Some Generalized Dependent Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and Their Application to Exploitation Investment Evaluation

Abstract

We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees of arguments indirectly and directly, based on which the Gaussian generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator (Gaussian-GIIFOWA) and geometric operator (Gaussian-GIIFOWG), the power generalized interval-valued intuitionistic fuzzy ordered weighted averaging (P-GIIFOWA) operator and geometric (P-GIIFOWA) operator are proposed to generalize a wide range of aggregation operators for decision makers to flexibly choose in decision modelling. And some desirable properties of the proposed operators are also analyzed. Further, application of an approach integrating proposed operators to exploitation investment evaluation of tourist spots has shown the effectiveness and practicality of developed methods; experimental results also verify the properties of proposed operators.

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

“…Additionally, based on these aggregation operators discussed above, Qi et al (2013) introduced some other generalized interval-valued intuitionistic fuzzy aggregation operators:…”

“…Definition 3.13 (Qi et al 2013) Let l be the mean value of given interval-valued intuitionistic fuzzy arguments, n be the variance of given IVIFNs, then the Gaussian weighting vector x ¼ x 1 ; x 2 ; . .…”

“…Definition 3.14 (Qi et al 2013) A Gaussian-GIVIFOWA operator of dimension n is a mapping Gaussian-GIVI-FOWA: X n ! X, which has an associated Gaussian weighting vector x ¼ x 1 ; x 2 ; .…”

“…Thus, the Gaussian-GIVI-FOWA and Gaussian-GIVIFOWG operators are neat and dependent operators. Afterwards, Qi et al (2013) defined a power generalized interval-valued intuitionistic fuzzy ordered weighted averaging (P-GIVIFOWA) operator and a power generalized interval-valued intuitionistic fuzzy ordered weighted geometric (P-GIVIFOWG) operator. Firstly, a hybrid support function can be defined as:…”

“…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;…”