A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems

Abstract

a b s t r a c tThe concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for ranking TIFNs. Firstly the concepts of TIFNs and cut sets as well as arithmetical operations are introduced. Then the values and ambiguities of the membership function and the non-membership function for a TIFN are defined. A new ranking method is developed on the basis of the concept of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFNs. The validity and applicability of the proposed method, as well as analysis of the comparison with other methods, are illustrated with a real example.

An Extended VIKOR-Based Approach for Pumped Hydro Energy Storage Plant Site Selection with Heterogeneous Information

“…Definition 1 [36]. A TIFN a = ((a, a, a); w a , u a ) is a special IFS on the real number set R, whose membership function and non-membership function are defined as follows:…”

“…Definition 2 [36]. Let a 1 = ((a 1 , a 1 , a 1 ); w a 1 , u a 1 ) and a 2 = ((a 2 , a 2 , a 2 ); w a 2 , u a 2 ) be two TIFNs and λ be a real number.…”

A Note on Solving a Fully Intuitionistic Fuzzy Linear Programming Problem based on Sign Distance

“…We get optimal solution of fully IFLP problem (6) using algorithm described in section (6). Thus the optimal solutions of decision variables are: And optimal value of the intuitionistic fuzzy objective function is .…”

“…Further, since these problems of intuitionistic fuzzy optimization contain the imprecise parameters as intuitionistic fuzzy numbers, their quantitative comparison need the ranking methods. There are several ranking methods for intuitionistic fuzzy numbers and are available in literature such as Szmidt and Kacprzyk [16], Wang and Xin [17], Nayagam et at [18], [20], Li [6], Li Nan, Zhang [19], Wei and Tang [21], Nehi [22], De and Das [23]. A distance based ranking of intuitionistic fuzzy numbers was developed by Guha and Chakrborty [25], Esmailzadeh [26], Zhang and Xu [24].…”

Proposed Model for Evaluating Information Systems Quality Based on Single Valued Triangular Neutrosophic Numbers

“…Then, they gave two multi-valued neutrosophic power aggregation operators and applied to multi-criteria group decision-making problems. Li [13] provides ratio ranking method for TIFNs and cut sets of intuitionistic trapezoidal fuzzy numbers. Li et al [14] introduced a ranking method of triangular intuitionistic fuzzy numbers that depend on value index and ambiguity index for solving multi criteria decision-making problems.…”