Abstract
AbstractTriangular intuitionistic fuzzy numbers (TIFNs) are a special kind of intuitionistic fuzzy sets (IFSs) on a real number set. TIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. The purpose of this paper is on developing a new ranking method of TIFNs and application to multiattribute group decision making (MAGDM) problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete. The weighted average operator of TIFNs is defined, the concepts of the possibility mean, variance of TIFNs as well as standard deviation are introduced. Hereby two new ranking indices considering the risk attitude of decision maker are developed to rank TIFNs. In the proposed group decision method, the collective overall attribute values of alternatives are obtained by using the weighted average operator of TIFNs We construct the multi-objective programming of maximizing the ranking indices of membership and non-mem...
Highlights
The intuitionistic fuzzy set (IFS) introduced by Atanassov[1] is a generalization of the fuzzy set (FS) (Zadeh[2])
Wan et al.[20] defined the weighted possibility means of Triangular intuitionistic fuzzy numbers (TIFNs) and proposed the extended VIKOR method to multi-attribute group decision making (MAGDM) with TIFNs
Hereby, considering the risk attitude of decision makers (DMs), we develop a new lexicographic ranking method for TIFNs, which can be summarized as follows: If RP (a1, O) RP (a2, O), a1 is smaller than a2, denoted by a1 a2 ; If RP (a1, O) ! RP (a2, O), a1 is bigger than a2, denoted by a1 ! a2 ; If RP (a1, O) RP (a2, O), (i) If RQ (a1, O) RQ (a2, O), a1 a2 ; (ii) If RQ (a1, O) RQ (a2, O), a1 and a2 represent the same information, denoted by a1 a2 ; (iii) If RQ (a1, O) ! RQ (a2, O), a1 ! a2
Summary
The intuitionistic fuzzy set (IFS) introduced by Atanassov[1] is a generalization of the fuzzy set (FS) (Zadeh[2]). Possibility method for triangular intuitionistic fuzzy multi-attribute group decision making standard deviation and applied to MADM with TIFNs. Wan et al.[20] defined the weighted possibility means of TIFNs and proposed the extended VIKOR method to MAGDM with TIFNs. the existing ranking methods of TIFNs (Li7; Li et al.[8]; Nan et al.[9]; Wan and Li19) ignored the risk attitudes of decision makers (DMs). We briefly review the definition, operation laws of TIFNs and define the weighted average operator of TIFNs
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