A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept

Abstract

Ranking of intuitionistic fuzzy numbers is a difficult task. Many methods have been proposed for ranking of intuitionistic fuzzy numbers. In this paper we have ranked both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept. Some of the properties of the ranking function have been studied. Also, comparative examples are given to show the effectiveness of the proposed method.Keywords Intuitionistic fuzzy set Á Trapezoidal intuitionistic fuzzy number Á Triangular intuitionistic fuzzy number Á Ranking of trapezoidal intuitionistic fuzzy number Á Centroid of an intuitionistic fuzzy number

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

“…Deli and Şubaş [6] adapted and generalized Li et al [14] method to SVN-numbers and the results show that this method is effective and feasible. Prakash et al [21] introduced a ranking method for both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept and showed the proposed method is flexible and effective.…”

7 Arithmetic operations on generalized semielliptic intuitionistic fuzzy numbers and their application in multicriteria decision making

“…IFS deals with such situations in an enhanced manner in comparison to FST. Due to growing complexities in making decisions, several intuitionistic fuzzy numbers (IFNs) have been developed [3][4][5]. More often, for simplicity, triangular or trapezoidal IFNs (TrIFNs) are employed to solve decision-making problems.…”

“…In literature, a few numbers of ranking approaches are encountered based on value and ambiguity [6], centroid point [7], centroid [3], magnitude [8], area [9], score and accuracy function [10], possibility mean [11], mean value [12], and improved possibility degree [13]. The approaches [3,4,6,[14][15][16][17][18][19][20][21][22][23][24] focused on the value as well as the ambiguity-based ranking method of IFNs and applied in MCDM problems. The approaches in [7] and [3] dealt with the centroid-based ranking method, the approach in [21] presented a ranking technique for IFNs by using the distance of each IFN from the fuzzy origin, and the approach in [9] developed a ranking method based on ðα, βÞ-cuts and area of IFNs.…”

“…The approaches [3,4,6,[14][15][16][17][18][19][20][21][22][23][24] focused on the value as well as the ambiguity-based ranking method of IFNs and applied in MCDM problems. The approaches in [7] and [3] dealt with the centroid-based ranking method, the approach in [21] presented a ranking technique for IFNs by using the distance of each IFN from the fuzzy origin, and the approach in [9] developed a ranking method based on ðα, βÞ-cuts and area of IFNs. Notwithstanding having some primacy of ranking approaches, these approaches have some deficiencies and do not provide a proper result, which produces predicament for judgment architects in any decision-making problem.…”

8 Method for solving intuitionistic fuzzy assignment problem

“…In this chapter, we have considered intuitionistic FAP (IFAP). To solve the IFAP, we have used a new ranking method based on centroid concept introduced by Arun Prakash et al [28]. Then the AP has been remodeled into an AP whose parameters are fixed/crisp valued and solved by linear programming method and/or Hungarian method [4].…”