%0 Journal Article
%T MADM Problems with Correlation Coefficient of Trapezoidal Fuzzy Intuitionistic Fuzzy Sets
%A John Robinson
%A Henry Amirtharaj
%J Advances in Decision Sciences
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/159126
%X This paper discusses on the notion of trapezoidal fuzzy intuitionistic fuzzy sets (TzFIFSs) and some of the arithmetic operations of the same. Correlation coefficient of TzFIFS is proposed based on the membership, nonmembership, and hesitation degrees. The weighted averaging (WA) operator and the weighted geometric (WG) operator are proposed for TzFIFSs. Based on these operators and the correlation coefficient defined for the TzFIFS, new multiattribute decision making (MADM) models are proposed and numerical illustration is given. 1. Introduction Intuitionistic fuzzy sets (IFSs) proposed by Atanassov [1¨C3] are a generalization of the concept of fuzzy sets. Atanassov and Gargov [4] expanded the IFSs, using interval value to express membership and nonmembership function of IFSs. Liu and Yuan [5] introduced the concept of fuzzy number IFSs as a further generalization of IFSs. Among the works done in IFSs, Szmidt and Kacprzyk [6¨C8] can be mentioned. To the best of our knowledge, Burillo et al. [9] proposed the definition of intuitionistic fuzzy number (IFN) and studied the perturbations of IFN and the first properties of the correlation between these numbers. Many researchers have applied the IFS theory to the field of decision making. Recently some researches [5, 10¨C14] showed great interest in the fuzzy number IFSs and applied it to the field of decision making. Based on the arithmetic aggregation operators, Xu and Yager [15], Xu and Chen [16, 17], and Wang [13] developed some new geometric aggregation operators and intuitionistic fuzzy ordered weighted averaging (IFOWA) operator. Szmidt and Kacprzyk [7] proposed some solution concepts in group decision making with intuitionistic (individual and social) fuzzy preference relations. Szmidt and Kacprzyk [8] investigated the consensus-reaching process in group decision making based on individual intuitionistic fuzzy preference relations. Herrera et al. [18] developed an aggregation process for combining numerical, interval valued, and linguistic information and then proposed different extensions of this process to deal with contexts in which information such as IFSs or multigranular linguistic information can appear. Xu and Yager [15] developed some geometric aggregation operators for MADM problems. Li [19] investigated MADM problems with intuitionistic fuzzy information and constructed several linear programming models to generate optimal weights for attributes. Multiattribute decision making (MADM) problems are of importance in most kinds of fields such as engineering, economics, and management. It is
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