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.
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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)