Interval-Valued Intuitionistic Fuzzy Information Aggregation

Abstract

In many real-world decision problems the values of the membership function and the non-membership function in an IFS are difficult to be expressed as exact numbers. Instead, the ranges of their values can usually be specified. In such cases, Atanassov and Gargov (1989) generalized the concept of IFS to interval-valued intuitionistic fuzzy set (IVIFS), and define some basic operational laws of IVIFSs. Xu (2007h) defined the concept of interval-valued intuitionistic fuzzy number (IVIFN), and gave some basic operational laws of IVIFNs. He put forward an interval-valued intuitionistic fuzzy weighted averaging operator and an interval-valued intuitionistic fuzzy weighted geometric operator, and defines the score function and the accuracy function of IVIFNs. He further presents a simple ranking method for IVIFNs, based on which an approach is proposed for multi-attribute decision making with intuitionistic fuzzy information. Xu and Chen (2007a) define an interval-valued intuitionistic fuzzy ordered weighted averaging operator and an interval-valued intuitionistic fuzzy hybrid averaging operator. Xu and Chen (2007c) investigate an interval-valued intuitionistic fuzzy ordered weighted geometric operator and an interval-valued intuitionistic fuzzy hybrid geometric operator. Xu and Yager (2011) extended the IFBMs to accommodate interva-valued intuitionistic fuzzy environments. Zhao et al. (2010) developed a series of generalized aggregation operators for IVIFNs. Xu (2010c) used Choquet integral to propose some operators for aggregating IVIFNs together with their correlative weights. All these aggregation techniques for interval-valued intuitionistic fuzzy information are generalizations of the intuitionistic fuzzy aggregation techniques introduced in Chapter 1.