- Email: [email protected]
The Design of a Fuzzy Expert System to Model Proliferation
5f-01 4
Copyright © 1996 IF AC 13th Triennial World Congress. San Francisco. USA
THE DESIGN OF A FUZZY EXPERT SYSTEM TO MODEL PROLIFERATION Claudio Antonini UniIJer!ity of Pretoria, PO Box 9£715, GleMtantia, 0010, South Africa
Abstract: A simplified model of proliferation is presented along with some general considerations concerning its modelling by fuzzy variables. A framework in which interaction exists amongst geographical factors and three qualitative variables (regional problerm, economy and proliferation) is introduced to represent the proliferation dynamics. The fuzzy mathematical operations are applied, in an e:dended way, to the qualitative variables. It is concluded that proliferation models cannot adequately represent reality for extended periods of time due to the growing scope, changing participants and variable motivations that fuel them in the real world. Keywords: Fuzzy expert systems; Fuzzy modelling; Expert systems; International Stability; Modelling
1. INTRODUCTION
For some time now, much effort has been devoted to the modelling of international relations. One particular case, proliferation, is the topic of this article. A number of difficulties regarding the modelling of social systems will be mentioned, along with possible solutions and assumptions. Some of these difficulties are associated with the general modelling of dynamic systems (structure, purpose and fuzziness of the variables), while others are particular to the topic of proliferation. The general issues will be presented first, and then those particular to the case of proliferation.
Social systems seem to behave as if they had structure. Motivated by this, philosophers such as Hobbes, Locke and Rousseau, borrowed ideas about structures that had appeared in the physical and biological sciences (and even music) and applied them, coupled to some utopian ultimate objectives, to create a number of deterministic, mechanistic, positivist theories for political, economic and social systems. These ideas about structures survived, subject only to minor changes, and are applied today to social science studies. However, to have a structure is not enough, because Ignorance of remote causes disposeth men to attribute all events to the causes immediate and instrumental: for these are all the causes they perceive. (Hobbes, 1985, Chapter XI)
Why would there be any interest in modelling proliferation ? Because Anxiety for the future time disposeth men to tnquire into the causes of things: because the knowledge of them maketh men the better able to order the present to their best advantage. (Hobbes, 1985, Chapter XI)
2. THE ISSUE OF STRUCTURE Two important contributions from the 17th and 18th centuries are the key to providing a foundation for any attempt at modelling political systems (EB, 1991), the first being the idea of structure.
This is where the second contribution appears: the idea of developmental change. The idea of a structure that changes takes one immediately to the concept of motion, of developmental change, so that "the present is an outgrowth of the past, the result of a long line of development in time and, furthermore, a line of development that has been caused, not by God or fortuitous factors, but by conditions and causes immanent in human society" (EB, 1991). This line of reasoning was followed by Condorcet, Rouss.lau and Adam Smith.
5699
Therefore, the fundamental concept necessary to simulate a social system-namely, the existence of a structure with variables that change-was laid down quite some time ago. Modernism only helped in that direction by justifying anything that could come out of a reasoned process. Exaggerating and simplifying, it could be said, after the mid 18th century: if it was the outcome of a reasoned process, t·t was valid. From this line of reasoning we deduce that if we could identify the "conditions and causes in human society" , we could hammer them down in an appropriate structure and, with a few turns of the wheel in the simulation apparatus, it would show us the path that would lead to the "ultimate objectives". Fukuyama (Fukuyama, 1993) referred to this process as "mechanistic metaphysics".
