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Evaluation of sustainability of a city through fuzzy logic
ARTICLE IN PRESS
Energy 32 (2007) 795–802 www.elsevier.com/locate/energy
Evaluation of sustainability of a city through fuzzy logic Francesco Gagliardia, Mariacristina Rosciab, Gheorghe Lazaroiuc, a
Department of Electric Engineering, University of Naples ‘‘Federico II’’ Italy,Via Claudio, 21- 80125 Napoli, Italy b Department of Electrical Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy c Department of Power Plants, University Polytechnic of Bucharest, Splaiul Independentei 313, Romania Received 11 March 2005
Abstract The sustainable indicators are characterized by a low degree of aggregation and a high amount of information. An indicator must show a synthetic representation of a real environmental, by using a value or a parameter, so that they can be easily used by policy makers. It is necessary to connect, therefore, the various systems in an appropriately integrated sustainable system. The indicators need to be aggregated based on the structure of the data. Each indicator must to be defined through a weight with reference to another weighted indicator. In this paper is illustrated the calculation of the assigned weights that uses a procedure based on fuzzy logic and to define a model that allows us to estimate the sustainability of a city. The final result is, therefore, a combination of values assigned by expert opinion for the various criteria, processed using fuzzy logic to obtain a weight with significant objectivity and as it is possible to estimate the sustainability of the city through the weights. r 2006 Elsevier Ltd. All rights reserved. Keywords: Sustainability; Fuzzy logic
1. Introduction The sustainability (or un-sustainability) is not easily measurable: in fact it is not directly indicated as a natural or direct consequence of the reading of the environmental indicators. One of the environmental observation methods that is increasingly prominent proceeds by the use of indicators, which concur ‘‘to read’’ the state of environment in its several aspects, selecting—among all information available—those characterized as meaningful to explain a particular situation, with a descriptive, valuable, predictive or decisional aim [1]. To this point, the problem is to define the meaning of an environmental indicator: an indicator furnishes a synthetic description of an environmental reality, by a value or a parameter. However, the information that follows is wider than the value itself and it must be specified in relation to the type of indicator and to the context in which it is placed. Corresponding author. Tel.: +40214029868; fax: +40214113161.
E-mail address: [email protected] (G. Lazaroiu). 0360-5442/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2006.04.014
The indicator must be dynamic and in continuous evolution, because the environment is a complex system that cannot be completely observed from a single perspective. Generally, three categories of users can be identified:
the public in a generalized manner; policy makers and the authorities; experts and scientists [1].
Some essential terms for the predisposition of environmental indicators are the following [1]: (a) identification of the space and temporal context that is taken as reference for the survey of the data base; (b) decision on the type of information that it must be transferred and choice of a synthesis method of the information; (c) check of some property that would characterize the definition of an environmental indicator.
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Therefore, it will be possible to equip the policy maker with information for ‘‘ready consultation’’, to provide him the information that puts him in a situation to attend and to estimate the effects of the intervention.
1
2. Sustainable indicators weight through fuzzy logic
a
The indicators arranged by the scientific community are commonly characterized by a low degree of aggregation and a high amount of information, while an increase in the degree of aggregation and a lessening of the amount of information would be necessary to policy makers. Since the different indicators are not homogeneous, as a result of their various structures, it is possible to assign a weight to each indicator to allow for possible aggregation. This assignment can be made by means of a combination of values assigned from different judges and different criteria, calculated using a procedure based on the ‘‘fuzzy logic’’. The daily natural language consists of indefinite, inaccurate and polyvalent concepts, that can make approximate decision processes. The theory of ‘‘fuzzy logic’’, or ‘‘fuzzy set theory’’, resembles human reasoning in its use of approximate information and uncertainty to generate decisions. It was specifically designed to mathematically represent uncertainty and vagueness and provide formalized tools for dealing with the imprecision intrinsic to many problems [2]. The scope of this work is to assign, by fuzzy logic, the weights to the different indicators that can be taken in consideration in an environmental impact, so to obtain a significant homogeneity and objectivity. Typically the base structure for an environmental plan is a matrix expressed with: A1 .. . AI
G1
...
GJ
j11 .. . jI1
...
j1J .. , . jIJ
...
d
Fig. 1. Typical membership of fuzzy number.
where a, b, g, d are real numbers that satisfy the relation apbpgpd, shown in Fig. 1 [3]. The weights of the indicators are given by the followings steps : 1. The judges express their opinion both in terms of the criteria of evaluation of the indicators and in terms of indicator’s importance relative to every criteria in the interval of values [0, L]. The matrix of criteria obtained is J1
J2
...
Jn
C1 T ¼ C2 .. .
,
(3)
bkj
Ck where bkj ¼ kj =zkj ; Zkj =ykj
(4)
and the alternatives matrix is J1
(1)
g
b
J2
...
Jn
A1 T k ¼ A2 .. .
(5) akij
where Gj indicates an objective or an environmental characteristic; G ¼ {G1, G2,y, GJ} is a set of J environmental characteristics, Ai is an alternative or option and A ¼ {A1, A2,y, AJ} is a set of mutually exclusive plans; jij indicates the result of the plan Ai regarding the objective Gj. Generally weights {w1, w2,y, wJ} are introduced to represent the different value of various opportunities. The following method allows for the assignment to m alternatives A1,y, Am their weights. Therefore, n experts or judges J1,y, Jn are used to provide information based on the C1,y, Ck criteria. The informations assigned by judges are fuzzy trapezoid numbers 1 given by a=b; g=d , (2)
2. The weight can be determined in two ways: (a) For every judge Ji the indicator weight is obtained by criteria shown as 2 h i 1 wij ¼ b a1ij b1j aK (7) Kj ij KL
1 The fuzzy number trapezoid are used because they are more comprehensible by the expert-judges. In fact, to say ‘‘about 7’’, can be indicated with notation (6/7, 7/8), while ‘‘included between 6 and 7’’ it can be indicated by notation (6/6), 7/7).
2 The symbol , represent a multiplication and addition fuzzy, respectively. For example if A ¼ (1, 2, 3, 4) and B ¼ (2, 3, 3, 4): AB ¼ (1 2, 2 3, 3 3, 4 4) ¼ (2,6,9,16) and AB ¼ (1+2, 2+3, 3+3, 4+4) ¼ (3,5,7,8).
