Generalized aggregation operators for intuitionistic fuzzy sets

Abstract

The generalized ordered weighted averaging (GOWA) operators are a new class of operators, which were introduced by Yager (Fuzzy Optim Decision Making 2004;3:93-107). However, it seems that there is no investigation on these aggregation operators to deal with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. In this paper, we first develop some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval-valued intuitionistic fuzzy weighted averaging operator, generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator, generalized interval-valued intuitionistic fuzzy hybrid average operator, which extend the GOWA operators to accommodate the environment in which the given arguments are both intuitionistic fuzzy sets that are characterized by a membership function and a nonmembership function, and interval-valued intuitionistic fuzzy sets, whose fundamental characteristic is that the values of its membership function and nonmembership function are intervals rather than exact numbers, and study their properties. Then, we apply them to multiple attribute decision making with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. C 2009 Wiley Periodicals, Inc.

An overview of interval-valued intuitionistic fuzzy information aggregations and applications

“…The advantage of the generalized operators is that it can consider all situations by changing the value of the variable k. Zhao et al (2010) developed a series of generalized aggregation operators for IVIFNs:…”

“…To overcome this limitation, Zhao et al (2010) introduced a generalized interval-valued intuitionistic fuzzy hybrid aggregation (GIVIFHA) operator: Definition 3.10 (Zhao et al 2010) A GIVIFHA operator of dimension n is a mapping GIVIFHA:h n !h, which has an associated vector x ¼ x 1 ; x 2 ; . .…”

“…Later, Chen et al (2012) proposed a new method for MCDM, which can overcome the drawback of Ye's method. Motivated by these basic operators and generalized forms, lots of operators have been developed and applied to different situations: Zhao et al (2010) developed the GIVIFWA and GIVIFHA operators and applied them to MADM with interval-valued intuitionistic fuzzy information. Moreover, Qi et al (2013) proposed the Gaussian-GIVIFOWA, the Gaussian-GIVI-FOWG, the P-GIVIFOWA and the P-GIVIFOWG operators.…”

“…Then, amounts of aggregation operators (Xu 2007b(Xu , c, 2010Chen 2007b, 2011;Shi and He 2013;Zhao et al 2010;Qi et al 2013;Xu and Yager 2009;Dong and Wan 2015;Liu et al 2015;Meng et al 2013aMeng et al , b, 2014Meng et al , 2015Yu 2013Yu , 2014He et al 2013;Xu and Xia 2011;Zhang and Qi 2012;Wei and Yi 2008;Li 2014;Wang and Liu 2013;Chen et al 2012;Wan and Dong 2014;Yager 2004;Zhou et al 2014;Yang and Yuan 2014;Gu et al 2014) have been proposed for dealing with the decision-making problems with interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operator (Xu 2007b), the interval-valued intuitionistic fuzzy weighted geometric (IVIFWG) operator (Xu 2007b), the interval-valued intuitionistic fuzzy ordered weighted averaging (IVIFOWA) operator (Xu and Chen 2007b), the generalized interval-valued intuitionistic fuzzy weighted averaging (GIVIFWA) operator (Zhao et al 2010), the induced generalized interval-valued intuitionistic fuzzy Choquet ordered averaging (I-GIVIFCOA) operator (Xu and Xia 2011), and the interval-valued intuitionistic fuzzy interactive weighted average (IVIFIWA) operator (Yu 2014), etc. In fact, all of these aggregation operations can be considered as granules in granular computing (GrC) (Pedrycz and Chen 2015;Peters and Weber 2016;Livi and Sadeghian 2016;…”

Interval-Valued Intuitionistic Fuzzy Einstein Geometric Choquet Integral Operator and Its Application to Multiattribute Group Decision-Making

“…Based on the algebraic operational laws on the IVIFS, Yu [7] defined the generalized interval-valued intuitionistic fuzzy weighted averaging operator and the generalized interval-valued intuitionistic fuzzy weighted geometric operator. Zhao et al [8] proposed the generalized intervalvalued intuitionistic fuzzy ordered weighted averaging operator and the generalized interval-valued intuitionistic fuzzy hybrid averaging operator. Lin and Zhang [9] proposed some interval-valued intuitionistic fuzzy continuous operators.…”