought Year 273 722 196 132 336 555 1 054 503 Election and Drought Year 245 135 463 150 1 105 011 Drought Year and the ®rst ®re season after Act 1734 was introduced 423 635 Election Year 385 934 Election Year 235 737 663 463 drought Year 540 492 Election Year 579 081
Figure 1.
Burnt areas in Greece from 1970 to 1994.
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1977, 1992, 1993 are either election or drought years. In some cases both drought and elections are present. It is obvious that the worst year so far is 1988 with the biggest burnt area. The year 1988 was a dry year, and it is the ®rst ®re season after Act 1734 `Arsonist Law' was introduced. This proves once more that the legislative framework of Greece affects the problem of forest ®res.
A brief description of the term `expert system' An Expert System is a computer program that emulates the reasoning process of a human expert in a speci®c domain. Expert Systems reason with imprecise and uncertain information (Jackson, 1992). Both the knowledge used and the data supplied are uncertain. Heuristics (rules of thumb) are also used in order to reach the goal. The knowledge base and the Inference Engine are the main parts of an Expert System (Jackson, 1992). The knowledge base consists of the domain knowledge that is necessary for the solution of the problem while the Inference Engine de®nes the strategy and the way all the rules will be used, in order for the best solution to be achieved. A good Expert System also provides an explanation facility that enables the potential user to consider in depth the reasoning process and justify the ®nal conclusion (Partridge and Hussain, 1995).
Developing a heuristic (rule of thumb) Under normal conditions, the number of forest ®res in Greece follows approximately the mean with small increases of 05 standard deviation or 1 standard deviation. However during the election years or during dry years, the increase over the mean is much higher and reaches 25 standard deviations or even 3 and 5 standard deviations. Table 2 clearly Table 2.
shows the in¯uence of the presence or absence of elections and drought in the number of forest ®re breakouts in the country. For a forecast in year t, the mean and the standard deviation is calculated for the period T [1970, tÿ1]. Num ®res which is denoted as Xt is the number of forest ®res, that the system predicts, for a certain year (denoted as t) from 1970 to 1993. Additionally, mT is the mean and sTis the standard deviation of the number of forest ®res, from 1970 till year tÿ1. In three cases, when both elections and drought are present, the number of forest ®res is equal to the current mean, plus 2, 4 and 5 standard deviations respectively. In six out of ten cases where neither of the two factors is present, the real number of forest ®res equals the current mean, in three cases it is equal to the mean plus one standard deviation and in one case it is equal to the mean plus 15 standard deviations. Using this approach a very interesting heuristic is produced which can be used by the system. Thus, depending on the input scenario, the most probable outcomes can be produced every time. Table 3 shows a comparison of election versus non-election periods on actual burnt area (Ha). There are 10 years without elections and ®ve election years. Burnt areas, Bt, is the burnt forest land for a certain year t, from 1970 to 1993. Additionally, mT is the mean and sT is the standard deviation, of the area of interest from 1970 till year tÿ1. It is clear from Table 3, that the standard deviations about the mean (areas burnt) are clearly greater in election years than in non-election years.
Using a heuristic in order to forecast a value for the number of ®res with a speci®c certainty factor The Greek Fire Management Expert System (GFMES) takes into account uncertainty, in order to make forecasts.
The In¯uence of Drought and Politics on forest ®re breakouts for a year t. T is the time period [1970, tÿ1]
Election and drought years
Neither election nor drought
Drought years
Election years
Frequency
Freq.
Freq.
Freq.
1 1 1
Num Fires Xt mT 2sT mT 4sT mT 5sT
6 3 1
Num Fires Xt mT mT sT mT 15sT
3 1
Num Fires Xt mT 25sT mT 35sT
1 2 1
Num Fires Xt mT sT mT 25sT mT 3sT
Forest ®re guidance in Greece Table 3. Comparison of election versus non-election periods on the forecast area burnt (Ha) for year t. T is the time period [1970, tÿ1] Election periods
Normal periods (No elections)
Frequency Burnt areas Bt (Ha)
Frequency
Burnt areas Bt (Ha)
3 1 4 2
mT sT mTÿ15sT mT mT 05sT
1 1 1 1 1
time time time time time
mT 3sT mTÿ02sT mT 52sT mT 46sT mT 36sT
times time times times
It was mentioned earlier that Greece's forest ®re problem is mainly political and the two principal factors were speci®ed to be `political unrest' and `drought' which follows a cycle of 4+1 years. The user of the system provides input on these two factors in the following manner. Firstly, the user is prompted to answer if he believes that there will be political unrest or drought during the year, also assigning a certainty value to his answer. Actually the user is not asked to input a certain probability directly, but to mark it on a graphically displayed scale from 0 to 1. Various scenarios can be produced in this way and the certainty factor (which is input by the user) is used by the system in order to produce a forecast. For example, an output forecast for the year could read as follows: There will be 1560 forest ®res with a certainty factor of 040; There will be 1900 forest ®res with a certainty factor of 015; There will be 2500 forest ®res with a certainty factor of 07. The value of this type of forecast is that the system outputs the most probable situation for each input scenario. This is a valuable forest management tool for decision making and prevention planning. The forecast can be focused either at the national level or over a local area of interest. The input certainty factor consists of two components. The two components are Ln (Logical Necessity) and Ls (Logical Suf®ciency) of the antecedent, in conjuction with p1 and p2 (p1 and p2 are the respective probabilities) (Krause and Clark, 1993). Logical Necessity is a real number lying between 0001 and 10 and which changes the odds of the outcome being true downwards if the antecedent is false. A value of 10 is the default and indicates
331
no effect on the initial odds (Leonardo User Guide, 1992). The Logical suf®ciency lies between 10 and 1000 and changes the odds of the consequent being true upwards if the antecedent is true. A value of 10 indicates no effect on the initial odds. Initially, the expert system uses its knowledge base in order to calculate the mean of the forest ®res and the standard deviation. Then it uses the data of Tables 2 and 3 in order to calculate the initial probabilities to have a certain increase in the number of forest ®res, over the mean. The increase is counted in numbers of standard deviations. Each one of the initial probabilities are assigned a Ls and a Ln value. A rule of this kind could be as follows: If elections are present and drought is present {Ls 10 Ln 0. 01} then increase is 2sT {Prior 025}. Increase is 05 sT {Prior 010} where Prior is the initial probability. The term `increase is 2sT', means that the predicted number of ®res for year t, equals the mean plus 2 standard deviations for the period [1970, tÿ1]. The system takes into consideration the number of Standard deviations that should be added to the mean in order to give the number of ®res for the next year. The ®rst thing that the system does is to calculate the increase over the mean (depending on the input scenario). Then the odds are adjusted by multiplying by the Logical Suf®ciency of the antecedent (if the clause is true) and the Logical necessity of each clause (if the clause is false) and 1 if the clause is unknown. Pr ob x 1 ÿ Pr ob x The Logical Suf®ciency and Logical Necessity factors can also be adjusted depending on the fact that the value of antecedent has been derived from a rule and it will have a probability of its own kind. This probability is given by the following formula: Odds(x)
Odds (x) Pr ob x= 1 ÿ Pr ob x and can be used to adjust Ls and Ln. New_Ls 1 (Old_Lsÿ1) 6 (Ante_probÿ05)/05 New_Ln 1ÿ(1ÿOld_Ln) 6 (05ÿAnte_prob)/05 In this way a completely dynamic system has been constructed.
