An interval type-2 fuzzy clustering solution for large-scale multiple-criteria group decision-making problems

Abstract

In order to deal with the fuzzy large-scale multiple-criteria group decision-making (FLMCGDM) problems, this paper incorporates clustering analysis and information aggregation operator into the problems of large-scale multiple-criteria group decision-making with interval type-2 fuzzy sets (IT2 FSs). The interval type-2 fuzzy equivalence clustering (IT2-FEC) analysis is used to classify decision-makers (DMs) to reduce the dimension of the large-scale DMs in the FLMCGDM problems. The combined weighted geometric averaging (CWGA) operator is extended into the case with IT2 FSs variables, which can take both the importance of individual and its relative position into account. Afterwards, a solution process for the FLMCGDM problems is proposed, in which the new equivalence clustering method and CWGA operator of IT2 FSs is incorporated. Finally, the reasonability and effectiveness of the proposed method are verified by an illustrative example. Compared with other methods, the IT2-FEC analysis can deal with the linguistic variables and produce dynamic clustering results in a more efficient way.

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

“…They used both fuzzy memberships and possibilistic typicalities to model the uncertainty implied in the data sets, and develop solutions to overcome the difficulties caused by Type-2 fuzzy sets, such as the construction of footprint of uncertainty, type-reduction and defuzzification. Rhee and Hwang [252] Sanchez et al [264] Golsefid and Zarandi [113] Rhee and Hwang [253] Golsefid et al [114] Nguyen and Nahavandi [215] Hwang and Rhee [131] Pham et al [243] Rhee [251] Rubio et al [258] Hwang and Rhee [359] Rubio et al [259] Min et al [198] Wu and Liu [309] Ji et al [134] Yao et al [324] Linda and Manic [166] Comas et al [60] Rubio and Castillo [256] Rubio and Castillo [257] In particular, they defined the lower and upper interval fuzzy membership and possibilistic typicality using, respectively, fuzzifiers ( m 1 ,m 2 ) and ( p 1 , p 2 ). Then, they computed the interval of a primary fuzzy membership as [ u ik , u ik ] and the interval of a primary possibilistic typicality as [ t ik , t ik ] (see, [134] ).…”

“…Other recent interesting Type-2 fuzzy clustering methods have been suggested by Dang et al [83] , Rubio and Castillo [256] , Sanchez et al [264] , Golsefid and Zarandi [113] , Golsefid et al [114] , Nguyen and Nahavandi [215] , Pham et al [243] , Rubio et al [258,259] , Wu and Liu [309] , Yao et al [324] , Comas et al [60] , Rubio and Castillo [257] .…”

A survey of type-2 fuzzy aggregation and application for multiple criteria decision making

“…In addition, since an interval type-2 fuzzy sets (IT2FSs) have the apparent merit in information representation and comprehensibility, many scholars paid more attention to the theory and application of IT2FSs. The former mainly includes the type reduction method (Karnik and Mendel 2001;Liu and Mendel 2011), ranking method (Wu and Mendel 2007a;Chen 2012;Sang and Liu 2016), aggregation operators and other knowledge (Mendel and John 2002;Mendel et al 2006;Wu and Mendel 2007b), and the later mainly involves the multiple criteria decision making (MCDM) problems (Wu and Liu 2016;Kundu et al 2017;Qin et al 2017). Type-2 fuzzy aggregation operators, as a key technique, have been investigated by many scholars.…”

“…Other type-2 fuzzy aggregation operators were presented such as interval type-2-dependent ordered weighted averaging (IT2DOWA) operator and interval type-2 power averaging (IT2PA) operator (Ma et al 2016). Wu and Liu proposed interval type-2 fuzzy weighted geometric averaging (WGA) operator and interval type-2 fuzzy combined weighted geometric averaging (CWGA) operator (Wu and Liu 2016). Based on multi-granular linguistic environment, 2-dimension interval type-2 trapezoidal fuzzy ordered weighted average (2DIT2TFOWA) operator and quasi-2dimension interval type-2 trapezoidal fuzzy ordered weighted 3 1 1 1 1 2 1 1 1 3 5 1 4 2 6 5 3 4 4 8 4 0 1 2 3 4 5 6 7 8 9 1975 1987 1992 1997 1998 2001 2002 2003 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 Numbers of paper PublicaƟon year Fig.…”

“…Based on multi-granular linguistic environment, 2-dimension interval type-2 trapezoidal fuzzy ordered weighted average (2DIT2TFOWA) operator and quasi-2dimension interval type-2 trapezoidal fuzzy ordered weighted 3 1 1 1 1 2 1 1 1 3 5 1 4 2 6 5 3 4 4 8 4 0 1 2 3 4 5 6 7 8 9 1975 1987 1992 1997 1998 2001 2002 2003 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 Numbers of paper PublicaƟon year Fig. 1 Papers related to type-2 fuzzy sets Table 1 Type-2 fuzzy aggregation operators and corresponding references Type-2 fuzzy aggregation operators References Type-2 fuzzy LWA (Wu and Mendel 2007b;John et al 2018) Type-2 fuzzy OWA (Zhou et al 2008;Zhou et al 2010) Interval type-2 fuzzy arithmetic average (Lee and Chen 2008;Chen and Lee 2010) Trapezoidal interval type-2 fuzzy generalizing weighted average (Bustince et al 2013) IT2F weighted averaging (IT2FWA) operator (Andelkovic and Saletic 2012) TIT2FFWA and TIT2FFWG (Qin and Liu 2014) TIT2AA, TIT2OWA, TIT2HWA (Wang et al 2015) TIT2FGBM and IT2FWGBM (Gong et al 2015) Interval type-2 fuzzy WGA, Interval type-2 fuzzy CWGA, (Wu and Liu 2016) STIT2FHM and WSTIT2FHM (Qin 2017) IT2DOWA and IT2PA (Ma et al 2016) 2DIT2TFOWA, quasi-2DIT2TFOWA (Wu et al 2017) TIT2FWA, GTIT2FWA, TIT2FOWA, GTIT2FOWA, TIT2FHA, GTIT2FHA (Zhang 2018) type-2 fuzzy Choquet integral (Havens et al 2010) type-2 fuzzy Sugeno integral (Bustince et al 2013) average (quasi-2DIT2TFOWA) operator were developed (Wu et al 2017). To consider the interaction among all the aggregated information, Qin presented the interval type-2 fuzzy Hamy mean (HM) operators, i.e.…”