3. THE ISSUE OF PURPOSE Social systems also seem to behave as if they had a purpose. The question of purpose is not usually mentioned when referring to simulations. In engineering simulations, the foundation of every model is Physics or Chemistry or some basic, quantifiable, separate process. This is not the case in social systems. It should be clear from the start that by selecting some variables and neglecting others it is possible to modify substantially the outcome of the simulation runs. This factor is easily checked in engineering simulations: if a missile is modelled not considering its propulsion, the drag and gravity will force a trajectory very different than the one observed in reality.
example-from the simulations presented in Meadows's books (Meadows, 1972; Meadows, 1992)-it is impossible to determine the effect of any policy on the production of cacao for Nicaragua or the number of troops to be recruited by the Army in Poland, ever, because they are not considered in the model. The purpose is imbedded in the model. The purpose, the motivation behind-and inherent in-the structure of the model on proliferation cannot be easily spelled out. It cannot be said that it is purposefully a Jungian model (domination, hunger for power; few masters, many slaves), or an utopian model (ultimate goal is everybody's contentment). It is not budt to behave in any of these ways, although it might be behaving like any of these models at one (simulation) time or the other. For the issue at hand-proliferation-the most relevant variables will be chosen (Antonini, 1995), although there is no consensus on which ones they are.
4. VARIABLES AND THEIR FUZZINESS In the previous sections, the existence of a structure with variables that change was considered basic to the modelling of social systems. A problem just as difficult as deciding what variables are necessary in a simulation (which fixes the purpose of the simulation) is deciding how those qualitative variables will be quantified. How does one quantify security or aggresiveness or passivity?
As in the missile example, in most engineering simulations the structure of the simulation can be tested in one way or the other because the validation comes from observing the behavior in the real world. The same does not happen in social systems, where some of the variables are not easily quantifiable, the time frame is real time and the connections with the real world are impossible to be severed. Consequently the structure, the variables and the purpose in social systems simulations have to be assumed correct. The validation usually comes late, the conclusions are historical and the conditions will not be repeated in future. Therefore, besides its traditional objectives, the validation -where possible- helps in checking the purpose of the simulation.
One type of variable that could be close to the ideal ones are the fuzzy variables. However, the usual definition of fuzzy variables might not be completely adequate for our purposes, because of its limited applicability: the concept of fuzziness corresponds to the partial inclusion into a set of the possible sets in which the domain of a variable is divided, not to the concept that the variable represents. For example, to measure the height of a person (the distance from feet to head, a "crisp" concept), different people will have an opinion on how "taW' or "medium" or "short" somebody is. Being "tall", "medium" or "short" is one of the many different sets in which opinions about the height of the person could be divided. These are the fuzzy sets. The fuzziness is in the inclusion of the opinion of the height of one person in each of these sets, not in the idea of height.
In simulations, once one includes the variables that are considered relevant (along with their causalities and initial conditions), the outcomes, the end results are determined, fixed. Thus, for
In the case of proliferation, the concepts making up the model are themselves fuzzy. For example, how does one quantify "Intent to divert attention from internal political problems?" (Kahn, 1976);
5700
is it enough to measure annual income per capita to estimate how "economically secure" the population of a country/region is?; is it sufficient to count how many airplanes or scientists working in military R&D a country has to indicate that the country is "proliferating" more than others? In this work, it will be assumed that the use of qualitative variables like these in the formalism of fuzzy mathematical operations is valid, simply because policy-makers and analysts use them to synthesize situations. Some of those qualitative variables might, in turn, be the aggregation of other quantitative and qualitative variables. Therefore, the expert system to be designed is a model of the conceptual model in the mind of a human expert, and some of those variables might be qualitative. It should be noted that the fuzzy mathematical operations will be formally applied (in an extended way) to membership functions corresponding to qualitative variables.
5. MODELLING OF PROLIFERATION Besides the general difficulties mentioned above, pertaining to all simulations of social problems, three characteristics are unique when one refers to proliferation. The first lies in its scope. What is considered "not proliferating" at one stage, might be "proliferating" a short time later. Therefore, it is impossible to forecast that one technology will be proliferating or not in the future. Let's take the case of nuclear energy. If one remembers the objective of the "Atoms for Peace" talk (Eisenhower, 1953a): who could predict that a few years later the same organization that heartedly offered the technology to other countries would be spearheading efforts to stop that technology from spreading?