General design principles of the GFMES The problem of forest ®res has proven to be so complex, that the use of classical logic (where
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L. S. Iliadis et al.
everything is true or false) or the use of typical statistical analysis does not provide signi®cant aid, towards the direction of ®re management. This is due to the fact that this approach can not penetrate the problem and make use of all the parameters that can not be modeled mathematically. Before going into a detailed analysis of the main design aspects of the system, a brief description of its two most important features should be done. The ®rst function of the system is the classi®cation of the country in forest ®re risk zones in order for the ®re protection policy to be effective. The classi®cation is based on totally dynamic criteria. The best way to achieve this was to introduce a characteristic interval that describes the case for each part of Greece. The interval produced is called Fuzzy Expected Interval and it is obtained by the use of Fuzzy logic. The data is grouped imprecisely using Fuzzy logic before the production of the interval. Secondly, the development of a system that handles uncertainty is a good approach towards the solution of the forecasting problem. The main targets of the ®re forecasting process were established to be the following. (a) The correct estimation of the degree of increase (or decrease) of the total burned areas for the following year; (b) The estimation of the percentage of certainty that could be assigned to the ®nal forecast.
Description of the inference engine GFMES was designed to be a rule based system that consists of Facts, Rules and Object-Frames. It was designed and constructed to have hundreds of rules in the main rule set and thousands of rules (totally) within the object frames. The most important part of an Expert System is the Inference Engine, which is the mechanism that leads to the goal. The Inference Engine strategy that was applied in GFMES was backward chaining with opportunistic forward, which means that it was designed to be a goal driven Expert System, to use Forward Chaining only for the phase of Data Gathering in order to make it faster. It starts from the goal and it evaluates only the necessary rules to reach the ®nal conclusion (Leonardo User Guide, 1992). Knowledge about real world objects is stored in the Object-Frames, which contain various types of slots. Each slot describes the properties and the characteristics of the associated object.
The concept and the use of fuzzy expected intervals in GFMES As mentioned before, GFMES was designed to calculate the Fuzzy Expected Interval (FEI) for an area of interest in Greece. This means that it can produce the characteristic interval that best describes the situation for that particular area. For example, the FEI could be 1200±1480. This would mean that forest ®res for the area would fall between 1200 and 1480 in most cases. In this way the FEI can be used as a ®re risk measure for each area in Greece. Thus, a classi®cation of all parts of the country, according to their ®re risk, can be achieved. It is important that the system manages to produce an interval that is as narrow as possible. The central idea is that statistically and practically there is no interest in forecasting the exact number, but rather in ®nding the general tendency and its direction. The main point is to know if forest ®res will increase from 1200 to 1900, or drop to 600 and not to estimate the precise number. This means that data can be grouped in an imprecise way (using various keywords) and thus Fuzzy logic can be applied. For example, if the statistical data are 980, 1010, 1090, and 999 forest ®res for 4 years, they can be grouped in the following way: On four occasions there are almost 1000 ®res. In this way the data can be grouped imprecisely. There are four types of sentences that can be used during the classi®cation of the data.
1st Type 2nd Type 3rd Type 4th Type
Keywords
Lower bound Upper bound
Almost More or less Over Much more than
xÿ10% xÿ10% x1 2x
xÿ1 x 10% x 10% 1
In a hypothetical situation using this approach forest ®res can be classi®ed imprecisely into groups in the following way: 5 8 3 2
times times times times
there there there there
were were were were
almost 600 ®res; more or less 850 ®res; over 1100 ®res; much more than 1500 ®res.
This is a very ¯exible way of classifying existing data. Fuzzy logic was introduced by Zadeh in 1965. All the theorems that are used in the following section were described by Kandel and Byatt (1978).
Forest ®re guidance in Greece
After the classi®cation, there are four steps that should follow according to Kandel (1992) and they are as follows: (a) The ®rst step is to input data from the imprecise classi®cation, into the characteristic function C(X) and ®nd all C's (Kandel, 1992). The characteristic function is the following: 8 0 if X 0 > < X C X if X 3000 > : 3000 1 otherwise where the number 3000 is used as the maximum number of forest ®res that can ever break in Greece according to the data existing so far. (It is the most extreme case according to the designers' judgment). This function is used for the forecast of the number of ®res. A similar function where 3000 is substituted with 50000 hectares of burned land is used for the forecast of the hectares of burned areas. (b) The second step, Kandel (1992) is to ®nd all m's, which are the candidate Fuzzy Expected Intervals. The m's are intervals of the form [LB, UB] and they can be calculated from the following equations: Pn ij MAX pi1 , pi2 UBj Pn Pjÿ1 ij MAX pi1 , pi2 i1 MIN pi1 , pi2 (1) This equation is used to ®nd the upper bound of every interval mi, where pi1 is the lowest bound of group i and pi2 is the upper bound of group i. Pn ij MIN pi1 , pi2 LBj Pn Pjÿ1 ij MIN pi1 , pi2 i1 MAX pi1 , pi2 (2) This equation is used to ®nd the lower bound of every interval mi, where pi1 is the lowest bound of group i and pi2 is the upper bound of group i. (c) The third task is to ®nd the minimum interval of each line using Theorems 3, 4 and 5 according to Kandel (1992). Theorem 3:
MIN S, R
R if rm 5 S1 S if Sn 5 r1
where S {S1, . . . Sn} R {r1, . . . , rm} and R \ S j. Theorem 4: MIN S, R
R S
if rm 5 Sn if Sn 5 rm
333
where R {r1, . . . , rm} S {S1, . . . , Sn} R \ S=j, S ÏR R ÏS. Theorem 5: If R {r1, . . . , rm} S {S1, . . . , Sn} and R ( S then MIN(S, R) [S1 . . . rm] (d) The ®nal task is to ®nd the maximum interval over the minima using the Theorems 6, 7 and 8 according to Kandel (1992). Theorem 6: If R {r1, . . . , rm} S {S1, . . . , Sn} and R \ S j. then MAX(S, R) R if r1 4 Sn and MAX (S, R) S if S1 4 rm. Theorem 7: If R {r1, . . . , rm} S {S1, . . . , Sn} and R \ S=j, S ÏR R ÏS. then MAX(S, R) R if rm 4 Sn and MAX(S, R) S if Sn 4 rm. Theorem 8: If R {r1, . . . , rm} S {S1, . . . , Sn} and R ( S then MAX(S, R) [r1, . . . , Sn]. The maximum interval found is the Fuzzy Expected Interval. Its bounds should be multiplied by the maximum number of ®re breakouts or the maximum number of burnt hectares in order to produce the real Fuzzy expected interval. This interval could indicate the expected situation for the following year in the whole country or in a part of Greece. It is obvious that the narrower this interval is, the more useful it is. To achieve a narrower interval, for example, 1500±1700 ®res for the following year, the classi®cation of the groups of frequencies should be successful. After the FEI is constructed for each prefecture of Greece, the intervals are compared to each other using the above equations and a classi®cation of the prefectures is performed, in the forest ®re risk zones of the country for which each has been assigned a certain forest ®re risk number. To achieve this the maximum of all the Fuzzy Expected Intervals is determined by the system and the prefectures are assigned a ®re risk value, depending on how far or close they are from the maximum. As a result the system produces clusters. Each cluster, which has a certain characteristic weight assigned to it, can be considered as a Fuzzy set. The data that are members of a Fuzzy set, are assigned a certain weight. This weight shows the degree of membership for each element. In this way each element can belong to more than one fuzzy sets at the same time, but it must have a different weight of membership for each Fuzzy set.
