Advances in Mathematical
Sciences and Applications
Vol. 26, No. 1 (2017), pp. 81–87

GAKKOTOSHOTOKYO JAPANFUZZY ESTIMATION OF ECOLOGICAL PERFORMANCEINDEX (EPI)

Malahat Murtuzaeva
Control Systems Institute of the National Academy of Sciences of Azerbaijan
AZ1141, Azerbaijan, Baku, B.Vahabzadeh str.,9(E-mail: malaxat-55@rambler.ru)

andSamir Pur Riza
Control Systems Institute of the National Academy of Sciences of Azerbaijan
AZ1141, Azerbaijan, Baku, B.Vahabzadeh str.,9(E-mail: pqs@rambler.ru)

Abstract.
The Environmental Performance Index (EPI) is a method of quantifying
and numerically marking the environmental performance of a state’s policies. Presentpaper studies questions of EPI calculation for country’s group with the purpose to range
the state of ecologic system using intuitionistic fuzzy modeling method.

Communicated by M. Efendiev; Received March 31, 2017.
AMS Subject Classification: 62P12, 62P20
Keywords: Environmental sustainability index, intuitionistic fuzzy sets (IFS), correlation coefficient,
intuitive entropy, weight coefficient.

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1Introduction

The purpose of this paper is to study the issue of ranking group of countries, which haveclose economic, geographic and historical ties with our country, on sustainable development. The concept of sustainable development of the countries is known to be associatedwith ESI (Environmental sustainability index) and EPI (Environmental performance index) notions, which have been calculated by Yale and Columbia universities in the USA
for the most countries in the world since 2006.
Environmental Performance Index (EPI) - is a method of quantifying and benchmarking the environmental policy of the world states. EPI ranks countries on performance inseveral categories, which are combined into two groups: the viability of ecosystems andecological health.
EPI for countries includes the measurement of development impacts in two ways: bypopulation health and viability of ecosystems through the behavior of 9 major factors in2016 (10 factors in 2012-2014 years). Initial data for the group of countries over the yearof 2016 are given in Table 1[6].
Country

Azerbaijan
RussiaTurkeyIranGeorgia

2016
EPI
Score
83,78
83,52
67.68
66,32
64.96

EH

EVHI

AQ

WSWRAGFOR

FISH

BAH

CAE

82,96
87,06
79.6
72,26
78.12

84,6
79,98
55.76
60,38
51.81

89,77
92,274,43
63,21
75,180,99
84,76
79,376,68
79,96

78,1284,22
85,06
76,89
79,31

69,16
91,28
78,99
55,91
098,1898,18
87,04
92,39
98,18

96,7
49,17
68,48
62.8
100

69.80
57,81
57,82
33,17
31,85

75,83
73,7
22,53
64,16
70,31

97,94
84,42
47,77
53,88
51,28

Table 1 Factors values of EPI by Yale University
EH - Environmental Health

AG - Agriculture;

HI - Health Impacts;

FOR - Forests;

AQ - Air Quality;

FISH - Fisheries;

WS - Water and Sanitation;

BAH - Biodiversity and Habitat;

EV - Environmental Vitality

CAE - Climate and Energy.

WR - Water Resources;
In the new approach, ranking values of EPI are used for calculating the correlation
coefficient of fuzzy decision-making, weight coefficient of correlation calculated on thebasis of intuitionistic fuzzy sets (IFS). IFS - contains two kinds of sides by means of themembership and non-membership concepts. By construction, the IFS have the following
assumptions:Definition 1. An IFS A in X in given byA = {hx, µA (x), υA (x)i|x ∈ X}

(1)

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where µA (x) : X → [0, 1] and υA (x) : X → [0, 1], with the condition 0 ≤ µA (x) + υA (x) ≤1. The numbers µA (x) and υA (x) represent, respectively, the membership degree andnonmembership degree of the element x to the set A [1].
The value of π is ”intuitive index”, which represents the degree of indecision, thefluctuation degree of inclusion of x variable to A set. Description of the numerical valuesof indicators calculated on a 100-point scale is normalized, then transferred to the intuitive
fuzzy numbers as follows. The actual data are grouped into five linguistic subsets (VL,L, M, H, VH). The logic is that if the actual value of the factor is included in VH in
the interval (0.8 - 1.0), the most likely entry hesitancy of the studied state belongs to
the interval (0 - 0.2). Moreover, values close to 0.8, corresponds the value of indecision
π(x) = 0.2. If the actual value of the factor is very close to 1, the value of intuitive index
will be π(x) = 0 (the compliance has a inversely symmetrical character). It is obvious thatin such a transformation the middles of the intervals become the exact middles (means)of intervals according to the values of indecision π(x). This can be described graphicallyas follows:0000

π - decreasing step function of µ (x), where µ (x) is the value of real-normalized data
for each factor of EPI.
The procedure of constructing IFS is demonstrated in HI (Health Impact) Index for
Azerbaijan, which is equal to normalized value 0.8977 in the year of 2016. Intuitive index
corresponding to this value is equal to π(x) = 0.1. Then the values of membership andnon-membership functions respectively equal to:µ(HIAZ ) = 0.8977 ∗ (1 − 0.1) = 0.81, υ(HIAZ ) = 1 − 0.81 − 0.1 = 0.09.
Thus, IFS for the value of HI in 2016 is described as triplet (0.81, 0.09, 0.1). Table 2
shows the calculated values of IFS over all factors of EPI in five countries.

