Abstract
The order relation of fuzzy number is important in decision making and optimization modeling, and ranking fuzzy numbers is difficult in nature. Ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) is more difficult due to the fact that the TrIFNs are a generalization of the fuzzy numbers. The aim of this paper is to develop a new methodology for ranking TrIFNs. We define the value-index and ambiguity-index based on the value and ambiguity of the membership and non-membership functions, and then propose a difference-index based ranking method, which is applied to multiattribute decision making (MADM) problems. The proposed method is compared to show its advantages and applicability.
Highlights
There is always existing uncertainty and imprecision in real-life decision making, the concept of the intuitionistic fuzzy (IF) set (IFS), introduced by Atanassov[1], is considered as a representation for these uncertain factors in real-life decision situations
Trapezoidal intuitionistic fuzzy numbers (TrIFNs) are special cases of IFSs defined on the set of real numbers, which may deal with more ill-known quantities, knowledge or experience
Nayagam et al [5] described a type of special IFNs and introduced a scoring method of the special IFNs, which is a generalization of the scoring method for ranking fuzzy numbers
Summary
There is always existing uncertainty and imprecision in real-life decision making, the concept of the intuitionistic fuzzy (IF) set (IFS), introduced by Atanassov[1], is considered as a representation for these uncertain factors in real-life decision situations. Li [9] proposed a ratio ranking method of TIFNs based on the concept of value-index and ambiguity-index. Yang proposed a value and ambiguity based ranking method through defining the values and ambiguities of the membership and non-membership degrees for TIFNs.Wang and Zhang [2] defined the TrIFNs and gave a ranking method, which transformed the ranking of TrIFNs into the ranking of interval numbers. From the existing research results, we can see that there exists little investigation on the ranking of TrIFNs. In addition, the TrIFNs are a generalization of IF numbers, and which are commonly used in real decision problems with the lack of information or imprecision of the available information in real situations is more serious. Introducing the value-index and ambiguity-index based ranking method is developed for TrIFNs and used in MADM problems.
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