334
L. S. Iliadis et al.
An example of a fuzzy expected interval derived for a local area The following example is hypothetical. The data in Table 4 are grouped using fuzzy logic. The imprecise classi®cation in a protected area is as follows: 1500 ®res occurred on 20±25 occasions. Between 1800 and 2500 ®res broke out more or less on 20 occasions. On 25 occasions there were almost 3000 ®res. STEP C. Find the minima MIN(1, [05±05]) [05±05] MIN([063±070], [060±083)] [060±070] MIN([034±039], [09±1]) [034±039] STEP D. Find the maximum over the minima. Max [060±070] The Fuzzy expected interval is found by multiplying the Upper bound and the Lower Bound of the maximum interval by the number 3000, which is the maximum number of forest ®re breakouts in Greece.
The de®nition of the triangular-shaped fuzzy membership function is as follows: Firstly let [Lb1,Ub1] be the maximum of all the Fuzzy Expected Intervals produced. Let [Lb12 , Ub12 ] be the interval that characterizes a certain cluster of prefectures. Finally [Lb12 , Ub12 ] can be divided in two intervals [Lb12 , a2] and [a2,Ub12 ]. Then a prefecture that has a Fuzzy Expected Interval of [x1, x2] \ has a degree of membership k to the cluster, that is produced by the following function: (i) k 0 IF min ([x1, x2], [Lb12 , a2]) [x1, x2] AND [x1,x2] \ ([Lb12 , a2] ; Figure 2 clearly describes this case. (ii) k [(a2ÿLb12 )/2ÿ(x2ÿx1)/2]/(a2ÿLb12 ) IF [x1, x2] [Lb12 , a2] and x1 5 Lb12 and x2 5 a2 Figure 3 describes the second case.
06063000ÿ07063000 1800ÿ2100
Creating clusters Once the Fuzzy Expected Intervals are produced they are then formed into clusters. Each cluster contains a set of protected areas that are classi®ed as having the same ®re risk. In this way ®ve main clusters have been formed, varying from the highest forest ®re risk cluster, to the lowest forest ®re risk cluster. A triangular-shaped fuzzy membership function is used to show the degree of association for each member of the cluster (Adeli and Hung, 1995). Using the degree of association, protected areas that belong to the same cluster can be differentiated from each other. For example areas A and B may belong to the same forest ®re risk cluster, but their degrees of association may be 075 and 025 respectively.
Figure 2.
The Degree of membership is equal to zero.
Figure 3.
The second case of the Degree of membership.
Figure 4.
The third case of the Degree of membership.
Figure 5.
The Degree of membership is equal to zero.
Table 4. The outcome that is produced after the completion of Steps A and B. Step A, Find the C's; Step B, Find m's Raw data 20 to 25 times More or less 20 times 25 times
C
m
Z
05±05 06±06 09±1
1±1 063±07 034±039
05±05 06±083 09±1
Forest ®re guidance in Greece Table 5.
Testing of the system for 1994
Protected area
Kefallinia Chania Attiki Thess/niki Kerkyra Chios Arta Hraklio Samos Lefkada Lasithi Rethimno Pieria Korinthos Preveza Drama Kiklades Zakinthos Arkadia Rodopi Karditsa Pireas All of the country
Table 6.
Forecasted number of forest ®res for 1994
Certainty of the 1994 forecast as it was produced by the system (%)
Real number of forest ®res for 1994
Accuracy of prediction (%)
53.5 38 55 52 45 72 79 69 50 46 47 47 48 82 71 72 71 46 72 69 70 47 8439
106 57 111 26 28 28 8 67 11 5 16 25 14 39 23 21 12 16 28 10 15 10 1916
9622 7719 99107 7692 7142 6785 50 776 100 80 69 68 9285 8974 86 100 833 75 9285 80 666 80 9176
Forecasted number of forest ®res for 1995
Probability of the 1995 forecast as it was produced by the system (%)
Real number of forest ®res for 1995
Accuracy of prediction (%)
115 50 108 22 41 22 10 42 20 6 20 36 12 25 20 12 ± 22 32 8 9 20 1750
69 45 71 70 47 82 47 72 82 72 46 47 47 48 47 47 ± 48 72 72 74 72 72
132 32 112 26 10 28 5 54 25 0 15 30 8 22 15 6 ± 14 37 8 9 20 1492
102 70 112 20 36 19 12 52 11 6 21 33 13 35 26 21 14 20 26 8 10 12 2088
Testing of the system for 1995
Protected area
Kefallinia Chania Attiki Thess/niki Kerkyra Chios Arta Hraklio Samos Lefkada Lasithi Rethimno Pieria Korinthos Preveza Drama Kiklades Zakinthos Arkadia Rodopi Karditsa Pireas All of the country
8712 4375 9642 8461 2439 7857 50 7777 80 ± 6666 80 50 8636 6666 50 ± 5714 8648 100 100 100 8525
335
336
L. S. Iliadis et al.
(iii) k [(Ub12 ÿa2)/2ÿ(x2ÿx1)/2]/(Ub12 ÿa2) IF [x1,x2] [a2,Ub12 ] and x1 5 a2 and x2 Ub1 Figure 4 depicts the third case. (iv) k 0 IF max ([x1, x2], [Lb12 , a2]) [x1, x2] AND [x1, x2] \ [Lb12 , a2] ; Figure 5 depicts the last case. 2
In this way a supervised fuzzy classi®cation algorithm is constructed which allows the members of the various clusters to vary.
Discussion The initial knowledge base of the system, included ®re data from 1970 to 1993. The expert system was tested to forecast the number of forest ®res for the years 1994 and 1995 for almost 50% of the protected areas. Actually the testing was done in 23 prefectures of Greece. The prefectures were selected to represent all parts of the country with all types of vegetation and climate conditions and all the levels of growth. The results produced were very impressive and they are described in Tables 5 and 6. It should be mentioned that the average accuracy of the predictions of the system was 8089% for 1994 and 7329% for 1995. At the same time the accuracy of the prediction for all of the country was 9176% for 1994 and 8525% for 1995. The scenario used for the years 1994 and 1995 was that there were no elections, political unrest and drought. This was done because no elections were held in 1994 and 1995 and both years were not considered as dry years by the forest scientists and
the meteorologists of the Aristotle University (Markalas and Pantelis, 1996). The system will be tested for years 1996 and 1997 as soon as forest ®re data is available. It should be mentioned that forest ®re data are provided by the Central Forest Service Department, which is located in Athens.