Am for every criteria Ck (1pkpK), and where akij is expressed as akij ¼ akij =bkij ; gkij =dkij (6)
ARTICLE IN PRESS F. Gagliardi et al. / Energy 32 (2007) 795–802
and so on for all judges; then the average value of fuzzy weight wij is 1 0 wi ¼ (8) ½wi1 win , nL
zero to the right of Zi with: aik k , K L
(16)
bik zk , K L
(17)
gik Zk , K L
(18)
K
Wi ¼ S
k¼1
which is again a fuzzy number. (b) The judge Ji makes akij =bkij ; gkij =dkij
fuzzy number akij ¼ and bkj ¼ kj =zkj ; Zkj =ykj then the average
n
aik ¼ S
j¼1
k¼1
akij
(9)
n
(10) (11)
weights can be expressed as W i ½L1 ; L2 X i ; Y i Zi ½U 1 ; U 2 ,
(13)
where the diagram of the membership function is [1]:
zero to the left of Wi, (14)
horizontal line by (Xi, 1) to (Yi, 1), U 1 y2 þ U 2 y þ Z i ¼ x in ½Y i ; Z i ,
dik yk , k¼1 K L K b aik ðzk k Þ ik , L1 ¼ S k¼1 K L K aik ðzk k Þ þ k b aik ik L2 ¼ S , k¼1 K L K dik g ik yk Zk U1 ¼ S , k¼1 K L K yk dik g ik þ dik yk Zk . U2 ¼ S k¼1 K L K
Zi ¼ S
then the indicator weight can be considered by Eq. (12): 1 wi ¼ (12) ½ðmi1 n1 Þ ðmiK nK Þ. K L 3. Once the value akij ; bkj or ðmik ; nk Þ is obtained, the
L1 y2 þ L2 y þ W i ¼ x in ½W i ; X i ,
k¼1
Yi ¼ S
to obtain mik ¼ aik =bik ; gik =dik , nk ¼ ek =zk ; Zk =yk ,
K
Xi ¼ S K
values are given by
(15)
797
(19)
(20)
(21)
(22)
(23)
The terms Wi, Xi, Yi, Zi represent the weight components (fuzzy number), while the terms L1, L2, U1, U2 are the coefficients of a second order polynomial, that represents the membership of the fuzzy number weight as illustrated in Fig. 2. The membership functions are: mik ¼ aik =bik ; gik =dik , (24) nk ¼ k =zk ; Zk =yk ,
Fig. 2. Membership of fuzzy number weight.
(25)
ARTICLE IN PRESS F. Gagliardi et al. / Energy 32 (2007) 795–802
798 Table 1 Criteria matrix Criteria
J1
Economy Environment Energy Urban plan
4 6 8 4
J2 5 7 8 5
5 7 9 6
6 8 9 7
5 5 6 5
J3 5 5 7 5
5 5 8 6
5 5 9 6
J4
6 7 6 4
7 8 6 6
7 8 7 7
8 9 7 7
J5
4 5 7 5
5 5 7 5
6 7 8 6
7 7 9 6
6 7 6 5
6 8 6 6
7 8 6 6
7 8 6 7
Table 2 Indicators matrix, evaluated by economy criteria Economy criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Pollution monitoring NO2 CO Water waste NO3 Cleaning efficiency RSU Separated littery Public transportation Only pedestrian way Cycling-path Green area Car GWh household Fuel Breath pathologies dead ISO certification Agenda XXI
5 6 6 4 6 6 5 6 7 4 3 7 8 9 9 7 4 2
5 6 7 5 6 6 5 6 7 5 4 7 8 9 9 8 4 3
6 6 7 6 7 6 6 6 8 5 5 8 9 9 9 8 5 3
6 6 7 6 7 6 6 6 8 5 5 8 9 9 9 9 6 4
5 5 5 5 6 6 5 6 7 4 3 7 7 9 9 7 4 3
J3 5 6 6 5 6 6 5 6 7 4 3 7 8 9 9 7 4 3
5 6 6 6 6 7 6 6 7 4 4 7 8 9 9 8 5 4
6 6 7 6 6 7 6 7 7 5 5 8 8 9 9 8 5 4
4 4 4 4 6 3 4 5 6 3 4 7 8 7 8 6 5 2
J4 5 5 5 4 6 3 4 5 6 4 4 7 8 7 8 6 5 3
6 6 5 5 6 4 4 6 7 4 4 7 8 8 8 7 6 4
6 6 5 5 7 4 4 6 7 5 4 7 8 8 7 7 6 5
J5
6 5 5 4 5 4 3 6 4 5 3 6 6 7 7 6 3 3
6 5 5 5 5 4 4 6 5 6 4 6 6 9 9 7 4 3
7 6 5 5 5 5 4 6 6 6 4 7 7 9 9 8 5 4
7 6 6 5 5 5 5 7 7 6 4 7 7 9 9 9 6 4
3 7 5 6 4 3 5 5 6 4 4 5 8 6 8 8 4 4
5 7 5 6 6 4 5 5 7 4 4 6 8 7 8 8 4 4
6 7 5 6 6 4 5 6 8 5 5 8 8 8 8 9 5 4
6 7 5 6 6 5 5 7 8 6 5 8 8 9 9 9 5 4
Table 3 Indicators matrix. evaluated by environment criteria Environment criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
7 7 7 5 7 8 8 7 5 5 3 6 6 5 6 6 4 2
7 7 7 6 7 8 9 8 6 5 4 6 6 6 7 6 4 2
8 7 7 6 7 9 9 8 6 5 5 7 6 7 7 6 5 3
8 7 7 7 7 9 9 9 7 5 6 7 6 8 7 6 5 3
7 6 7 5 7 7 8 7 5 4 3 6 6 5 6 5 5 4
J3 7 7 7 5 7 8 8 7 5 4 4 7 6 5 6 5 5 4
7 7 7 5 7 8 8 8 5 5 4 7 6 6 7 6 5 5
7 7 7 6 7 8 9 9 6 5 4 7 6 6 7 6 5 5
6 6 5 6 6 6 7 7 5 3 3 5 6 4 6 4 4 3
J4 7 6 5 6 6 6 7 7 5 4 3 5 6 4 7 4 4 3
7 7 7 6 7 7 8 8 6 5 4 7 6 6 8 6 5 4
7 7 7 6 7 7 8 8 6 6 4 7 7 6 8 6 5 4
6 6 5 6 7 6 6 6 4 3 5 6 7 5 6 5 4 5
J5 6 6 6 6 8 6 6 7 5 3 5 6 7 5 6 5 5 5
7 8 7 7 8 8 8 7 6 5 5 6 7 6 8 6 6 6
7 8 8 7 8 8 8 8 7 5 5 6 7 6 8 6 6 6
8 7 6 5 6 6 8 6 6 4 4 6 5 6 5 6 3 3
8 7 6 7 7 7 8 6 6 4 4 6 6 6 6 6 3 3
9 7 7 8 8 8 8 8 7 5 4 6 7 7 6 6 5 4
9 7 7 8 8 9 8 8 7 5 4 7 7 8 6 6 5 4
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they are equal to: 0 for xpa and xXd and xpe and xXy, respectively, equal to 1 for bpxpg and zpxph, respectively. In the average range, as between ai and bi the membership functions are linear and can be expressed by xi ¼ bi ai y þ ai . (26)