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Country
Azerbaijan
RussiaTurkeyIranGeorgia

0,81
0,82
0,520,380,53

HI
0,090,070,180,220,170,10,10,30,40,30,650,680,630,610,64AQ
0,150,120,170,190,160,20,20,20,20,20,620,670,770,620,64

WS
0,180,130,140,180,160,20,20,10,20,20,480,820,630,340

WR0,220,08
0,170,260

0,30,10,20,4
1

0,98
0,98
0,780,830,98

AG
0,020,020,120,070,02

Continued Table 2Country
Azerbaijan
RussiaTurkeyIranGeorgia

0,97
0,250,480,380,1

FOR0,030,250,220,220

00,50,30,400,430,350,350,10,1FISH0,210,250,250,20,20,30,40,40,70,70,610,520,050,390,49

BAH
0,190,180,160,210,210,20,30,80,40,30,979
0,680,290,270,26CAE
0,020,120,210,230,240,001
0,20,50,50,5Table 2 Calculated values of IFS over all factors of EPI

According to the method presented in [2] we directly calculate the EPI values for theabove mentioned countries taking into account the definition of the relevant concepts,
which are necessary to calculate the fuzzy correlation coefficient between the two IFS
introduced in [5], [4], [7] and [2].
Definition 2. The correlation coefficient between the IFS, as defined in
X = {x1 , x2 , ..., xn } [5]k(A, B) = √ C(A,B)

T (A)∗T (B),(2)

000,10,10

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where
C(A, B) =n
X(µA (xi ) ∗ µB (xi ) − υA (xi ) ∗ υB (xi )),

(3)

i=1

T (A) =nX(µ2A (xi ) + υA2 (xi )).

(4)

i=1

T (A), T (B) - the so-called information and intuitive energy of A and B sets respectively.
Definition 3. Definition of intuitive entropy of IFS is given in [4]:55X
XH(A) =
(1 − µA (xi ) − υA (xi )) =πA (xi ).
i=1(5)

i=1Definition 4. Weight coefficient of correlation is calculated as follows [7]:Pnj (µA (cj ))∗Wi (A , Ai ) = qP.
n22(c))(c)+υw∗(µAi jAi jj=1 j(6)In case of the information about the weight criterion Cj being generally unknown, theentropy weights model for defining the weight criterion is used by means of the formula(7):1 − HiPWi =.
(7)n − nj=1 (Hj )Step 1. According to the formula (5) we calculate the entropy of each criterion andplace in table 3. For example,
P5
H1 =

1 (H1i )5P5=

0.1 + 0.1 + 0.3 + 0.4 + 0.3= 0.225,
51 (H2i )

H2 =

5

=

0.2 + 0.2 + ... + 0.2= 0.2.
5

Therefore, fill in Table 3.
H10.225

H20.2

H30.175

H40.25

H50.05

H60.35

H70.55

H80.425

H90.3

P91 (Hi )2.66

9−P91 (Hi )6.34

Table 3 Values of the entropy criteria
Step 2. Using the formula (7) the weight of entropy criteria is calculated and placedin Table 4.
w1
0.1199w20.1262

w30.129

w40.095

w50.1514

w60.1136

w70.066w80.0946

w90.1041

Table 4 Obtained values of the weights of entropy criteria

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Step 3. Next, on the basis of IFS values (Table 2) and calculated weights of thecriteria according the formula (7) the correlation coefficients for five countries, which will
eventually give a ranking of country groups with EPI index are computed. According toour calculations, EPI ranking values have been converged with results calculated for thesecountries by Yale and Columbia universities in the USA [6].
According to our calculations, the following values for EPI 2016 have been obtained:
RankCountries

EPI 2016

EPI 2016(Yale)

EPI
weight ingroup

1
2
3
4
5

Azerbaijan
RussiaTurkeyIranGeorgia

95.43
92.71
88.07
85.29
84.46

83.78
83.52
67.68
66.3264.96

0.21390.20790.19750.19120.1894

Changedirection ofEPI values
with regard
to Yale values
0.229
0.228
0.185
0.181
0.177

Table 5 Obtained results for EPI 2016

EPI calculation of Yale method is a simplified calculation of mean arithmetic values,
which is not adequate enough in case of data with extreme estimates. The use of intuitive
fuzzy entropy weights makes possible to achieve computing the value of the ecological stateof countries in more sophisticated mathematical way. As seen from the table 5 there isno difference in EPI sequence of priority values of the countries, however specific weights
have changed. As a result, we can state that regarding to our estimations calculationof EPI shares by Yale University is overstated for values of Azerbaijan and Russia, andunderstated for the rest of the countries, which is clearly seen from the above given Figure3.

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2Conclusion

Applying the proposed method, we came to the conclusion that in our case the ranks of theecological state index by countries did not change, however the accuracy of calculations
increased through the identifying dynamics in the vicinity of the values of these indices.

References[1] K.Atanassov, Intuitionistic fuzzy sets, Soft and Systems, 20, 1986, North-Holland,
87 - 96.
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Performance Index Using Weighted Correlation Coefficient in Intuitionistic Fuzzy sets: A
case of ASEAN Countries, Modern Applied Science, Vol.7, No. 6, 2013.
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[6] Yale Center for Environmental Law and Policy and Center for International Earth
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