A New Ranking of Environmental Performance Index Using Weighted Correlation Coefficient in Intuitionistic Fuzzy Sets: A Case of ASEAN Countries

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Introduction
Sustainable development can be defined generally as the situation when development and preservation on environment get balance.However, other issues like economy sustainability and socio-political sustainability are not neglected.There are many types of sustainable development such as environmental sustainability, economical sustainability, socio-political sustainability, ecological sustainability and cultural sustainability.Environmental sustainability is a process to make sure that the daily life activities and any usage of environment is friendly environmental and preserved environment.An unsustainable environment is the situation where the usage and development does not preserve the environment and the nature's source had been used is more than the replenished.The widely method used to assess the environmental sustainability are Emergy Evaluation (EME) and Ecological Footprint Analysis (EFA).The outcomes of the assessment are focused on resources depletion, consumption patterns, waste production and absorption (Marchetinni et al., 2007).Environmental impact is measured by the emergy investment ratio defined as the ratio of the emergy purchased from the economy divided by the emergy from the local environment (Odum, 1998).Ecological footprint analysis compares human demand on nature with the biosphere's ability to regenerate resources and provide services.It is done by assessing the biologically productive land and marine area required to produce the resources a population consumes and absorb the corresponding waste using prevailing technology (Eco Greenwares, 2009).Per capita ecological footprint (EF) is comparing consumption and lifestyles and checking this against nature's ability to provide for this consumption (Cui & Yu, 2009).
Performance in handling environmental policy categories is another perspective in environmental assessment.using AHP, the decision problem is decomposed into a number of subsystems in which substantial number of pair wise comparisons need to be completed.Number of pair wise comparisons to be made may become very large depending on the size of matrix.The relation (n(n−1)/2) where n is size of decision matrix clearly lead to a lengthy task (Macharis et al., 2004).Another disadvantage of the AHP method is the artificial limitation of the use of the 9-point scale.Sometimes the decision maker might find difficult to distinguish among them.Also, the AHP method cannot cope with the fact that an alternative is 25 times more important than another alternative (Belton & Gear, 1983;Belton, 1986).
As an effort to overcome these weaknesses, a new approach in calculating environmental performance index is proposed.The proposed method for measuring environmental performance is taken into account weight of each policy category.The method was originally proposed by Ye (2010) as a method in fuzzy decision-making method based on the weighted correlation coefficient.To the best of authors' knowledge, this dual assessment method has not been tested to environmental performance.The weight of each policy category and two-sided memberships of intuitionistic fuzzy sets (IFSs) is considered as an important characteristic in this calculation.The aim of this paper is to propose weights for policy categories and subsequently propose a new rank of EPI.Nine ASEAN countries are tested to the weighted correlation coefficient method as an alternative method in calculating new EPI.The paper unfolds as follows.The next section briefly introduces some definitions related to the method.Section 3 describes the weighted correlation coefficient in IFSs proposed by Ye (2010).Section 4 presents weights for policy categories and a new ranking of EPI.Discussions section presents a new ranking of EPI.A comparison between original EPI and related study is made in this section.Conclusions appear in the last section.

Preliminaries
This section introduces some definitions that self-contained to the paper.
indicates the membership degree of the element x to the set A.
An IFS in X is an expression A is defined by represent respectively the membership degree and non-membership degree of the element x to the set A. For each IFS in X: the two relations are follows: (1) Definition 3 Correlation coefficient of IFSs (Gerstenkorn & Manko, 1991) Let A and B be two IFSs in the universe of discourse }. ,..., , { The correlation coefficient of A and B is given by , respectively.The correlation coefficient of two IFSs A and B satisfies the following properties: Definition 4 Intuitionistic entropy of IFSs (Burillo & Bustince, 1996) Let A be an IFS in the universe of discourse }. ,..., , { The intuitionistic fuzzy entropy of an IFS A is defined as follows: (Ye, 2010) Based on the correlation coefficient between IFSs proposed by Gernstenkorn and Manko (1991), the correlation coefficient between an alternative A i and the ideal alternative A * with entropy weights for criteria can be measured by the weighted correlation coefficient

Weighted Correlation Coefficient
If the information about weight j w of the criterion ) ...., , 2 , 1 ( n j C j  is completely unknown, then the model of entropy weights is applied to determine the criteria weight: where The larger the value of weighted correlation coefficient , i W the better alternative , i A as the alternative , i A is closer to the alternative .