nates in Biology and simply means "replication": once a technology starts in a country, it seems to "spread" inside the country and to neighboring ones. The third characteristic of proliferation and vital to these considerations is that those weapons or technologies seem to imply a belligerent/dubious attitude, perhaps because ... the nature of war consisteth not in actual fighting, but in the known disposition thereto during all the time there is no assurance to the contrary. All other time is peace. (Hobbes, 1985, Chapter XIII) In a broad sense, proliferating technologies are "destabilizing", although it is usually not clear whether the departure is meant to be from a status-quo or from an assumed, utopian situation. Summarizing, the basics of the model is the propagation of an attitude; in other words, of an intention. This intention is always pressumed to have negative connotations and, because of its circumstantial nature, a. short-term applicability. Thus, simulations cannot be applicable for long periods of time (say, fifty years) unless basic models on attitudes and development (at social/country/regional levels) are invoked (although they should probably have to be found first) .
If one accepts these constraints, diffusion modelssuch as those used for technology forecasting (Martino, 1993) or Conway's Game of Life-could be used to represent this limited propagating behavior. The elements that are common to these models are a geographical structure on which the diffusion takes place and a few rules that determine the increments in the variables for the next run (as it was mentioned in a previous section: a structure and the developmental changes).
The second problem is a consequence of the first: there seems to be no standard definition for this widely used term. It started off being applied to "nuclear weapons", then to "ballistic missiles", later to "chemical, biological and toxic materials/weapons"; lately to "smart weapons, aircraft, missiles" and, in general, to any technology or technique that could be used with dubious, dual purposes, such as stealth technologies, lasers, advanced simulations, supercomputers and even cryptography (Chellaney, 1993). (It would seem that the definition of "proliferation" also "proliferates" .)
One structure to model proliferation was mentioned by Antonini (1995). The structure presented below is different in that takes the "geography" of the "world" into account, allowing the study of regional patterns and alliances. Given that different variables will be defined for each of the cells of the "world", different regional patterns and alliances can be specified for different types of variables. In this way, for example, the influence of international treaties could be simulated.
However, what is common to all these cases, and what makes them "proliferant", is exactly the intrinsic definition of the term, which origi-
The basic idea behind the model presented is that proliferation is a country's reaction to a perceived threat from its neighbors and it also depends on
6. SIMPLIFIED MODELLING
5701
5702
7. CONCLUSIONS To represent a simplified model of the proliferation dynamics, a framework in which interaction exists amongst geographical factors and three qualitative variables (regional problems, economy and proliferation) was introduced. Simulations corresponding to that model were presented. Due to the particularities of constantly growing scope, changing participants and variable motivations involved, the modelling of proliferation has to be limited in time: no model will be valid for a fifty year span. REFERENCES Antonini, C. (1995). The use of Fuzzy Variables in Forecasting Proliferation Capabili ties. International Symposium on Forecasting. Toronto, Canada. Chellaney, B. (1993). Chapter on Containing the Proliferation of Advanced Technologies, in Nuclear Proliferation, The US-Indian Conflict. Sangam Books. Dunn, L. and Kahn, H. (1976). Final Report, Trends in Nuclear Proliferation, 1975-1995. HI-2336/3-RR, Hudson Institute. EB, (1991). Encyclopaedia Britannica, 27, page 367, Chicago Press. Eisenhower, D. (1953a), from The Chance for Peace, address of April 16, 1953, quoted in html document, http://history.cc. ukans.edu/heritage / abilene /ikequot.html Eisenhower, D. {1953b}, from Atoms for Peace, address of December 8, 1953, United Nations. Fukuyama, F. {1992}. The End of History and The Last Man, Penguin Books. Hobbes, T. (1985), Leviathan, Penguin Classics, London. Martino, J. (1993), Technological Forecasting for Decision Making (Srd Ed), McGraw-Hill, New York. Meadows, D., Meadows D. and Randers, J., (1992). Beyond the limits, Chelsea Green Publishing Company, Post Mills, Vermont. The Limits to Meadows, D. et al {1972}. Growth. New York, Universe Books.
5703
regional problem 5
economy
0,6
~----~ 0,6 iim~~~~~
0,4
0,4
0,2
0,2
0,8
O,8 • •
50
100
150
200
150
200
50
100
150
pro life ratio n
0,8 0,6
0,4 0,2 50
100
Fig.I. Simplified model of proliferation. Effects on regional problems and economy.