References Adeli, H. and Hung, S. L. (1995). Machine Learning. New York: John Wiley and sons. Dimitrakopoulos, A. (1994). Analysis of forest ®re causes in Greece. MA of Chania Greece. Dimitrakopoulos, A. (1997). Conference `Protection from ®re and theft'. Thessaloniki. Jackson, M. (1992). Understanding expert systems using Crystal. John Willey & Sons. Jackson, P. (1993). Introduction to Expert Systems 2nd Edition. Addison Wesley. Kailidis, D. (1990). Forest Fires. Giachoudi Giapouli Editions. Thessaloniki. Kandel, A. and Byatt, W. J. (1978). Fuzzy sets, fuzzy algebra, and fuzzy statistics. Proc. IEEE 66, 1619. Kandel, A. (1992). Fuzzy Expert Systems. CRC Press. Krause, P. and Clark, D. (1993). Reprecenting Uncertain Knowledge. Intellect ltd. Leonardo user guide. (1992). By Bezant limited. Markalas, S. and Pantelis, S. (1996). Forest Fires in Greece in the Last Years. Aristotle University of Thessaloniki. Thessaloniki. Papastravrou, A. (1992). Social ®nancial and cultural aspects and legal frames of forest ®res in Greece. Vol LE/1. Aristotle University of Thessaloniki. Scienti®c annals of the Department of Forestry and Natural Environment. Thessaloniki. Partridge, D. and Hussain, K. (1995). Knowledge Based Information Systems. McGraw Hill. Zadeh, L. A. (1965). Fuzzy Sets Inf. Control, 8338.
1
A heuristic expert system for forest ®re guidance in Greece Lazaros S. Iliadis²Anastasios K. Papastavrou* ³ Panagiotis D. Lefakis§ ²
Assistant Professor of Forest Informatics, Dimokriteio University of Thrace Professor of Forest Policy, and § Lecturer of Forest Informatics, Aristoteleio University of Thessaloniki ³
Received 29 September 1999; accepted 8 February 2001
Forests and forestlands are common inheritance for all Greeks and a piece of the national wealth that must be handed over to the next generations in the best possible condition. After 1974, Greece faces a severe forest ®re problem and forest ®re forecasting is the process that will enable the Greek ministry of Agriculture to reduce the destruction. This paper describes the basic design principles of an Expert System that performs forest ®re forecasting (for the following ®re season) and classi®cation of the prefectures of Greece into forest ®re risk zones. The Expert system handles uncertainty and uses heuristics in order to produce scenarios based on the presence or absence of various qualitative factors. The initial research focused on the construction of a mathematical model which attempted to describe the annual number of forest ®res and burnt area in Greece based on historical data. However this has proven to be impossible using regression analysis and time series. A closer analysis of the ®re data revealed that two qualitative factors dramatically affect the number of forest ®res and the hectares of burnt areas annually. The ®rst is political stability and national elections and the other is drought cycles. Heuristics were constructed that use political stability and drought cycles, to provide forest ®re guidance. Fuzzy logic was applied to produce a fuzzy expected interval for each prefecture of Greece. A fuzzy expected interval is a narrow interval of values that best describes the situation in the country or a part of the country for a certain time period. A successful classi®cation of the prefectures of Greece in forest ®re risk zones was done by the system, by comparing the fuzzy expected intervals to each other. The system was tested for the years 1994 and 1995. The testing has clearly shown that the system can predict accurately, the number of forest ®res for each prefecture for the following year. The average accuracy was as high as 8525% for 1995 and 8089% for 1994. This makes the Expert System a very important tool for forest ®re prevention planning. # 2002 Elsevier Science Ltd. All rights reserved.
Keywords: forest ®re risk forecasting, forest ®re risk classi®cation, expert system, heuristics, fuzzy logic.
Introduction Firstly, it is essential to brie¯y describe the forest ®re problem of Greece. The Greek mainland covers an area of 13 200 000 Ha. The term `forestlands' is used to describe, collectively, all the land categories such as `forests', `partly forested and brushlands' and `pastures'. Forestlands cover approximately 2/3 of the total area (Dimitrakopoulos, 1994). Greece has the most severe forest ®re problem among the EU countries, not only according to the * Corresponding author. Email: omega@net®les.gr 0301-4797/02/$ ± see front matter
number of ®res that break out every year, but also, according to the average burnt area per ®re. It has been estimated that almost 394 Ha are burnt per ®re in Greece, 2847 Ha in Spain, 1974 Ha in Italy and 1529 Ha in Portugal (Dimitrakopoulos, 1994). Greece faces an environmental disaster each summer, caused by forest ®res. It is neither a problem related to climatic conditions nor vegetation, but rather a problem of political will, related to the existing forest policy and forest laws (Papastavrou, 1992). The constitution of 1975 introduced, for the ®rst time, laws that protect forestlands in the country. According to article 117, paragraph 3 `forestlands' # 2002 Elsevier Science Ltd. All rights reserved.
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(public or private) remain characterized as forestlands after their destruction and it is compulsory for them to be reforested. It is forbidden for those burnt forestlands to be used for any other purposes (Papastavrou, 1992). On the other hand, Act Number 1734, which was introduced in 26/10/1987, gives authorities the right to rename the burned forests as `pastures' and in this way it indirectly encourages the destruction of the forests. This Act has been called `The arsonist Law' (Papastavrou, 1992). Other more recent acts also indirectly encourage this practice. In other words, the legal `status' motivates people to burn down the forests (Papastavrou, 1992). There seems to be two main factors that affect forest ®res in Greece. The ®rst is political. Every time National elections are held, the number of forest ®res and the total burnt areas, increase signi®cantly. This is due to the fact that individuals, during an election period, promise to legalize all the illegal buildings that have been built inside forest areas, or to change the legal characterization of `forestlands'. This is done due to the lack of cadastral survey. There is a special Act 998/79 which de®nes that every Greek citizen should own at least 4000 square meters of land, in order to build a house near the sea. Many people who do not own exactly 4000 square meters burn down the nearby forests in order to change the boundaries of their property. This is possible, since there is no cadastral survey. There is also the problem of administration within the Forestry Department both at election time and during periods of political unrest. The in¯uence of the political factor to the problem of forest ®res in Greece, has been shown for the ®rst time by Kailidhs (1990), and it was discussed recently in a scienti®c conference regarding ®re-protection (Dimitrakopoulos, 1997). It should be mentioned that all the National elections so far, have been held inside the forest ®re seasons, from March to October. The second important factor is drought. It has been estimated by forest scientists Markalas and Pantelis (1996), that drought cycles follow a periodicity of 3±5 years in Greece. Statistics show that 29% of the forest ®res in the country are caused by arson but the real percentage is believed to be as high as 42% since about 50% of the forest ®res that are classi®ed as unknown, are probably due to arson. Greece's neighboring countries do not face such a severe forest ®re problem, because they already have a cadastral survey and their forest ®res are not caused by arson due to property or land-use problems. Greece is the only European country that does not have a cadastral survey.