799
following relations: L1 y2 þ L2 y þ W i ¼ x, U 1 y2 þ U 2 y þ Z i ¼ x,
ð27Þ
consequently the weight wi are expressed by (Wi[L1, L2]/Xi, Yi/Zi[U1, U2]) [2,4]. 4. Once the weights, that are fuzzy numbers, are obtained, it is necessary to obtain a real number or ‘‘crisp’’
Considering that the fuzzy products, the membership functions of the weights obtained, are expressed by
Table 4 Indicators matrix. evaluated by energy criteria Energy criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
3 5 5 1 5 2 2 2 6 2 2 1 7 8 8 4 1 4
4 5 5 1 5 2 2 2 6 2 2 1 7 8 8 4 1 5
4 6 6 2 6 3 3 3 7 3 3 3 8 8 8 5 1 6
4 6 6 2 6 4 4 3 7 3 3 3 8 8 8 6 1 7
2 4 4 1 4 1 1 1 7 1 1 2 6 7 7 3 1 5
J3 3 5 5 2 5 2 2 2 7 2 2 2 6 7 7 3 1 5
4 6 6 2 6 2 2 3 8 3 3 3 7 9 9 4 2 6
4 7 7 3 7 3 3 4 8 3 3 3 7 9 9 5 2 6
3 5 5 2 5 2 2 2 7 2 2 1 5 6 6 4 2 6
J4 3 6 6 2 6 3 3 2 7 2 2 2 6 7 7 4 2 6
4 6 6 2 6 3 3 3 8 2 2 2 7 8 8 5 2 7
4 6 6 2 6 4 4 3 8 2 2 3 8 9 9 5 2 7
2 6 6 2 6 2 2 2 6 3 3 2 5 7 7 1 1 7
J5 3 6 6 2 6 3 3 2 7 3 3 2 5 7 7 2 1 7
4 7 7 3 7 4 4 4 8 3 3 3 8 8 8 3 2 7
4 7 7 3 7 5 5 4 9 3 3 3 8 8 8 4 2 7
2 5 5 2 5 1 1 3 7 2 2 1 7 7 7 2 1 5
2 5 5 3 5 2 2 3 7 2 2 1 7 7 7 2 1 5
2 6 6 4 6 3 3 4 8 3 3 1 9 8 8 3 1 6
2 6 6 4 6 4 4 4 9 3 3 1 9 9 9 3 1 6
1 1 1 1 1 7 7 3 8 7 4 6 6 3 1 3 1 6
2 2 2 1 2 9 8 3 8 9 6 7 6 3 2 3 1 7
2 2 2 1 2 9 9 3 8 9 6 8 7 3 2 3 1 7
Table 5 Indicators matrix. evaluated by urban plan criteria Urban plan criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 3 3 1 3 6 7 3 7 7 5 9 6 2 2 2 1 5
1 3 3 1 3 6 7 4 7 8 5 9 6 2 2 2 1 5
2 3 3 1 3 7 7 5 8 8 6 9 6 3 2 3 1 6
2 3 3 1 3 7 7 5 8 8 6 9 6 3 2 3 1 6
2 2 2 1 2 7 7 4 6 8 4 6 6 3 1 3 1 5
J3 2 2 2 1 2 7 7 4 6 8 4 6 6 3 1 3 1 5
3 3 3 1 3 8 8 6 8 9 5 8 7 4 2 3 1 6
3 3 3 1 3 8 8 6 8 9 6 8 7 4 2 3 1 6
1 2 2 1 2 5 7 2 6 6 5 7 6 1 2 1 1 4
J4 1 2 2 1 2 6 7 2 7 6 5 7 6 1 2 1 1 4
1 2 2 1 2 7 9 3 8 8 5 8 8 2 3 3 1 6
1 2 2 1 2 8 9 3 8 8 5 8 8 2 3 3 1 6
2 2 2 1 2 7 6 2 8 7 6 6 5 2 1 2 1 6
J5 2 2 2 1 2 7 6 2 8 7 6 7 5 2 1 2 1 6
2 3 3 1 3 8 8 4 9 7 6 8 9 2 1 2 1 6
2 3 3 1 3 8 8 4 9 8 6 9 9 2 1 2 1 6
1 1 1 1 1 7 6 3 8 7 4 5 5 3 1 3 1 5
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number by a ‘‘defuzzification’’ method. One of these methods is based on the average values using the following relation [5]: Z 1 F ðAi Þ ¼ 1=2 g1 y Ai þ g2 y Ai dy 0
1 1 1 ¼ ðL1i þ U 1i Þ þ ðL2i þ U 2i Þ þ ðZ i þ W i Þ. 6 4 2 ð28Þ
3. Sustainable indicators weight and application of sustainable urban model The example considers as obtaining the weights of a number of indicators. It is obtained using 5 judges, 4 criteria (economy, environment, energy and urban plan) and 18 indicators. For giving the indicators homogeneity as indicators, so as to compare them, their weights are calculated with fuzzy logic [6]. The methodology is the following: judges express by fuzzy numbers their opinion on the criteria and evaluate the indicators with respect to all evaluated criteria. The criteria and indicators matrix obtained are shown in the Tables 1–5. The resulted data base is used for calculating the weights from the averages values of the criteria and by indicators
5 6 6.6 4.6
5.6 6.6 6.8 5.4
6 7 7.6 6.2
Table 8 Weights components
6.6 7.4 8 6.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
7.6 7.2 7.2 6.8 7.4 8.2 8.4 8.4 6.6 5.2 4.6 6.8 6.6 6.8 7.2 6 5.2 4.4
m13 m23 m33 m43 m53 m63 m73 m83 m93 m103 m113 m123 m133 m143 m153 m163 m173 m183
Table 6 Criteria average value n1 n2 n3 n4
given by the judges. The fuzzy average value nk obtained by criteria and the value mik obtained by ith indicator for kth criteria are shown in Tables 6 and 7 and the weights components are obtained as in Table 8. For obtaining the crisp number of the weight, the ‘‘defuzzification’’, reported in Table 9, is made using the average value method and then normalized as average weight as shown in the Table 10. The analysis of the weight results shows that, based on the opinion expressed by the judges, the sustainable city is particularly influenced by public transportation, fuel, household GWh and cars, while a low sensitivity is associated with hydro consumption and ISO 14000 certified companies.