5704
200
Copyright © 1996 IF AC 13th Triennial World Congress. San Francisco. USA
THE DESIGN OF A FUZZY EXPERT SYSTEM TO MODEL PROLIFERATION Claudio Antonini UniIJer!ity of Pretoria, PO Box 9£715, GleMtantia, 0010, South Africa
Abstract: A simplified model of proliferation is presented along with some general considerations concerning its modelling by fuzzy variables. A framework in which interaction exists amongst geographical factors and three qualitative variables (regional problerm, economy and proliferation) is introduced to represent the proliferation dynamics. The fuzzy mathematical operations are applied, in an e:dended way, to the qualitative variables. It is concluded that proliferation models cannot adequately represent reality for extended periods of time due to the growing scope, changing participants and variable motivations that fuel them in the real world. Keywords: Fuzzy expert systems; Fuzzy modelling; Expert systems; International Stability; Modelling
1. INTRODUCTION
For some time now, much effort has been devoted to the modelling of international relations. One particular case, proliferation, is the topic of this article. A number of difficulties regarding the modelling of social systems will be mentioned, along with possible solutions and assumptions. Some of these difficulties are associated with the general modelling of dynamic systems (structure, purpose and fuzziness of the variables), while others are particular to the topic of proliferation. The general issues will be presented first, and then those particular to the case of proliferation.
Social systems seem to behave as if they had structure. Motivated by this, philosophers such as Hobbes, Locke and Rousseau, borrowed ideas about structures that had appeared in the physical and biological sciences (and even music) and applied them, coupled to some utopian ultimate objectives, to create a number of deterministic, mechanistic, positivist theories for political, economic and social systems. These ideas about structures survived, subject only to minor changes, and are applied today to social science studies. However, to have a structure is not enough, because Ignorance of remote causes disposeth men to attribute all events to the causes immediate and instrumental: for these are all the causes they perceive. (Hobbes, 1985, Chapter XI)
Why would there be any interest in modelling proliferation ? Because Anxiety for the future time disposeth men to tnquire into the causes of things: because the knowledge of them maketh men the better able to order the present to their best advantage. (Hobbes, 1985, Chapter XI)
2. THE ISSUE OF STRUCTURE Two important contributions from the 17th and 18th centuries are the key to providing a foundation for any attempt at modelling political systems (EB, 1991), the first being the idea of structure.
This is where the second contribution appears: the idea of developmental change. The idea of a structure that changes takes one immediately to the concept of motion, of developmental change, so that "the present is an outgrowth of the past, the result of a long line of development in time and, furthermore, a line of development that has been caused, not by God or fortuitous factors, but by conditions and causes immanent in human society" (EB, 1991). This line of reasoning was followed by Condorcet, Rouss.lau and Adam Smith.
5699
Therefore, the fundamental concept necessary to simulate a social system-namely, the existence of a structure with variables that change-was laid down quite some time ago. Modernism only helped in that direction by justifying anything that could come out of a reasoned process. Exaggerating and simplifying, it could be said, after the mid 18th century: if it was the outcome of a reasoned process, t·t was valid. From this line of reasoning we deduce that if we could identify the "conditions and causes in human society" , we could hammer them down in an appropriate structure and, with a few turns of the wheel in the simulation apparatus, it would show us the path that would lead to the "ultimate objectives". Fukuyama (Fukuyama, 1993) referred to this process as "mechanistic metaphysics".
3. THE ISSUE OF PURPOSE Social systems also seem to behave as if they had a purpose. The question of purpose is not usually mentioned when referring to simulations. In engineering simulations, the foundation of every model is Physics or Chemistry or some basic, quantifiable, separate process. This is not the case in social systems. It should be clear from the start that by selecting some variables and neglecting others it is possible to modify substantially the outcome of the simulation runs. This factor is easily checked in engineering simulations: if a missile is modelled not considering its propulsion, the drag and gravity will force a trajectory very different than the one observed in reality.