It is obvious that the pattern of land-use keeps changing in Greece, in a fast rate. The increasing demand for goods and services, effectively de®nes the way of land-use (Papastavrou, 1992). Greece's forest ®re problem is so complex, that only an Expert System that takes into consideration the in¯uence of the human factor, can penetrate the problem and provide reliable guidance in the direction of forest ®re management. Expert Systems solve problems by heuristic or approximate methods. Such methods are used in the cases for which algorithmic solutions can not be applied. A heuristic is essentially a rule of thumb which encodes a piece of knowledge about how to solve problems in some domain. Such methods are approximate in the sense that they do not require perfect data and the solutions derived, may be proposed with varying degrees of certainty (Jackson, 1993). This is exactly how this Expert System operates. The system produces a forest ®re forecasting for each prefecture of Greece (for the following ®re season). Each forecast has a degree of certainty assigned to it. The system also evaluates imprecise data in order to classify the prefectures or the forest ®re departments of Greece in forest ®re risk zones. It has been proven by the testing of the system, that both operations of the system, function with remarkable accuracy. It is the ®rst time (internationally) that such a system has been constructed, due to the speci®c nature of Greece's problem. Most of the existing computer programs, for forest ®re management, make use of the meteorological conditions and the types of vegetation for a certain area of interest. On the other hand, human factor is the most important factor affecting forest ®res in Greece and it can only be modeled by the use of heuristics, inside the knowledge base of an Expert System.
The development of Greece's forest ®re problem in the last three decades During the decade 1955±1964, the average number of forest ®res was 6378 with a standard deviation of 1935. The minimum was 303 ®res and the maximum 883. Between 1965 and 1974 the mean remained almost stable 6548 ®res, while the standard deviation was a little higher 217. For those 20 years the number of forest ®res remained stable at approximately 640 forest ®res per year. During the decade 1975±1984 the average number
Forest ®re guidance in Greece
of forest ®res per year, increased from 640 to 1018 also, there was a signi®cant change in the standard deviation. After 1985 the number of forest ®res keeps on rising and in 1993 there were 2711 forest ®re breakouts. Naturally there has been no change in the climate conditions or in the existing vegetation of Greece. The only way to explain this significant change in the number of forest ®res and in the burnt area after 1974, is the legislative framework. Data for the last 42 years was gathered in order to perform regression analysis. These data included the number of ®re breakouts and the areas burnt. A time series was formed out, of the number of ®res for each year and a time series of the total areas burnt. Using regression analysis, the number of ®res in the ®rst four years 1955±1958 can be described by a cubic function with coef®cients b0ÿ2289, b1 4523, b2ÿ2001, b3 266. It should be mentioned that R2 is equal to 1 in this case. This means that 100% of the cases can be described by this curve. The situation for the years 1959±1964 can be described by a quadratic function with coef®cients b0 ÿ2620, b1 855 711, b2 ÿ53 661 with R2 079. This means that 79% of the cases for the period 1959±1964 can be described by this curve. Therefore, regression analysis satisfactory describes the number of forest ®res over the period 1955±1964. Regression analysis fails completely for the decade 1975±1984 and there is no curve that describes the number of forest ®res. Various types of regression were tried to ®nd a description of the period; (logistics, logarithmic, inverse, quadratic, cubic, power, S, exp, growth) but the best ®t is that of the cubuc with R2 0449 and coef®cients b0 41183, b1 30081, b3 2292, b2 ÿ45238. Regression analysis also fails for the following decade 1985±1994, when the average climbs to 1547 forest ®res per year. The situation can be described as `out of control' and the curve that ®ts best is a cubic with R2 0267. This means that the best curve describes only 267% of the cases. Table 1 shows the number of forest ®res in Greece and area burnt for each year from 1970 to 1985. Also indicated are the years when elections and drought occurred. Larger numbers of ®res and greater areas burnt tend to occur in years when elections are held and/or drought occurs. The years 1974, 1977, 1981, 1985, 1988, 1992 are characterized as dry years (Markalas and Pantelis, 1996). The in¯uence of political stability and drought in the total burnt area is also obvious in Figure 1. The years with the most burnt areas, 1988, 1985, 1981,
Table 1.
329
Fire data for Greece from 1970 till 1995
Year
Number of forest ®res
Burned area in thousands of square meters
1970 1971 1972 1973 1974
558 525 378 610 768
1975 1976 1977
768 590 1253
1978 1979 1980 1981
828 1076 1207 1159
1982 1983 1984 1985
1045 968 1284 1442
1986 1987 1988
1082 1266 1898
1989
1284
1990
1322
1991 1992
1036 1921
1993
2711
1994 1995
1546 1171
91 889 103 627 85 810 195 000 318 688 Election and Drought Year 209 553 83 887 537 632 Election and Drought Year 200 025 211 803 329 653 814 173 Election and Drought Year 273 722 196 132 336 555 1 054 503 Election and Drought Year 245 135 463 150 1 105 011 Drought Year and the ®rst ®re season after Act 1734 was introduced 423 635 Election Year 385 934 Election Year 235 737 663 463 drought Year 540 492 Election Year 579 081
Figure 1.
Burnt areas in Greece from 1970 to 1994.
330
L. S. Iliadis et al.
1977, 1992, 1993 are either election or drought years. In some cases both drought and elections are present. It is obvious that the worst year so far is 1988 with the biggest burnt area. The year 1988 was a dry year, and it is the ®rst ®re season after Act 1734 `Arsonist Law' was introduced. This proves once more that the legislative framework of Greece affects the problem of forest ®res.
A brief description of the term `expert system' An Expert System is a computer program that emulates the reasoning process of a human expert in a speci®c domain. Expert Systems reason with imprecise and uncertain information (Jackson, 1992). Both the knowledge used and the data supplied are uncertain. Heuristics (rules of thumb) are also used in order to reach the goal. The knowledge base and the Inference Engine are the main parts of an Expert System (Jackson, 1992). The knowledge base consists of the domain knowledge that is necessary for the solution of the problem while the Inference Engine de®nes the strategy and the way all the rules will be used, in order for the best solution to be achieved. A good Expert System also provides an explanation facility that enables the potential user to consider in depth the reasoning process and justify the ®nal conclusion (Partridge and Hussain, 1995).