W
X
Y
Z
L1
L2
U1
U2
2.152 2.69 2.58 1.764 2.72 2.54 2.683 2.342 3.394 2.205 1.847 2.66 3.459 3.108 3.211 2.345 1.413 2.326
2.582 3.089 2.995 2.165 3.155 3.098 3.224 2.718 3.915 2.65 2.214 3.131 3.924 3.527 3.673 2.673 1.62 2.663
3.224 3.771 3.646 2.609 3.776 3.959 3.995 3.562 4.883 3.398 2.83 3.961 4.918 4.402 4.418 3.444 2.149 3.517
3.479 4.064 4.031 2.907 4.101 4.528 4.565 4.056 5.435 3.799 3.127 4.418 5.362 4.892 4.801 3.878 2.371 3.85
0.015 0.011 0.014 0.017 0.014 0.017 0.014 0.011 0.017 0.017 0.013 0.015 0.011 0.013 0.016 0.007 0.006 0.011
0.415 0.388 0.401 0.384 0.421 0.541 0.527 0.365 0.504 0.428 0.354 0.456 0.454 0.406 0.446 0.321 0.201 0.326
0.003 0.002 0.01 0.006 0.005 0.017 0.017 0.017 0.013 0.013 0.007 0.011 0.006 0.011 0.004 0.012 0.006 0.008
0.258 0.295 0.395 0.304 0.33 0.586 0.587 0.511 0.565 0.414 0.304 0.468 0.45 0.501 0.387 0.446 0.228 0.341
2.4 5 5 1.6 5 1.6 1.6 2 6.6 2 2 1.4 6 7 7 2.8 1.2 5.4
3 5.4 5.4 2 5.4 2.4 2.4 2.2 6.8 2.2 2.2 1.6 6.2 7.2 7.2 3 1.2 5.6
3.6 6.2 6.2 2.6 6.2 3 3 3.4 7.8 2.8 2.8 2.4 7.8 8.2 8.2 4 1.6 6.4
Table 7 Indicators average value m11 m21 m31 m41 m51 m61 m71 m81 m91 m10 m111 m121 m131 m141 m151 m161 m171 m181
4.6 5.4 5 4.6 5.4 4.4 4.4 5.6 6 4 3.4 6.4 7.4 7.6 8.2 6.8 4 2.8
5.2 5.8 5.6 5 5.8 4.6 4.6 5.6 6.4 4.6 3.8 6.6 7.6 8.2 8.6 7.2 4.2 3.2
6 6.2 5.6 5.6 6 5.2 5 6 7.2 4.8 4.4 7.4 8 8.6 8.6 8 5.2 3.8
6.2 6.2 6 5.6 6.2 5.4 5.2 6.6 7.4 5.4 4.6 7.6 8 8.8 8.6 8.4 5.6 4.2
m12 m22 m32 m42 m52 m62 m72 m82 m92 m102 m112 m122 m132 m142 m152 m162 m172 m182
6.8 6.4 6 5.4 6.6 6.6 7.4 6.6 5 3.8 3.6 5.8 6 5 5.8 5.2 4 3.4
7 6.6 6.2 6 7 7 7.6 7 5.4 4 4 6 6.2 5.2 6.4 5.2 4.2 3.4
7.6 7.2 7 6.4 7.4 8 8.2 7.8 6 5 4.4 6.6 6.4 6.4 7.2 6 5.2 4.4
3.6 6.4 6.4 2.8 6.4 4 4 3.6 8.2 2.8 2.8 2.6 8 8.6 8.6 4.6 1.6 6.6
m14 m24 m34 m44 m54 m64 m74 m84 m94 m104 m114 m124 m134 m144 m154 m164 m174 m184
1.4 2 2 1 2 6.4 6.6 2.8 7 7 4.8 6.6 5.6 2.2 1.4 2.2 1 5
1.4 2 2 1 2 6.6 6.8 3 7.2 7.2 4.8 7 5.8 2.2 1.4 2.2 1 5.2
2 2.6 2.6 1 2.6 7.8 8 4.2 8.2 8.2 5.6 8 7.2 2.8 2 2.8 1 6.2
2 2.6 2.6 1 2.6 8 8.2 4.2 8.2 8.4 5.8 8.4 7.4 2.8 2 2.8 1 6.2
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The judges use the data reported in the statistics and in The ‘‘Environmental Reports’’ prepared by Associations and Organizations [7]. It has been carried out an application for the city of Naples, Italy through the weights calculated with fuzzy logic, then it allows us to estimate the sustainability of the city connected to the goals prefixed. For every indicator it was determined a ‘‘sustainable goal’’ or ‘‘environmental quality’’, equal to 100, without to attribute the weights. Therefore, every indicator can to assume a value between 0 (min) to 100 (max).
Table 9 Defuzzification
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Defuzzification
Weight normal
2.858 3.402 3.311 2.359 3.436 3.528 3.614 3.167 4.404 3.011 2.503 3.54 4.414 3.98 4.024 3.083 1.887 3.087
0.48 0.57 0.56 0.4 0.58 0.59 0.61 0.53 0.74 0.51 0.42 0.59 0.74 0.67 0.68 0.52 0.32 0.52
801
Through the elaboration of data base reported in [1], it is possible to obtain the values of the 18 indicator normalized (and specified in Table 2), for the aforesaid city. Fig. 3 shows the outline of the environmental conditions and the ‘‘ideal’’ outline of sustainability, in this case equal to 100, without considering the weights. The grey area shows the ‘‘real’’ values of the chosen 18th indicators. The values were supplied by [7]. Each indicator has a different ‘‘weight’’ on the sustainability either with respect to other indicators or with respect to the evaluation criteria. Moreover, Fig. 4 shows the same outline of the environmental conditions but compared to a ‘‘real’’ outline of sustainability, where the edges are weighed for an ‘‘ideal’’ but not utopian city. Fig. 4 highlights how the sustainability objective changes weighting the chosen indicators. For the specific case of the city of Naples
Fig. 3. Environmental conditions and ‘‘ideal’’ outline of sustainability, without considering the weights.
Table 10 Indicators value normalised 1
2
3
4
5
6
High sustainable objective Lower objective Fuzzy weight Objective weighed Indicators value normalized
100 0 0.48 48 95
100 0 0.57 57 67.22
100 0 0.56 56 55
100 0 0.4 40 65.11
100 0 0.58 58 84.44
100 0 0.59 59 38
High objective Lower objective Fuzzy weight Objective weighed Indicators value normalized
7 100 0 0.51 51 22.5
8 100 0 0.42 42 0
9 100 0 0.59 59 12.5
10 100 0 0.74 74 48.48
11 100 0 0.67 67 74.78
12 100 0 0.68 68 99.25
High objective Lower objective Fuzzy weight Objective weighed Indicators value normalized
13 100 0 0.61 61 45.62
14 100 0 0.53 53 2.5
15 100 0 0.74 74 29.14
16 100 0 0.52 52 73.76
17 100 0 0.32 32 2.857
18 100 0 0.52 52 0
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F. Gagliardi et al. / Energy 32 (2007) 795–802
Fig. 4. Environmental conditions and ‘‘real’’ outline of sustainability, considering the weights.
(Italy) it is emphasized how some parameters widely respect the sustainability and how others parameters need work for limiting them inside the sustainability area. It can be seen as only some parameters do not respect the sustainability, while others respect totally the goals.
of an indicator with regard to another indicator, every decision maker is brought to reason in a less objective way. An urban planner, for example, will give more importance to a cycle path or green areas, but on the contrary a chemical engineering will be concerned with air pollution problems. In spite of this, the proposed systems, even starting from subjective evaluation, permits the combination of different opinions on various indicators, by means of different criteria. Moreover, the final results will be a combination of values assigned by different judges for various criteria by fuzzy number which translates verbal expression in a numerical quantity. Therefore it is possible to obtain a more careful evaluation of the sustainability of the cities, based on quality objects, more open-minded and dynamics, integrating the point of view of decision maker’s in the weight to give to the different indicators. Acknowledgement The authors thank Prof. D. Zaninelli for his precious contribution. References
4. Conclusion The example reported in this paper to calculate the weight, is on a hypothetical sustainable city and the evaluation of the weight, criteria and indicator have not been carried out by experts of the specific fields. In order for the case of a real city to establish the just values, the contribution of the experts in the various chosen fields will be necessary. This method, presented in the paper, is applied to the city of Naples, Italy. It can be noted that the application is done by the authors basing their calculation methodology on the documents reported in [1,7]. The applied methodology for calculating indicator weights for selected criteria, points out the importance of decision maker’s subjectivity. In fact, assigning the weight
[1] Gagliardi F, Roscia M. Method of allocation of the weights by fuzzy logic for a sustainable urban model. In: Conference ‘‘sustainable development of energy, water and environment systems’’ Dubrovnik, Croatia, 2–7 June 2002. [2] Smith PN. Applications of Fuzzy sets in the environmental evaluation of projects. J. Environ. Manage. 1994;42(4):365–88. [3] Buckley JJ. Ranking alternatives using fuzzy numbers. Fuzzy Sets Syst 1985;15(1):21–31. [4] Yager RR. Fuzzy decision making including unequal objectives. Fuzzy Sets Syst 1978;1(2):87–95. [5] Yager RR. A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 1981;24(2):143–61. [6] Buckley JJ. The fuzzy mathematics of finance. Fuzzy Sets Syst 1987;21(3):257–73. [7] Italian Environment Research Institute, Environmental Quality of the District Capitals (Sesto Rapporto sulla Qualita` Ambientale dei Comuni Capoluogo), Report no. 6, 1999. Legambient (http://legambiente.com/ documenti/1997-1999/ecosistema_urbano _1999), 1999 (in Italian).
