Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making

A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets

“…Assume that the characteristics for alternatives A i are presented by the IVHFS as follows: (22) where h A i (x j ) indicates the degree that the alternative A i satisfies the attribute x j . This also means that, if the decision makers provide several intervalvalued values for the alternative A i under the attribute x j on condition of anonymity, these values can be considered as an interval-valued hesitant fuzzy element h A i (x j ).…”

“…Quiros 16 studied entropy measures under interval-valued hesitant fuzzy environment and built the entropy measure using three different measures: fuzziness, lack of knowledge and hesitance. Wei 22 proposed a variety of distance measures for IVHFSs, based on which the corresponding similarity measures are derived, and some properties of these distance measures and similarity measures were investigated, but the general definition of distance measures and similarity measure are not given like the notions of fuzzy sets. Farhadini 9 gave the axiom definition of distance measures of HFSs and IVHFSs, and all distance must be in [0,1], however, there are many distance measures beyond [0,1].…”

“…So we modify the axiom definitions of distance and similarity measures for IVHFSs and propose some new distance and similarity measures between IVHFSs, the new distance measures are more reasonable since they are very similar with the existing ones except for some minor modification of the expression. Wei 22 introduced a generalized interval-valued hesitant Hamming-Hausdorff distance which is a generalization of interval-valued hesitant normal Hamming-Hausdorff distance, we will introduce new distance measure whose limit is the interval-valued hesitant normal HammingHausdorff distance from the point of view of L p metric. They are another new reasonable distance measures from different point of view and the main advantages of the new distance measures is that they do not need to be normalized and more reasonable since they are very similar with the existing ones except for some minor modification of the expression.…”

A note on operations of hesitant fuzzy sets

“…Copyright: the authorslems based on hesitant fuzzy sets, many hesitant fuzzy distance measures and aggregation operators have been proposed, such as the entropy of hesitant fuzzy sets and interval-valued hesitant fuzzy sets [6], generalized hesitant fuzzy synergetic weighted distance measure [14] and hesitant normalized Hamming, hesitant normalized Hausdorff distance and their generalizations [25]; interval-valued hesitant fuzzy aggregation operators [4], operations of generalized hesitant fuzzy sets according to score function and consistency function [15], hesitant fuzzy prioritized operators and hesitant interval-valued fuzzy aggregation operators [21,22], hesitant fuzzy ordered weighted averaging operator, hesitant fuzzy ordered weighted geometric operator and their generalization operators [24], TOPSIS and the maximizing deviation method with hesitant fuzzy information [26], the generalized hesitant fuzzy prioritized weighted average and generalized hesitant fuzzy prioritized weighted geometric operators [28], E-VIKOR method with hesitant fuzzy information for the multiple criteria decision making [31], hesitant fuzzy power aggregation operators [32], and hesitant fuzzy geometric Bonferroni means [33], etc. To deal with linguistic group decision making in hesitant situations, hesitant fuzzy linguistic term sets and corresponding with hesitant fuzzy linguistic aggregation have been proposed in [8-10, 16, 17, 23, 34].…”

A TOPSIS method based on intuitionistic fuzzy values: a case study of North African airports

“…IFS treats vague information by considering membership function and non-membership function and this can minimize the imprecision degree in complex systems. Intuitionistic fuzzy TOPSIS has been applied in some studies (Boran et al, 2009;Xu, 2007;Tan & Chen, 2010;Wei et al, 2013;Aloini et al, 2014;Zhang & Yu, 2012;Joshi & Kumar, 2014).…”