example-from the simulations presented in Meadows's books (Meadows, 1972; Meadows, 1992)-it is impossible to determine the effect of any policy on the production of cacao for Nicaragua or the number of troops to be recruited by the Army in Poland, ever, because they are not considered in the model. The purpose is imbedded in the model. The purpose, the motivation behind-and inherent in-the structure of the model on proliferation cannot be easily spelled out. It cannot be said that it is purposefully a Jungian model (domination, hunger for power; few masters, many slaves), or an utopian model (ultimate goal is everybody's contentment). It is not budt to behave in any of these ways, although it might be behaving like any of these models at one (simulation) time or the other. For the issue at hand-proliferation-the most relevant variables will be chosen (Antonini, 1995), although there is no consensus on which ones they are.
4. VARIABLES AND THEIR FUZZINESS In the previous sections, the existence of a structure with variables that change was considered basic to the modelling of social systems. A problem just as difficult as deciding what variables are necessary in a simulation (which fixes the purpose of the simulation) is deciding how those qualitative variables will be quantified. How does one quantify security or aggresiveness or passivity?
As in the missile example, in most engineering simulations the structure of the simulation can be tested in one way or the other because the validation comes from observing the behavior in the real world. The same does not happen in social systems, where some of the variables are not easily quantifiable, the time frame is real time and the connections with the real world are impossible to be severed. Consequently the structure, the variables and the purpose in social systems simulations have to be assumed correct. The validation usually comes late, the conclusions are historical and the conditions will not be repeated in future. Therefore, besides its traditional objectives, the validation -where possible- helps in checking the purpose of the simulation.
One type of variable that could be close to the ideal ones are the fuzzy variables. However, the usual definition of fuzzy variables might not be completely adequate for our purposes, because of its limited applicability: the concept of fuzziness corresponds to the partial inclusion into a set of the possible sets in which the domain of a variable is divided, not to the concept that the variable represents. For example, to measure the height of a person (the distance from feet to head, a "crisp" concept), different people will have an opinion on how "taW' or "medium" or "short" somebody is. Being "tall", "medium" or "short" is one of the many different sets in which opinions about the height of the person could be divided. These are the fuzzy sets. The fuzziness is in the inclusion of the opinion of the height of one person in each of these sets, not in the idea of height.
In simulations, once one includes the variables that are considered relevant (along with their causalities and initial conditions), the outcomes, the end results are determined, fixed. Thus, for
In the case of proliferation, the concepts making up the model are themselves fuzzy. For example, how does one quantify "Intent to divert attention from internal political problems?" (Kahn, 1976);
5700
is it enough to measure annual income per capita to estimate how "economically secure" the population of a country/region is?; is it sufficient to count how many airplanes or scientists working in military R&D a country has to indicate that the country is "proliferating" more than others? In this work, it will be assumed that the use of qualitative variables like these in the formalism of fuzzy mathematical operations is valid, simply because policy-makers and analysts use them to synthesize situations. Some of those qualitative variables might, in turn, be the aggregation of other quantitative and qualitative variables. Therefore, the expert system to be designed is a model of the conceptual model in the mind of a human expert, and some of those variables might be qualitative. It should be noted that the fuzzy mathematical operations will be formally applied (in an extended way) to membership functions corresponding to qualitative variables.
5. MODELLING OF PROLIFERATION Besides the general difficulties mentioned above, pertaining to all simulations of social problems, three characteristics are unique when one refers to proliferation. The first lies in its scope. What is considered "not proliferating" at one stage, might be "proliferating" a short time later. Therefore, it is impossible to forecast that one technology will be proliferating or not in the future. Let's take the case of nuclear energy. If one remembers the objective of the "Atoms for Peace" talk (Eisenhower, 1953a): who could predict that a few years later the same organization that heartedly offered the technology to other countries would be spearheading efforts to stop that technology from spreading?
nates in Biology and simply means "replication": once a technology starts in a country, it seems to "spread" inside the country and to neighboring ones. The third characteristic of proliferation and vital to these considerations is that those weapons or technologies seem to imply a belligerent/dubious attitude, perhaps because ... the nature of war consisteth not in actual fighting, but in the known disposition thereto during all the time there is no assurance to the contrary. All other time is peace. (Hobbes, 1985, Chapter XIII) In a broad sense, proliferating technologies are "destabilizing", although it is usually not clear whether the departure is meant to be from a status-quo or from an assumed, utopian situation. Summarizing, the basics of the model is the propagation of an attitude; in other words, of an intention. This intention is always pressumed to have negative connotations and, because of its circumstantial nature, a. short-term applicability. Thus, simulations cannot be applicable for long periods of time (say, fifty years) unless basic models on attitudes and development (at social/country/regional levels) are invoked (although they should probably have to be found first) .