Energy 32 (2007) 795–802 www.elsevier.com/locate/energy
Evaluation of sustainability of a city through fuzzy logic Francesco Gagliardia, Mariacristina Rosciab, Gheorghe Lazaroiuc, a
Department of Electric Engineering, University of Naples ‘‘Federico II’’ Italy,Via Claudio, 21- 80125 Napoli, Italy b Department of Electrical Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy c Department of Power Plants, University Polytechnic of Bucharest, Splaiul Independentei 313, Romania Received 11 March 2005
Abstract The sustainable indicators are characterized by a low degree of aggregation and a high amount of information. An indicator must show a synthetic representation of a real environmental, by using a value or a parameter, so that they can be easily used by policy makers. It is necessary to connect, therefore, the various systems in an appropriately integrated sustainable system. The indicators need to be aggregated based on the structure of the data. Each indicator must to be defined through a weight with reference to another weighted indicator. In this paper is illustrated the calculation of the assigned weights that uses a procedure based on fuzzy logic and to define a model that allows us to estimate the sustainability of a city. The final result is, therefore, a combination of values assigned by expert opinion for the various criteria, processed using fuzzy logic to obtain a weight with significant objectivity and as it is possible to estimate the sustainability of the city through the weights. r 2006 Elsevier Ltd. All rights reserved. Keywords: Sustainability; Fuzzy logic
1. Introduction The sustainability (or un-sustainability) is not easily measurable: in fact it is not directly indicated as a natural or direct consequence of the reading of the environmental indicators. One of the environmental observation methods that is increasingly prominent proceeds by the use of indicators, which concur ‘‘to read’’ the state of environment in its several aspects, selecting—among all information available—those characterized as meaningful to explain a particular situation, with a descriptive, valuable, predictive or decisional aim [1]. To this point, the problem is to define the meaning of an environmental indicator: an indicator furnishes a synthetic description of an environmental reality, by a value or a parameter. However, the information that follows is wider than the value itself and it must be specified in relation to the type of indicator and to the context in which it is placed. Corresponding author. Tel.: +40214029868; fax: +40214113161.
E-mail address: [email protected] (G. Lazaroiu). 0360-5442/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2006.04.014
The indicator must be dynamic and in continuous evolution, because the environment is a complex system that cannot be completely observed from a single perspective. Generally, three categories of users can be identified:
the public in a generalized manner; policy makers and the authorities; experts and scientists [1].
Some essential terms for the predisposition of environmental indicators are the following [1]: (a) identification of the space and temporal context that is taken as reference for the survey of the data base; (b) decision on the type of information that it must be transferred and choice of a synthesis method of the information; (c) check of some property that would characterize the definition of an environmental indicator.
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Therefore, it will be possible to equip the policy maker with information for ‘‘ready consultation’’, to provide him the information that puts him in a situation to attend and to estimate the effects of the intervention.
1
2. Sustainable indicators weight through fuzzy logic
a
The indicators arranged by the scientific community are commonly characterized by a low degree of aggregation and a high amount of information, while an increase in the degree of aggregation and a lessening of the amount of information would be necessary to policy makers. Since the different indicators are not homogeneous, as a result of their various structures, it is possible to assign a weight to each indicator to allow for possible aggregation. This assignment can be made by means of a combination of values assigned from different judges and different criteria, calculated using a procedure based on the ‘‘fuzzy logic’’. The daily natural language consists of indefinite, inaccurate and polyvalent concepts, that can make approximate decision processes. The theory of ‘‘fuzzy logic’’, or ‘‘fuzzy set theory’’, resembles human reasoning in its use of approximate information and uncertainty to generate decisions. It was specifically designed to mathematically represent uncertainty and vagueness and provide formalized tools for dealing with the imprecision intrinsic to many problems [2]. The scope of this work is to assign, by fuzzy logic, the weights to the different indicators that can be taken in consideration in an environmental impact, so to obtain a significant homogeneity and objectivity. Typically the base structure for an environmental plan is a matrix expressed with: A1 .. . AI
G1
...
GJ
j11 .. . jI1
...
j1J .. , . jIJ
...
d
Fig. 1. Typical membership of fuzzy number.
where a, b, g, d are real numbers that satisfy the relation apbpgpd, shown in Fig. 1 [3]. The weights of the indicators are given by the followings steps : 1. The judges express their opinion both in terms of the criteria of evaluation of the indicators and in terms of indicator’s importance relative to every criteria in the interval of values [0, L]. The matrix of criteria obtained is J1
J2
...
Jn
C1 T ¼ C2 .. .
,
(3)
bkj
Ck where bkj ¼ kj =zkj ; Zkj =ykj
(4)
and the alternatives matrix is J1
(1)
g
b
J2
...
Jn
A1 T k ¼ A2 .. .
(5) akij
where Gj indicates an objective or an environmental characteristic; G ¼ {G1, G2,y, GJ} is a set of J environmental characteristics, Ai is an alternative or option and A ¼ {A1, A2,y, AJ} is a set of mutually exclusive plans; jij indicates the result of the plan Ai regarding the objective Gj. Generally weights {w1, w2,y, wJ} are introduced to represent the different value of various opportunities. The following method allows for the assignment to m alternatives A1,y, Am their weights. Therefore, n experts or judges J1,y, Jn are used to provide information based on the C1,y, Ck criteria. The informations assigned by judges are fuzzy trapezoid numbers 1 given by a=b; g=d , (2)
2. The weight can be determined in two ways: (a) For every judge Ji the indicator weight is obtained by criteria shown as 2 h i 1 wij ¼ b a1ij b1j aK (7) Kj ij KL
1 The fuzzy number trapezoid are used because they are more comprehensible by the expert-judges. In fact, to say ‘‘about 7’’, can be indicated with notation (6/7, 7/8), while ‘‘included between 6 and 7’’ it can be indicated by notation (6/6), 7/7).
2 The symbol , represent a multiplication and addition fuzzy, respectively. For example if A ¼ (1, 2, 3, 4) and B ¼ (2, 3, 3, 4): AB ¼ (1 2, 2 3, 3 3, 4 4) ¼ (2,6,9,16) and AB ¼ (1+2, 2+3, 3+3, 4+4) ¼ (3,5,7,8).