Developing a heuristic (rule of thumb) Under normal conditions, the number of forest ®res in Greece follows approximately the mean with small increases of 05 standard deviation or 1 standard deviation. However during the election years or during dry years, the increase over the mean is much higher and reaches 25 standard deviations or even 3 and 5 standard deviations. Table 2 clearly Table 2.
shows the in¯uence of the presence or absence of elections and drought in the number of forest ®re breakouts in the country. For a forecast in year t, the mean and the standard deviation is calculated for the period T [1970, tÿ1]. Num ®res which is denoted as Xt is the number of forest ®res, that the system predicts, for a certain year (denoted as t) from 1970 to 1993. Additionally, mT is the mean and sTis the standard deviation of the number of forest ®res, from 1970 till year tÿ1. In three cases, when both elections and drought are present, the number of forest ®res is equal to the current mean, plus 2, 4 and 5 standard deviations respectively. In six out of ten cases where neither of the two factors is present, the real number of forest ®res equals the current mean, in three cases it is equal to the mean plus one standard deviation and in one case it is equal to the mean plus 15 standard deviations. Using this approach a very interesting heuristic is produced which can be used by the system. Thus, depending on the input scenario, the most probable outcomes can be produced every time. Table 3 shows a comparison of election versus non-election periods on actual burnt area (Ha). There are 10 years without elections and ®ve election years. Burnt areas, Bt, is the burnt forest land for a certain year t, from 1970 to 1993. Additionally, mT is the mean and sT is the standard deviation, of the area of interest from 1970 till year tÿ1. It is clear from Table 3, that the standard deviations about the mean (areas burnt) are clearly greater in election years than in non-election years.
Using a heuristic in order to forecast a value for the number of ®res with a speci®c certainty factor The Greek Fire Management Expert System (GFMES) takes into account uncertainty, in order to make forecasts.
The In¯uence of Drought and Politics on forest ®re breakouts for a year t. T is the time period [1970, tÿ1]
Election and drought years
Neither election nor drought
Drought years
Election years
Frequency
Freq.
Freq.
Freq.
1 1 1
Num Fires Xt mT 2sT mT 4sT mT 5sT
6 3 1
Num Fires Xt mT mT sT mT 15sT
3 1
Num Fires Xt mT 25sT mT 35sT
1 2 1
Num Fires Xt mT sT mT 25sT mT 3sT
Forest ®re guidance in Greece Table 3. Comparison of election versus non-election periods on the forecast area burnt (Ha) for year t. T is the time period [1970, tÿ1] Election periods
Normal periods (No elections)
Frequency Burnt areas Bt (Ha)
Frequency
Burnt areas Bt (Ha)
3 1 4 2
mT sT mTÿ15sT mT mT 05sT
1 1 1 1 1
time time time time time
mT 3sT mTÿ02sT mT 52sT mT 46sT mT 36sT
times time times times
It was mentioned earlier that Greece's forest ®re problem is mainly political and the two principal factors were speci®ed to be `political unrest' and `drought' which follows a cycle of 4+1 years. The user of the system provides input on these two factors in the following manner. Firstly, the user is prompted to answer if he believes that there will be political unrest or drought during the year, also assigning a certainty value to his answer. Actually the user is not asked to input a certain probability directly, but to mark it on a graphically displayed scale from 0 to 1. Various scenarios can be produced in this way and the certainty factor (which is input by the user) is used by the system in order to produce a forecast. For example, an output forecast for the year could read as follows: There will be 1560 forest ®res with a certainty factor of 040; There will be 1900 forest ®res with a certainty factor of 015; There will be 2500 forest ®res with a certainty factor of 07. The value of this type of forecast is that the system outputs the most probable situation for each input scenario. This is a valuable forest management tool for decision making and prevention planning. The forecast can be focused either at the national level or over a local area of interest. The input certainty factor consists of two components. The two components are Ln (Logical Necessity) and Ls (Logical Suf®ciency) of the antecedent, in conjuction with p1 and p2 (p1 and p2 are the respective probabilities) (Krause and Clark, 1993). Logical Necessity is a real number lying between 0001 and 10 and which changes the odds of the outcome being true downwards if the antecedent is false. A value of 10 is the default and indicates
331
no effect on the initial odds (Leonardo User Guide, 1992). The Logical suf®ciency lies between 10 and 1000 and changes the odds of the consequent being true upwards if the antecedent is true. A value of 10 indicates no effect on the initial odds. Initially, the expert system uses its knowledge base in order to calculate the mean of the forest ®res and the standard deviation. Then it uses the data of Tables 2 and 3 in order to calculate the initial probabilities to have a certain increase in the number of forest ®res, over the mean. The increase is counted in numbers of standard deviations. Each one of the initial probabilities are assigned a Ls and a Ln value. A rule of this kind could be as follows: If elections are present and drought is present {Ls 10 Ln 0. 01} then increase is 2sT {Prior 025}. Increase is 05 sT {Prior 010} where Prior is the initial probability. The term `increase is 2sT', means that the predicted number of ®res for year t, equals the mean plus 2 standard deviations for the period [1970, tÿ1]. The system takes into consideration the number of Standard deviations that should be added to the mean in order to give the number of ®res for the next year. The ®rst thing that the system does is to calculate the increase over the mean (depending on the input scenario). Then the odds are adjusted by multiplying by the Logical Suf®ciency of the antecedent (if the clause is true) and the Logical necessity of each clause (if the clause is false) and 1 if the clause is unknown. Pr ob x 1 ÿ Pr ob x The Logical Suf®ciency and Logical Necessity factors can also be adjusted depending on the fact that the value of antecedent has been derived from a rule and it will have a probability of its own kind. This probability is given by the following formula: Odds(x)
Odds (x) Pr ob x= 1 ÿ Pr ob x and can be used to adjust Ls and Ln. New_Ls 1 (Old_Lsÿ1) 6 (Ante_probÿ05)/05 New_Ln 1ÿ(1ÿOld_Ln) 6 (05ÿAnte_prob)/05 In this way a completely dynamic system has been constructed.
General design principles of the GFMES The problem of forest ®res has proven to be so complex, that the use of classical logic (where
332
L. S. Iliadis et al.
everything is true or false) or the use of typical statistical analysis does not provide signi®cant aid, towards the direction of ®re management. This is due to the fact that this approach can not penetrate the problem and make use of all the parameters that can not be modeled mathematically. Before going into a detailed analysis of the main design aspects of the system, a brief description of its two most important features should be done. The ®rst function of the system is the classi®cation of the country in forest ®re risk zones in order for the ®re protection policy to be effective. The classi®cation is based on totally dynamic criteria. The best way to achieve this was to introduce a characteristic interval that describes the case for each part of Greece. The interval produced is called Fuzzy Expected Interval and it is obtained by the use of Fuzzy logic. The data is grouped imprecisely using Fuzzy logic before the production of the interval. Secondly, the development of a system that handles uncertainty is a good approach towards the solution of the forecasting problem. The main targets of the ®re forecasting process were established to be the following. (a) The correct estimation of the degree of increase (or decrease) of the total burned areas for the following year; (b) The estimation of the percentage of certainty that could be assigned to the ®nal forecast.