If one accepts these constraints, diffusion modelssuch as those used for technology forecasting (Martino, 1993) or Conway's Game of Life-could be used to represent this limited propagating behavior. The elements that are common to these models are a geographical structure on which the diffusion takes place and a few rules that determine the increments in the variables for the next run (as it was mentioned in a previous section: a structure and the developmental changes).
The second problem is a consequence of the first: there seems to be no standard definition for this widely used term. It started off being applied to "nuclear weapons", then to "ballistic missiles", later to "chemical, biological and toxic materials/weapons"; lately to "smart weapons, aircraft, missiles" and, in general, to any technology or technique that could be used with dubious, dual purposes, such as stealth technologies, lasers, advanced simulations, supercomputers and even cryptography (Chellaney, 1993). (It would seem that the definition of "proliferation" also "proliferates" .)
One structure to model proliferation was mentioned by Antonini (1995). The structure presented below is different in that takes the "geography" of the "world" into account, allowing the study of regional patterns and alliances. Given that different variables will be defined for each of the cells of the "world", different regional patterns and alliances can be specified for different types of variables. In this way, for example, the influence of international treaties could be simulated.
However, what is common to all these cases, and what makes them "proliferant", is exactly the intrinsic definition of the term, which origi-
The basic idea behind the model presented is that proliferation is a country's reaction to a perceived threat from its neighbors and it also depends on
6. SIMPLIFIED MODELLING
5701
5702
7. CONCLUSIONS To represent a simplified model of the proliferation dynamics, a framework in which interaction exists amongst geographical factors and three qualitative variables (regional problems, economy and proliferation) was introduced. Simulations corresponding to that model were presented. Due to the particularities of constantly growing scope, changing participants and variable motivations involved, the modelling of proliferation has to be limited in time: no model will be valid for a fifty year span. REFERENCES Antonini, C. (1995). The use of Fuzzy Variables in Forecasting Proliferation Capabili ties. International Symposium on Forecasting. Toronto, Canada. Chellaney, B. (1993). Chapter on Containing the Proliferation of Advanced Technologies, in Nuclear Proliferation, The US-Indian Conflict. Sangam Books. Dunn, L. and Kahn, H. (1976). Final Report, Trends in Nuclear Proliferation, 1975-1995. HI-2336/3-RR, Hudson Institute. EB, (1991). Encyclopaedia Britannica, 27, page 367, Chicago Press. Eisenhower, D. (1953a), from The Chance for Peace, address of April 16, 1953, quoted in html document, http://history.cc. ukans.edu/heritage / abilene /ikequot.html Eisenhower, D. {1953b}, from Atoms for Peace, address of December 8, 1953, United Nations. Fukuyama, F. {1992}. The End of History and The Last Man, Penguin Books. Hobbes, T. (1985), Leviathan, Penguin Classics, London. Martino, J. (1993), Technological Forecasting for Decision Making (Srd Ed), McGraw-Hill, New York. Meadows, D., Meadows D. and Randers, J., (1992). Beyond the limits, Chelsea Green Publishing Company, Post Mills, Vermont. The Limits to Meadows, D. et al {1972}. Growth. New York, Universe Books.
5703
regional problem 5
economy
0,6
~----~ 0,6 iim~~~~~
0,4
0,4
0,2
0,2
0,8
O,8 • •
50
100
150
200
150
200
50
100
150
pro life ratio n
0,8 0,6
0,4 0,2 50
100
Fig.I. Simplified model of proliferation. Effects on regional problems and economy.
5704
200