Abstract
The aim of this paper is to develop a method for ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) in the process of decision making in the intuitionistic fuzzy environment. Firstly, the concept of TrIFNs is introduced. Arithmetic operations and cut sets over TrIFNs are investigated. Then, the values and ambiguities of the membership degree and the nonmembership degree for TrIFNs are defined as well as the value-index and ambiguity-index. Finally, a value and ambiguity-based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TrIFNs. A numerical example is examined to demonstrate the implementation process and applicability of the method proposed in this paper. Furthermore, comparison analysis of the proposed method is conducted to show its advantages over other similar methods.
Highlights
Multiattribute decision making (MADM) is an important research field of decision science, operational research, and management science
The aim of this paper is to develop a method for ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) in the process of decision making in the intuitionistic fuzzy environment
We have studied two characteristics of a TrIFN, that is, the value and ambiguity, which are used to define the value index and ambiguity index of the TrIFN
Summary
Multiattribute decision making (MADM) is an important research field of decision science, operational research, and management science. Fuzzy numbers are a special case of fuzzy sets and are of importance for fuzzy multiattribute decision making problems [7,8,9,10,11,12]. For decision making using the IF sets, it is required to rank the IFNs. So far, several methods have been developed for ranking the IFNs. Mitchell [14] interpreted IFNs as an ensemble of ordinary fuzzy numbers and defined a characteristic vagueness factor and a ranking method for IFNs. Nan et al [15] defined the concept of average indexes for ranking triangular IFNs. Nehi [16] generalized the concept of characteristic value introduced for the membership and the nonmembership functions and proposed a ranking method based on this concept.
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