Am for every criteria Ck (1pkpK), and where akij is expressed as akij ¼ akij =bkij ; gkij =dkij (6)
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and so on for all judges; then the average value of fuzzy weight wij is 1 0 wi ¼ (8) ½wi1 win , nL
zero to the right of Zi with: aik k , K L
(16)
bik zk , K L
(17)
gik Zk , K L
(18)
K
Wi ¼ S
k¼1
which is again a fuzzy number. (b) The judge Ji makes akij =bkij ; gkij =dkij
fuzzy number akij ¼ and bkj ¼ kj =zkj ; Zkj =ykj then the average
n
aik ¼ S
j¼1
k¼1
akij
(9)
n
(10) (11)
weights can be expressed as W i ½L1 ; L2 X i ; Y i Zi ½U 1 ; U 2 ,
(13)
where the diagram of the membership function is [1]:
zero to the left of Wi, (14)
horizontal line by (Xi, 1) to (Yi, 1), U 1 y2 þ U 2 y þ Z i ¼ x in ½Y i ; Z i ,
dik yk , k¼1 K L K b aik ðzk k Þ ik , L1 ¼ S k¼1 K L K aik ðzk k Þ þ k b aik ik L2 ¼ S , k¼1 K L K dik g ik yk Zk U1 ¼ S , k¼1 K L K yk dik g ik þ dik yk Zk . U2 ¼ S k¼1 K L K
Zi ¼ S
then the indicator weight can be considered by Eq. (12): 1 wi ¼ (12) ½ðmi1 n1 Þ ðmiK nK Þ. K L 3. Once the value akij ; bkj or ðmik ; nk Þ is obtained, the
L1 y2 þ L2 y þ W i ¼ x in ½W i ; X i ,
k¼1
Yi ¼ S
to obtain mik ¼ aik =bik ; gik =dik , nk ¼ ek =zk ; Zk =yk ,
K
Xi ¼ S K
values are given by
(15)
797
(19)
(20)
(21)
(22)
(23)
The terms Wi, Xi, Yi, Zi represent the weight components (fuzzy number), while the terms L1, L2, U1, U2 are the coefficients of a second order polynomial, that represents the membership of the fuzzy number weight as illustrated in Fig. 2. The membership functions are: mik ¼ aik =bik ; gik =dik , (24) nk ¼ k =zk ; Zk =yk ,
Fig. 2. Membership of fuzzy number weight.
(25)
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798 Table 1 Criteria matrix Criteria
J1
Economy Environment Energy Urban plan
4 6 8 4
J2 5 7 8 5
5 7 9 6
6 8 9 7
5 5 6 5
J3 5 5 7 5
5 5 8 6
5 5 9 6
J4
6 7 6 4
7 8 6 6
7 8 7 7
8 9 7 7
J5
4 5 7 5
5 5 7 5
6 7 8 6
7 7 9 6
6 7 6 5
6 8 6 6
7 8 6 6
7 8 6 7
Table 2 Indicators matrix, evaluated by economy criteria Economy criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Pollution monitoring NO2 CO Water waste NO3 Cleaning efficiency RSU Separated littery Public transportation Only pedestrian way Cycling-path Green area Car GWh household Fuel Breath pathologies dead ISO certification Agenda XXI
5 6 6 4 6 6 5 6 7 4 3 7 8 9 9 7 4 2
5 6 7 5 6 6 5 6 7 5 4 7 8 9 9 8 4 3
6 6 7 6 7 6 6 6 8 5 5 8 9 9 9 8 5 3
6 6 7 6 7 6 6 6 8 5 5 8 9 9 9 9 6 4
5 5 5 5 6 6 5 6 7 4 3 7 7 9 9 7 4 3
J3 5 6 6 5 6 6 5 6 7 4 3 7 8 9 9 7 4 3
5 6 6 6 6 7 6 6 7 4 4 7 8 9 9 8 5 4
6 6 7 6 6 7 6 7 7 5 5 8 8 9 9 8 5 4
4 4 4 4 6 3 4 5 6 3 4 7 8 7 8 6 5 2
J4 5 5 5 4 6 3 4 5 6 4 4 7 8 7 8 6 5 3
6 6 5 5 6 4 4 6 7 4 4 7 8 8 8 7 6 4
6 6 5 5 7 4 4 6 7 5 4 7 8 8 7 7 6 5
J5
6 5 5 4 5 4 3 6 4 5 3 6 6 7 7 6 3 3
6 5 5 5 5 4 4 6 5 6 4 6 6 9 9 7 4 3
7 6 5 5 5 5 4 6 6 6 4 7 7 9 9 8 5 4
7 6 6 5 5 5 5 7 7 6 4 7 7 9 9 9 6 4
3 7 5 6 4 3 5 5 6 4 4 5 8 6 8 8 4 4
5 7 5 6 6 4 5 5 7 4 4 6 8 7 8 8 4 4
6 7 5 6 6 4 5 6 8 5 5 8 8 8 8 9 5 4
6 7 5 6 6 5 5 7 8 6 5 8 8 9 9 9 5 4
Table 3 Indicators matrix. evaluated by environment criteria Environment criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
7 7 7 5 7 8 8 7 5 5 3 6 6 5 6 6 4 2
7 7 7 6 7 8 9 8 6 5 4 6 6 6 7 6 4 2
8 7 7 6 7 9 9 8 6 5 5 7 6 7 7 6 5 3
8 7 7 7 7 9 9 9 7 5 6 7 6 8 7 6 5 3
7 6 7 5 7 7 8 7 5 4 3 6 6 5 6 5 5 4
J3 7 7 7 5 7 8 8 7 5 4 4 7 6 5 6 5 5 4
7 7 7 5 7 8 8 8 5 5 4 7 6 6 7 6 5 5
7 7 7 6 7 8 9 9 6 5 4 7 6 6 7 6 5 5
6 6 5 6 6 6 7 7 5 3 3 5 6 4 6 4 4 3
J4 7 6 5 6 6 6 7 7 5 4 3 5 6 4 7 4 4 3
7 7 7 6 7 7 8 8 6 5 4 7 6 6 8 6 5 4
7 7 7 6 7 7 8 8 6 6 4 7 7 6 8 6 5 4
6 6 5 6 7 6 6 6 4 3 5 6 7 5 6 5 4 5
J5 6 6 6 6 8 6 6 7 5 3 5 6 7 5 6 5 5 5
7 8 7 7 8 8 8 7 6 5 5 6 7 6 8 6 6 6
7 8 8 7 8 8 8 8 7 5 5 6 7 6 8 6 6 6
8 7 6 5 6 6 8 6 6 4 4 6 5 6 5 6 3 3
8 7 6 7 7 7 8 6 6 4 4 6 6 6 6 6 3 3
9 7 7 8 8 8 8 8 7 5 4 6 7 7 6 6 5 4
9 7 7 8 8 9 8 8 7 5 4 7 7 8 6 6 5 4
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they are equal to: 0 for xpa and xXd and xpe and xXy, respectively, equal to 1 for bpxpg and zpxph, respectively. In the average range, as between ai and bi the membership functions are linear and can be expressed by xi ¼ bi ai y þ ai . (26)
