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Triangular norm‐based cuts and possibility characteristics of triangular intuitionistic fuzzy numbers for decision making
Author(s) -
Yi ZhiHong,
Li HongQuan
Publication year - 2018
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21974
Subject(s) - mathematics , vagueness , norm (philosophy) , standard deviation , ranking (information retrieval) , variance (accounting) , mathematical optimization , fuzzy number , weighted arithmetic mean , group decision making , fuzzy logic , fuzzy set , computer science , artificial intelligence , statistics , accounting , political science , law , business
Triangular intuitionistic fuzzy numbers (TIFNs) is one of the useful tools to manage the fuzziness and vagueness in expressing decision data and solving decision making problems. In this paper, triangular norm (t‐norm) based cuts of TIFNs are developed to synthesize the membership and nonmembership functions in describing the cut sets, then the possibility characteristics of TIFNs, i.e., the possibility mean, the possibility variance, and the possibility mean‐standard deviation ratio, are given. Thereby, on the ground of the possibility mean‐standard deviation ratio, a ranking method of TIFNs is introduced. With these elements, an approach to multiple attributes decision making (MADM) is proposed and illustrated by a numerical example. It is shown that the approach to MADM comprehensively considers both the membership and nonmembership functions and can lead to objective and reasonable results.