Description of the inference engine GFMES was designed to be a rule based system that consists of Facts, Rules and Object-Frames. It was designed and constructed to have hundreds of rules in the main rule set and thousands of rules (totally) within the object frames. The most important part of an Expert System is the Inference Engine, which is the mechanism that leads to the goal. The Inference Engine strategy that was applied in GFMES was backward chaining with opportunistic forward, which means that it was designed to be a goal driven Expert System, to use Forward Chaining only for the phase of Data Gathering in order to make it faster. It starts from the goal and it evaluates only the necessary rules to reach the ®nal conclusion (Leonardo User Guide, 1992). Knowledge about real world objects is stored in the Object-Frames, which contain various types of slots. Each slot describes the properties and the characteristics of the associated object.
The concept and the use of fuzzy expected intervals in GFMES As mentioned before, GFMES was designed to calculate the Fuzzy Expected Interval (FEI) for an area of interest in Greece. This means that it can produce the characteristic interval that best describes the situation for that particular area. For example, the FEI could be 1200±1480. This would mean that forest ®res for the area would fall between 1200 and 1480 in most cases. In this way the FEI can be used as a ®re risk measure for each area in Greece. Thus, a classi®cation of all parts of the country, according to their ®re risk, can be achieved. It is important that the system manages to produce an interval that is as narrow as possible. The central idea is that statistically and practically there is no interest in forecasting the exact number, but rather in ®nding the general tendency and its direction. The main point is to know if forest ®res will increase from 1200 to 1900, or drop to 600 and not to estimate the precise number. This means that data can be grouped in an imprecise way (using various keywords) and thus Fuzzy logic can be applied. For example, if the statistical data are 980, 1010, 1090, and 999 forest ®res for 4 years, they can be grouped in the following way: On four occasions there are almost 1000 ®res. In this way the data can be grouped imprecisely. There are four types of sentences that can be used during the classi®cation of the data.
1st Type 2nd Type 3rd Type 4th Type
Keywords
Lower bound Upper bound
Almost More or less Over Much more than
xÿ10% xÿ10% x1 2x
xÿ1 x 10% x 10% 1
In a hypothetical situation using this approach forest ®res can be classi®ed imprecisely into groups in the following way: 5 8 3 2
times times times times
there there there there
were were were were
almost 600 ®res; more or less 850 ®res; over 1100 ®res; much more than 1500 ®res.
This is a very ¯exible way of classifying existing data. Fuzzy logic was introduced by Zadeh in 1965. All the theorems that are used in the following section were described by Kandel and Byatt (1978).
Forest ®re guidance in Greece
After the classi®cation, there are four steps that should follow according to Kandel (1992) and they are as follows: (a) The ®rst step is to input data from the imprecise classi®cation, into the characteristic function C(X) and ®nd all C's (Kandel, 1992). The characteristic function is the following: 8 0 if X 0 > < X C X if X 3000 > : 3000 1 otherwise where the number 3000 is used as the maximum number of forest ®res that can ever break in Greece according to the data existing so far. (It is the most extreme case according to the designers' judgment). This function is used for the forecast of the number of ®res. A similar function where 3000 is substituted with 50000 hectares of burned land is used for the forecast of the hectares of burned areas. (b) The second step, Kandel (1992) is to ®nd all m's, which are the candidate Fuzzy Expected Intervals. The m's are intervals of the form [LB, UB] and they can be calculated from the following equations: Pn ij MAX pi1 , pi2 UBj Pn Pjÿ1 ij MAX pi1 , pi2 i1 MIN pi1 , pi2 (1) This equation is used to ®nd the upper bound of every interval mi, where pi1 is the lowest bound of group i and pi2 is the upper bound of group i. Pn ij MIN pi1 , pi2 LBj Pn Pjÿ1 ij MIN pi1 , pi2 i1 MAX pi1 , pi2 (2) This equation is used to ®nd the lower bound of every interval mi, where pi1 is the lowest bound of group i and pi2 is the upper bound of group i. (c) The third task is to ®nd the minimum interval of each line using Theorems 3, 4 and 5 according to Kandel (1992). Theorem 3:
MIN S, R
R if rm 5 S1 S if Sn 5 r1
where S {S1, . . . Sn} R {r1, . . . , rm} and R \ S j. Theorem 4: MIN S, R
R S
if rm 5 Sn if Sn 5 rm
333
where R {r1, . . . , rm} S {S1, . . . , Sn} R \ S=j, S ÏR R ÏS. Theorem 5: If R {r1, . . . , rm} S {S1, . . . , Sn} and R ( S then MIN(S, R) [S1 . . . rm] (d) The ®nal task is to ®nd the maximum interval over the minima using the Theorems 6, 7 and 8 according to Kandel (1992). Theorem 6: If R {r1, . . . , rm} S {S1, . . . , Sn} and R \ S j. then MAX(S, R) R if r1 4 Sn and MAX (S, R) S if S1 4 rm. Theorem 7: If R {r1, . . . , rm} S {S1, . . . , Sn} and R \ S=j, S ÏR R ÏS. then MAX(S, R) R if rm 4 Sn and MAX(S, R) S if Sn 4 rm. Theorem 8: If R {r1, . . . , rm} S {S1, . . . , Sn} and R ( S then MAX(S, R) [r1, . . . , Sn]. The maximum interval found is the Fuzzy Expected Interval. Its bounds should be multiplied by the maximum number of ®re breakouts or the maximum number of burnt hectares in order to produce the real Fuzzy expected interval. This interval could indicate the expected situation for the following year in the whole country or in a part of Greece. It is obvious that the narrower this interval is, the more useful it is. To achieve a narrower interval, for example, 1500±1700 ®res for the following year, the classi®cation of the groups of frequencies should be successful. After the FEI is constructed for each prefecture of Greece, the intervals are compared to each other using the above equations and a classi®cation of the prefectures is performed, in the forest ®re risk zones of the country for which each has been assigned a certain forest ®re risk number. To achieve this the maximum of all the Fuzzy Expected Intervals is determined by the system and the prefectures are assigned a ®re risk value, depending on how far or close they are from the maximum. As a result the system produces clusters. Each cluster, which has a certain characteristic weight assigned to it, can be considered as a Fuzzy set. The data that are members of a Fuzzy set, are assigned a certain weight. This weight shows the degree of membership for each element. In this way each element can belong to more than one fuzzy sets at the same time, but it must have a different weight of membership for each Fuzzy set.
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An example of a fuzzy expected interval derived for a local area The following example is hypothetical. The data in Table 4 are grouped using fuzzy logic. The imprecise classi®cation in a protected area is as follows: 1500 ®res occurred on 20±25 occasions. Between 1800 and 2500 ®res broke out more or less on 20 occasions. On 25 occasions there were almost 3000 ®res. STEP C. Find the minima MIN(1, [05±05]) [05±05] MIN([063±070], [060±083)] [060±070] MIN([034±039], [09±1]) [034±039] STEP D. Find the maximum over the minima. Max [060±070] The Fuzzy expected interval is found by multiplying the Upper bound and the Lower Bound of the maximum interval by the number 3000, which is the maximum number of forest ®re breakouts in Greece.
