Preference Attitude-Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection

Complexity, Feb 2018

Many applications of intuitionistic fuzzy sets depend on ranking or comparing intuitionistic fuzzy numbers. This paper presents a novel ranking method for intuitionistic fuzzy numbers based on the preference attitudinal accuracy and score functions. The proposed ranking method considers not only the preference attitude of decision maker, but also all the possible values in feasible domain. Some desirable properties of preference attitudinal accuracy and score functions are verified in detail. A total order on the set of intuitionistic fuzzy numbers is established by using the proposed two functions. The proposed ranking method is also applied to select renewable energy. The advantage and validity of the proposed method are shown by comparing with some representative ranking methods.

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Preference Attitude-Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection

World Journal Preference Attitude-Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection Jian Lin 1 2 Fanyong Meng Riqing Chen 0 Sigurdur F. Hafstein 0 School of Business, Central South University , Changsha 410083 , China 1 Institute of Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University , Fuzhou 350002 , China 2 College of Computer and Information, Fujian Agriculture and Forestry University , Fuzhou 350002 , China 3 School of Management and Economics, Beijing Institute of Technology , Beijing 100081 , China Many applications of intuitionistic fuzzy sets depend on ranking or comparing intuitionistic fuzzy numbers. This paper presents a novel ranking method for intuitionistic fuzzy numbers based on the preference attitudinal accuracy and score functions. The proposed ranking method considers not only the preference attitude of decision maker, but also all the possible values in feasible domain. Some desirable properties of preference attitudinal accuracy and score functions are verified in detail. A total order on the set of intuitionistic fuzzy numbers is established by using the proposed two functions. The proposed ranking method is also applied to select renewable energy. The advantage and validity of the proposed method are shown by comparing with some representative ranking methods. - 1. Introduction Atanassov [1] introduced the concept of intuitionistic fuzzy sets characterized by a membership function, a nonmembership function, and a hesitancy function. Due to the increasing complexity of real life problems, intuitionistic fuzzy set is very suitable for representing fuzzy information under complicated and uncertain settings as an extension of traditional fuzzy set. Intuitionistic fuzzy set theory has been deeply discussed by many scholars since the notations appearance and applied in various fields, such as decision-making [2–7], supplier selection [8–10], pattern recognition [11–14], medical diagnosis [15, 16], and artificial intelligence [17, 18]. Many applications of intuitionistic fuzzy sets depend on ranking or comparing intuitionistic fuzzy numbers. A number of researchers focus on the order relation of intuitionistic fuzzy numbers over the past two decades. Chen and Tan [19] proposed a score function to evaluate the score of intuitionistic fuzzy values. Through analysis on the limitation of Chen and Tan’s score function, Hong and Choi [20] improved their ranking method by adding an accuracy function. Xu [21] gave a kind of order relation to rank the intuitionistic fuzzy numbers by combining the score and accuracy function. Wang et al. [22] introduced a novel score function to measure the degree of suitability. Some desirable properties of the novel score function were discussed. Ye [23] developed an improved algorithm for score functions based on hesitancy degree. By using the intuitionistic fuzzy point operators, Liu and Wang [24] defined a series of new score functions for dealing with multicriteria decision-making problems. Jafarian and Rezvani [25] presented a method for mapping the intuitionistic fuzzy numbers into the crisp values and described the concept of spread value of intuitionistic fuzzy number. To analyze the fuzzy meaning of an intuitionistic fuzzy value, Yu et al. [26] formalized an intuitionistic fuzzy value as a fuzzy subset and determined the dominance relation between two intuitionistic fuzzy values. Guo [27] built a new ranking model based on the viewpoint of amount of information. A total order which extended the usual partial order was analyzed in deep. Zhang and Xu [28] used a where () and V () are the membership degree and nonmembership degree of to , respectively, such that (), V () ∈ [0, 1], ()+ V () ≤ 1. The hesitation degree of to is denoted by () = 1 − () − V (). Obviously, for each ∈ , we have () ∈ [0, 1]. For simplicity, = (, V) is called an intuitionistic fuzzy number (IFN), such that , V ∈ [0, 1], + V ≤ 1, and () = 1 − − V. The set of all IFNs is denoted by IFN. Let 1 = ( 1, V1) and 2 = ( 2, V2) be two IFNs. Clearly, 1 = 2 if and only if 1 = 2 and V1 = V2. Based on the score function [19] and accuracy function [20], Xu [21] introduced the operational laws and ordering relation among intuitionistic fuzzy numbers as follows. Definition 2. Let 1 = ( 1, V1) and 2 = ( 2, V2) be two IFNs; then ( 1 ) 1 ⊕ 2 = ( 1 + 2 − 1 2, V1V2), ( 2 ) ⊗ 1 = (1 − ( 1 − 1 ) , V1 ), > 0 . Definition 3. Let = (, V)be an IFN. The accuracy and score function of are, respectively, represented by ( ) = + V, ( ) = − V. special function to define the order of intuitionistic fuzzy numbers. Some good mathematical properties on algebraic intuitionistic fuzzy numbers were also given. Lakshmana et al. [29] derived a total order on the entire class of intuitionistic fuzzy number by applying upper lower dense sequence to the interval. Gupta et al. [30] utilized relative comparisons based on the advantage (...truncated)


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Jian Lin, Fanyong Meng, Riqing Chen, Qiang Zhang. Preference Attitude-Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection, Complexity, 2018, 2018, DOI: 10.1155/2018/6251384