799
following relations: L1 y2 þ L2 y þ W i ¼ x, U 1 y2 þ U 2 y þ Z i ¼ x,
ð27Þ
consequently the weight wi are expressed by (Wi[L1, L2]/Xi, Yi/Zi[U1, U2]) [2,4]. 4. Once the weights, that are fuzzy numbers, are obtained, it is necessary to obtain a real number or ‘‘crisp’’
Considering that the fuzzy products, the membership functions of the weights obtained, are expressed by
Table 4 Indicators matrix. evaluated by energy criteria Energy criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
3 5 5 1 5 2 2 2 6 2 2 1 7 8 8 4 1 4
4 5 5 1 5 2 2 2 6 2 2 1 7 8 8 4 1 5
4 6 6 2 6 3 3 3 7 3 3 3 8 8 8 5 1 6
4 6 6 2 6 4 4 3 7 3 3 3 8 8 8 6 1 7
2 4 4 1 4 1 1 1 7 1 1 2 6 7 7 3 1 5
J3 3 5 5 2 5 2 2 2 7 2 2 2 6 7 7 3 1 5
4 6 6 2 6 2 2 3 8 3 3 3 7 9 9 4 2 6
4 7 7 3 7 3 3 4 8 3 3 3 7 9 9 5 2 6
3 5 5 2 5 2 2 2 7 2 2 1 5 6 6 4 2 6
J4 3 6 6 2 6 3 3 2 7 2 2 2 6 7 7 4 2 6
4 6 6 2 6 3 3 3 8 2 2 2 7 8 8 5 2 7
4 6 6 2 6 4 4 3 8 2 2 3 8 9 9 5 2 7
2 6 6 2 6 2 2 2 6 3 3 2 5 7 7 1 1 7
J5 3 6 6 2 6 3 3 2 7 3 3 2 5 7 7 2 1 7
4 7 7 3 7 4 4 4 8 3 3 3 8 8 8 3 2 7
4 7 7 3 7 5 5 4 9 3 3 3 8 8 8 4 2 7
2 5 5 2 5 1 1 3 7 2 2 1 7 7 7 2 1 5
2 5 5 3 5 2 2 3 7 2 2 1 7 7 7 2 1 5
2 6 6 4 6 3 3 4 8 3 3 1 9 8 8 3 1 6
2 6 6 4 6 4 4 4 9 3 3 1 9 9 9 3 1 6
1 1 1 1 1 7 7 3 8 7 4 6 6 3 1 3 1 6
2 2 2 1 2 9 8 3 8 9 6 7 6 3 2 3 1 7
2 2 2 1 2 9 9 3 8 9 6 8 7 3 2 3 1 7
Table 5 Indicators matrix. evaluated by urban plan criteria Urban plan criteria J2
J1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 3 3 1 3 6 7 3 7 7 5 9 6 2 2 2 1 5
1 3 3 1 3 6 7 4 7 8 5 9 6 2 2 2 1 5
2 3 3 1 3 7 7 5 8 8 6 9 6 3 2 3 1 6
2 3 3 1 3 7 7 5 8 8 6 9 6 3 2 3 1 6
2 2 2 1 2 7 7 4 6 8 4 6 6 3 1 3 1 5
J3 2 2 2 1 2 7 7 4 6 8 4 6 6 3 1 3 1 5
3 3 3 1 3 8 8 6 8 9 5 8 7 4 2 3 1 6
3 3 3 1 3 8 8 6 8 9 6 8 7 4 2 3 1 6
1 2 2 1 2 5 7 2 6 6 5 7 6 1 2 1 1 4
J4 1 2 2 1 2 6 7 2 7 6 5 7 6 1 2 1 1 4
1 2 2 1 2 7 9 3 8 8 5 8 8 2 3 3 1 6
1 2 2 1 2 8 9 3 8 8 5 8 8 2 3 3 1 6
2 2 2 1 2 7 6 2 8 7 6 6 5 2 1 2 1 6
J5 2 2 2 1 2 7 6 2 8 7 6 7 5 2 1 2 1 6
2 3 3 1 3 8 8 4 9 7 6 8 9 2 1 2 1 6
2 3 3 1 3 8 8 4 9 8 6 9 9 2 1 2 1 6
1 1 1 1 1 7 6 3 8 7 4 5 5 3 1 3 1 5
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number by a ‘‘defuzzification’’ method. One of these methods is based on the average values using the following relation [5]: Z 1 F ðAi Þ ¼ 1=2 g1 y Ai þ g2 y Ai dy 0
1 1 1 ¼ ðL1i þ U 1i Þ þ ðL2i þ U 2i Þ þ ðZ i þ W i Þ. 6 4 2 ð28Þ
3. Sustainable indicators weight and application of sustainable urban model The example considers as obtaining the weights of a number of indicators. It is obtained using 5 judges, 4 criteria (economy, environment, energy and urban plan) and 18 indicators. For giving the indicators homogeneity as indicators, so as to compare them, their weights are calculated with fuzzy logic [6]. The methodology is the following: judges express by fuzzy numbers their opinion on the criteria and evaluate the indicators with respect to all evaluated criteria. The criteria and indicators matrix obtained are shown in the Tables 1–5. The resulted data base is used for calculating the weights from the averages values of the criteria and by indicators
5 6 6.6 4.6
5.6 6.6 6.8 5.4
6 7 7.6 6.2
Table 8 Weights components
6.6 7.4 8 6.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
7.6 7.2 7.2 6.8 7.4 8.2 8.4 8.4 6.6 5.2 4.6 6.8 6.6 6.8 7.2 6 5.2 4.4
m13 m23 m33 m43 m53 m63 m73 m83 m93 m103 m113 m123 m133 m143 m153 m163 m173 m183
Table 6 Criteria average value n1 n2 n3 n4
given by the judges. The fuzzy average value nk obtained by criteria and the value mik obtained by ith indicator for kth criteria are shown in Tables 6 and 7 and the weights components are obtained as in Table 8. For obtaining the crisp number of the weight, the ‘‘defuzzification’’, reported in Table 9, is made using the average value method and then normalized as average weight as shown in the Table 10. The analysis of the weight results shows that, based on the opinion expressed by the judges, the sustainable city is particularly influenced by public transportation, fuel, household GWh and cars, while a low sensitivity is associated with hydro consumption and ISO 14000 certified companies.