The de®nition of the triangular-shaped fuzzy membership function is as follows: Firstly let [Lb1,Ub1] be the maximum of all the Fuzzy Expected Intervals produced. Let [Lb12 , Ub12 ] be the interval that characterizes a certain cluster of prefectures. Finally [Lb12 , Ub12 ] can be divided in two intervals [Lb12 , a2] and [a2,Ub12 ]. Then a prefecture that has a Fuzzy Expected Interval of [x1, x2] \ has a degree of membership k to the cluster, that is produced by the following function: (i) k 0 IF min ([x1, x2], [Lb12 , a2]) [x1, x2] AND [x1,x2] \ ([Lb12 , a2] ; Figure 2 clearly describes this case. (ii) k [(a2ÿLb12 )/2ÿ(x2ÿx1)/2]/(a2ÿLb12 ) IF [x1, x2] [Lb12 , a2] and x1 5 Lb12 and x2 5 a2 Figure 3 describes the second case.
06063000ÿ07063000 1800ÿ2100
Creating clusters Once the Fuzzy Expected Intervals are produced they are then formed into clusters. Each cluster contains a set of protected areas that are classi®ed as having the same ®re risk. In this way ®ve main clusters have been formed, varying from the highest forest ®re risk cluster, to the lowest forest ®re risk cluster. A triangular-shaped fuzzy membership function is used to show the degree of association for each member of the cluster (Adeli and Hung, 1995). Using the degree of association, protected areas that belong to the same cluster can be differentiated from each other. For example areas A and B may belong to the same forest ®re risk cluster, but their degrees of association may be 075 and 025 respectively.
Figure 2.
The Degree of membership is equal to zero.
Figure 3.
The second case of the Degree of membership.
Figure 4.
The third case of the Degree of membership.
Figure 5.
The Degree of membership is equal to zero.
Table 4. The outcome that is produced after the completion of Steps A and B. Step A, Find the C's; Step B, Find m's Raw data 20 to 25 times More or less 20 times 25 times
C
m
Z
05±05 06±06 09±1
1±1 063±07 034±039
05±05 06±083 09±1
Forest ®re guidance in Greece Table 5.
Testing of the system for 1994
Protected area
Kefallinia Chania Attiki Thess/niki Kerkyra Chios Arta Hraklio Samos Lefkada Lasithi Rethimno Pieria Korinthos Preveza Drama Kiklades Zakinthos Arkadia Rodopi Karditsa Pireas All of the country
Table 6.
Forecasted number of forest ®res for 1994
Certainty of the 1994 forecast as it was produced by the system (%)
Real number of forest ®res for 1994
Accuracy of prediction (%)
53.5 38 55 52 45 72 79 69 50 46 47 47 48 82 71 72 71 46 72 69 70 47 8439
106 57 111 26 28 28 8 67 11 5 16 25 14 39 23 21 12 16 28 10 15 10 1916
9622 7719 99107 7692 7142 6785 50 776 100 80 69 68 9285 8974 86 100 833 75 9285 80 666 80 9176
Forecasted number of forest ®res for 1995
Probability of the 1995 forecast as it was produced by the system (%)
Real number of forest ®res for 1995
Accuracy of prediction (%)
115 50 108 22 41 22 10 42 20 6 20 36 12 25 20 12 ± 22 32 8 9 20 1750
69 45 71 70 47 82 47 72 82 72 46 47 47 48 47 47 ± 48 72 72 74 72 72
132 32 112 26 10 28 5 54 25 0 15 30 8 22 15 6 ± 14 37 8 9 20 1492
102 70 112 20 36 19 12 52 11 6 21 33 13 35 26 21 14 20 26 8 10 12 2088
Testing of the system for 1995
Protected area
Kefallinia Chania Attiki Thess/niki Kerkyra Chios Arta Hraklio Samos Lefkada Lasithi Rethimno Pieria Korinthos Preveza Drama Kiklades Zakinthos Arkadia Rodopi Karditsa Pireas All of the country
8712 4375 9642 8461 2439 7857 50 7777 80 ± 6666 80 50 8636 6666 50 ± 5714 8648 100 100 100 8525
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(iii) k [(Ub12 ÿa2)/2ÿ(x2ÿx1)/2]/(Ub12 ÿa2) IF [x1,x2] [a2,Ub12 ] and x1 5 a2 and x2 Ub1 Figure 4 depicts the third case. (iv) k 0 IF max ([x1, x2], [Lb12 , a2]) [x1, x2] AND [x1, x2] \ [Lb12 , a2] ; Figure 5 depicts the last case. 2
In this way a supervised fuzzy classi®cation algorithm is constructed which allows the members of the various clusters to vary.
Discussion The initial knowledge base of the system, included ®re data from 1970 to 1993. The expert system was tested to forecast the number of forest ®res for the years 1994 and 1995 for almost 50% of the protected areas. Actually the testing was done in 23 prefectures of Greece. The prefectures were selected to represent all parts of the country with all types of vegetation and climate conditions and all the levels of growth. The results produced were very impressive and they are described in Tables 5 and 6. It should be mentioned that the average accuracy of the predictions of the system was 8089% for 1994 and 7329% for 1995. At the same time the accuracy of the prediction for all of the country was 9176% for 1994 and 8525% for 1995. The scenario used for the years 1994 and 1995 was that there were no elections, political unrest and drought. This was done because no elections were held in 1994 and 1995 and both years were not considered as dry years by the forest scientists and
the meteorologists of the Aristotle University (Markalas and Pantelis, 1996). The system will be tested for years 1996 and 1997 as soon as forest ®re data is available. It should be mentioned that forest ®re data are provided by the Central Forest Service Department, which is located in Athens.
References Adeli, H. and Hung, S. L. (1995). Machine Learning. New York: John Wiley and sons. Dimitrakopoulos, A. (1994). Analysis of forest ®re causes in Greece. MA of Chania Greece. Dimitrakopoulos, A. (1997). Conference `Protection from ®re and theft'. Thessaloniki. Jackson, M. (1992). Understanding expert systems using Crystal. John Willey & Sons. Jackson, P. (1993). Introduction to Expert Systems 2nd Edition. Addison Wesley. Kailidis, D. (1990). Forest Fires. Giachoudi Giapouli Editions. Thessaloniki. Kandel, A. and Byatt, W. J. (1978). Fuzzy sets, fuzzy algebra, and fuzzy statistics. Proc. IEEE 66, 1619. Kandel, A. (1992). Fuzzy Expert Systems. CRC Press. Krause, P. and Clark, D. (1993). Reprecenting Uncertain Knowledge. Intellect ltd. Leonardo user guide. (1992). By Bezant limited. Markalas, S. and Pantelis, S. (1996). Forest Fires in Greece in the Last Years. Aristotle University of Thessaloniki. Thessaloniki. Papastravrou, A. (1992). Social ®nancial and cultural aspects and legal frames of forest ®res in Greece. Vol LE/1. Aristotle University of Thessaloniki. Scienti®c annals of the Department of Forestry and Natural Environment. Thessaloniki. Partridge, D. and Hussain, K. (1995). Knowledge Based Information Systems. McGraw Hill. Zadeh, L. A. (1965). Fuzzy Sets Inf. Control, 8338.