*
A Therefore, all the alternatives can be ranked according to the weighted correlation coefficients so that the best alternatives can be selected.The weighted correlation coefficient

Environmental Performance Index 2012
Environmental Performance Index 2012 and ranking issued by Yale Center for Environmental Law and Policy and Center for International Earth Science Information Network (2012) among nine ASEAN countries are given in Table 1.Nine ASEAN countries are indicated as Ai (i=1,2,3,4,5,6,7,8,9).i=1, 2, 3, 4, 5, 6, 7, 8, 9, 10) were retrieved as secondary data in proposing a new ranking of EPI.Environmental burden of disease, air pollution (impact on humans), water (impact on humans), air pollution (impact on ecosystem), water (impact on ecosystem), biodiversity, forestry, fisheries, agriculture and climate change were the nine policy categories.The index for each policy category shall be converted into intuitionistic fuzzy sets (IFSs) notation to fit with the weighted correlation coefficient formula.
The weighted correlation coefficient between an alternative A i and the ideal alternative A * with entropy weights for criteria, * ( , ) ( 1,2,3,4,5,6,7,8,9) i W A A i  is measured using Equation ( 6).The weighted correlation coefficient The calculation is executed to other eight countries.Weighted correlation coefficients are listed in Table 5.Table 5 shows the weighted correlation coefficients for each country.The larger value of weighted correlation coefficients indicates the better alternative in environmental performance.

Discussion
A new EPI ranking for ASEAN countries using weighted correlation coefficient is obtained.The new ranking was established after considering the weights in each policy category.The membership and non-membership values in IFSs are the main characteristics prior to introducing the weights.The memberships are embedded with fuzzy correlation coefficient to find the best alternatives.The best alternative represents the better country in environmental performance.
The results show that Thailand leads in the first place followed by Malaysia and Brunei while the last three countries are Myanmar, Cambodia and Vietnam.The obtained ranking is illustrated and compared with the original EPI 2012 and EPI 2012 using AHP.The new ranking and ranking from the other two methods are illustrated in Figure 3.It can be seen that the new ranking differs from original EPI 2012 and EPI 2012 using AHP.The original EPI indicates that Malaysia is the first among ASEAN countries in environmental performance followed by Brunei and Thailand.However, Brunei takes the first spot when AHP method is used, followed by Singapore and Malaysia.Contrarily, Thailand leads in first spot followed by Malaysia and Brunei when the calculation is made using the weighted correlation coefficients.The inconsistency in ranking can be related due to membership and non-membership of IFSs.

Conclusion
This paper has shown the capability of decision tool weighted correlation coefficient of IFSs in proposing the new ranking of EPI 2012 among ASEAN countries.The original EPI is used arithmetic mean in calculating the ten policy categories.Neglecting some extreme values was among the weakness of this simple mathematical operation.Thus, weighted correlation coefficient based on IFSs was proposed.This mathematical model was successfully proposed weights in each of category policies of environmental performance.The advantage of IFSs lies on the two-sided measurements, membership and non membership values.A new ranking of EPI among ASEAN countries show that Thailand is at the first place followed by Malaysia and Brunei.The method could be extended to other countries as this method offer an alternative measure in evaluating environmental performance.
As a further research, the weighted correlation coefficient may consider the extension version interval-valued intuitionistic fuzzy sets in the calculation.It might provide a comprehensive evaluation due to its interval values thereby offer a more reliable EPI.

Figure 3 .
Figure 3. Ranking of EPI 2012 for ASEAN countries: comparison analysis

Table 1 .
Environmental performance index (EPI) 2012 Table 2(a) and 2(b) shows the data for ASEAN countries extracted from Yale Center for Environmental Law and Policy and Center for International Earth Science Information Network (2012).
Memberships for other policy categories of ASEAN countries are calculated with the similar fashion.It is listed in Table 4(a), Table 4(b) and Table 4(c).

Table 5 .
Weighted correlation coefficient of ASEAN countries