W
X
Y
Z
L1
L2
U1
U2
2.152 2.69 2.58 1.764 2.72 2.54 2.683 2.342 3.394 2.205 1.847 2.66 3.459 3.108 3.211 2.345 1.413 2.326
2.582 3.089 2.995 2.165 3.155 3.098 3.224 2.718 3.915 2.65 2.214 3.131 3.924 3.527 3.673 2.673 1.62 2.663
3.224 3.771 3.646 2.609 3.776 3.959 3.995 3.562 4.883 3.398 2.83 3.961 4.918 4.402 4.418 3.444 2.149 3.517
3.479 4.064 4.031 2.907 4.101 4.528 4.565 4.056 5.435 3.799 3.127 4.418 5.362 4.892 4.801 3.878 2.371 3.85
0.015 0.011 0.014 0.017 0.014 0.017 0.014 0.011 0.017 0.017 0.013 0.015 0.011 0.013 0.016 0.007 0.006 0.011
0.415 0.388 0.401 0.384 0.421 0.541 0.527 0.365 0.504 0.428 0.354 0.456 0.454 0.406 0.446 0.321 0.201 0.326
0.003 0.002 0.01 0.006 0.005 0.017 0.017 0.017 0.013 0.013 0.007 0.011 0.006 0.011 0.004 0.012 0.006 0.008
0.258 0.295 0.395 0.304 0.33 0.586 0.587 0.511 0.565 0.414 0.304 0.468 0.45 0.501 0.387 0.446 0.228 0.341
2.4 5 5 1.6 5 1.6 1.6 2 6.6 2 2 1.4 6 7 7 2.8 1.2 5.4
3 5.4 5.4 2 5.4 2.4 2.4 2.2 6.8 2.2 2.2 1.6 6.2 7.2 7.2 3 1.2 5.6
3.6 6.2 6.2 2.6 6.2 3 3 3.4 7.8 2.8 2.8 2.4 7.8 8.2 8.2 4 1.6 6.4
Table 7 Indicators average value m11 m21 m31 m41 m51 m61 m71 m81 m91 m10 m111 m121 m131 m141 m151 m161 m171 m181
4.6 5.4 5 4.6 5.4 4.4 4.4 5.6 6 4 3.4 6.4 7.4 7.6 8.2 6.8 4 2.8
5.2 5.8 5.6 5 5.8 4.6 4.6 5.6 6.4 4.6 3.8 6.6 7.6 8.2 8.6 7.2 4.2 3.2
6 6.2 5.6 5.6 6 5.2 5 6 7.2 4.8 4.4 7.4 8 8.6 8.6 8 5.2 3.8
6.2 6.2 6 5.6 6.2 5.4 5.2 6.6 7.4 5.4 4.6 7.6 8 8.8 8.6 8.4 5.6 4.2
m12 m22 m32 m42 m52 m62 m72 m82 m92 m102 m112 m122 m132 m142 m152 m162 m172 m182
6.8 6.4 6 5.4 6.6 6.6 7.4 6.6 5 3.8 3.6 5.8 6 5 5.8 5.2 4 3.4
7 6.6 6.2 6 7 7 7.6 7 5.4 4 4 6 6.2 5.2 6.4 5.2 4.2 3.4
7.6 7.2 7 6.4 7.4 8 8.2 7.8 6 5 4.4 6.6 6.4 6.4 7.2 6 5.2 4.4
3.6 6.4 6.4 2.8 6.4 4 4 3.6 8.2 2.8 2.8 2.6 8 8.6 8.6 4.6 1.6 6.6
m14 m24 m34 m44 m54 m64 m74 m84 m94 m104 m114 m124 m134 m144 m154 m164 m174 m184
1.4 2 2 1 2 6.4 6.6 2.8 7 7 4.8 6.6 5.6 2.2 1.4 2.2 1 5
1.4 2 2 1 2 6.6 6.8 3 7.2 7.2 4.8 7 5.8 2.2 1.4 2.2 1 5.2
2 2.6 2.6 1 2.6 7.8 8 4.2 8.2 8.2 5.6 8 7.2 2.8 2 2.8 1 6.2
2 2.6 2.6 1 2.6 8 8.2 4.2 8.2 8.4 5.8 8.4 7.4 2.8 2 2.8 1 6.2
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The judges use the data reported in the statistics and in The ‘‘Environmental Reports’’ prepared by Associations and Organizations [7]. It has been carried out an application for the city of Naples, Italy through the weights calculated with fuzzy logic, then it allows us to estimate the sustainability of the city connected to the goals prefixed. For every indicator it was determined a ‘‘sustainable goal’’ or ‘‘environmental quality’’, equal to 100, without to attribute the weights. Therefore, every indicator can to assume a value between 0 (min) to 100 (max).
Table 9 Defuzzification
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Defuzzification
Weight normal
2.858 3.402 3.311 2.359 3.436 3.528 3.614 3.167 4.404 3.011 2.503 3.54 4.414 3.98 4.024 3.083 1.887 3.087
0.48 0.57 0.56 0.4 0.58 0.59 0.61 0.53 0.74 0.51 0.42 0.59 0.74 0.67 0.68 0.52 0.32 0.52
801
Through the elaboration of data base reported in [1], it is possible to obtain the values of the 18 indicator normalized (and specified in Table 2), for the aforesaid city. Fig. 3 shows the outline of the environmental conditions and the ‘‘ideal’’ outline of sustainability, in this case equal to 100, without considering the weights. The grey area shows the ‘‘real’’ values of the chosen 18th indicators. The values were supplied by [7]. Each indicator has a different ‘‘weight’’ on the sustainability either with respect to other indicators or with respect to the evaluation criteria. Moreover, Fig. 4 shows the same outline of the environmental conditions but compared to a ‘‘real’’ outline of sustainability, where the edges are weighed for an ‘‘ideal’’ but not utopian city. Fig. 4 highlights how the sustainability objective changes weighting the chosen indicators. For the specific case of the city of Naples
Fig. 3. Environmental conditions and ‘‘ideal’’ outline of sustainability, without considering the weights.
Table 10 Indicators value normalised 1
2
3
4
5
6
High sustainable objective Lower objective Fuzzy weight Objective weighed Indicators value normalized
100 0 0.48 48 95
100 0 0.57 57 67.22
100 0 0.56 56 55
100 0 0.4 40 65.11
100 0 0.58 58 84.44
100 0 0.59 59 38
High objective Lower objective Fuzzy weight Objective weighed Indicators value normalized
7 100 0 0.51 51 22.5
8 100 0 0.42 42 0
9 100 0 0.59 59 12.5
10 100 0 0.74 74 48.48
11 100 0 0.67 67 74.78
12 100 0 0.68 68 99.25
High objective Lower objective Fuzzy weight Objective weighed Indicators value normalized
13 100 0 0.61 61 45.62
14 100 0 0.53 53 2.5
15 100 0 0.74 74 29.14
16 100 0 0.52 52 73.76
17 100 0 0.32 32 2.857
18 100 0 0.52 52 0
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F. Gagliardi et al. / Energy 32 (2007) 795–802
Fig. 4. Environmental conditions and ‘‘real’’ outline of sustainability, considering the weights.
(Italy) it is emphasized how some parameters widely respect the sustainability and how others parameters need work for limiting them inside the sustainability area. It can be seen as only some parameters do not respect the sustainability, while others respect totally the goals.
of an indicator with regard to another indicator, every decision maker is brought to reason in a less objective way. An urban planner, for example, will give more importance to a cycle path or green areas, but on the contrary a chemical engineering will be concerned with air pollution problems. In spite of this, the proposed systems, even starting from subjective evaluation, permits the combination of different opinions on various indicators, by means of different criteria. Moreover, the final results will be a combination of values assigned by different judges for various criteria by fuzzy number which translates verbal expression in a numerical quantity. Therefore it is possible to obtain a more careful evaluation of the sustainability of the cities, based on quality objects, more open-minded and dynamics, integrating the point of view of decision maker’s in the weight to give to the different indicators. Acknowledgement The authors thank Prof. D. Zaninelli for his precious contribution. References
4. Conclusion The example reported in this paper to calculate the weight, is on a hypothetical sustainable city and the evaluation of the weight, criteria and indicator have not been carried out by experts of the specific fields. In order for the case of a real city to establish the just values, the contribution of the experts in the various chosen fields will be necessary. This method, presented in the paper, is applied to the city of Naples, Italy. It can be noted that the application is done by the authors basing their calculation methodology on the documents reported in [1,7]. The applied methodology for calculating indicator weights for selected criteria, points out the importance of decision maker’s subjectivity. In fact, assigning the weight
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