Method for Aggregating Triangular Fuzzy Intuitionistic Fuzzy Information and Its Application to Decision Making / Numanomų Neapibrėžtųjų Aibių Teorija Ir Jos Taikymas Priimant Sprendimus

Abstract

Abstract. On the foundation of the theory of the intuitionistic fuzzy set, this paper uses the triangular fuzzy number to denote the membership degree and the non-membership degree and proposes the triangular intuitionistic fuzzy number. Then the operation rules of triangular intuitionistic fuzzy numbers are defined. The weighted arithmetic averaging operator and the weighted geometric average operator are presented and used to the decision making area after defined the score function and the accuracy function. An effective solution is offered for multi-attitude decision-making problem and an active try is made.

Special Issue “Intuitionistic Fuzzy Theory and Its Application in Economy, Technology and Management”

“…Because of the complexity of objective things, the fuzziness of human thinking, as well as the limits of decision time, cost and the decision-maker's knowledge, there are still many limitations to express the decision information in the form of intuitionistic fuzzy sets. On the one hand, sometimes, it is difficult for people to express membership degree and non-membership degree by real numbers, so, there are a lot of researches about the extensions of intuitionistic fuzzy sets, for example, the membership degree and non-membership degree are extended to interval numbers (Atanassov, Gargov 1989), triangular fuzzy numbers (Zhang, Liu 2010), fuzzy numbers (Wang, Zhang 2009) and linguistic variables (Chen et al 2015). Obviously, these extensions have improved the ability of intuitionistic fuzzy sets to express uncertain information.…”

Choquet Integrals of Weighted Triangular Fuzzy Linguistic Information and Their Applications to Multiple Attribute Decision Making

“…Multiple attribute decision making (MADM) refers to making choice of the best alternative from among a finite set of decision alternatives in terms of multiple usually conflicting attributes (or called criteria) (Liu 2009a(Liu , 2009bZhang, Liu 2010a, 2010bLiu, Su 2010;Liu, Zhang 2010Liu et al 2011aLiu et al , 2011bLiu, Wang 2011;Merigó, Gil-Lafuente 2009Merigó, Casanovas 2009Merigó 2010;Tan, Chen 2010;Wang 2009aWang , 2009bWang , 2010Wei 2008Wei , 2009aWei -b, 2010aWei et al 2010aWei et al , 2010bXu 2004aXu -c, 2005aXu -c, 2006aXu -d, 2007aXu -c, 2009bYe 2009aYe , 2009b. However, under many conditions, for the real multiple attribute decision making problems, the decision information about alternatives is usually uncertain or fuzzy due to the increasing complexity of the socio-economic environment and the vagueness of inherent subjective nature of human think, thus, numerical values are inadequate or insufficient to model real-life decision problems.…”

A Method for Multi-attribute Group Decision Making with Triangular Intuitionistic Fuzzy Numbers and Application to Trustworthy Service Selection

“…Zhang and Liu [21] de ned the concepts of TIFN in which the membership and the non-membership degrees are denoted by triangular fuzzy number. Then, the weighted geometric averaging operator and the weighted arithmetic average operator are presented and used for the decision-making area.…”

“…A number of achievements on TIFNs have been proposed. Roughly, these achievements may be divided into two types: ranking methods of TIFNs and their applications to decision making problems [13][14][15][16][17][18][19][20][21] and aggregation operators of TIFNs and their applications to decision making problems [22][23][24][25][26][27], which are brie y reviewed in the following, respectively.…”