Interval-valued hesitant preference relations and their applications to group decision making

An Attitudinal DICE Distance Based IVHF-TODIM for Selecting Agricultural Sensors under IOT Environment

“…Definition 1 [6]: Let X be a reference set, and it is the set of all closed subintervals of [0,1]which can be represented as the following mathematical symbol:…”

“…In order to solve the ambiguity in the decision-making process, Zadeh [4](1965) proposed the fuzzy sets to deal with imprecise and vague information, it has been widely used in various fields. This theory has attracted the attention of many scholars, subsequently, many foreign scholars extended the fuzzy sets, proposing the intuitionistic fuzzy sets type-2 fuzzy sets and hesitant fuzzy sets [5], but the scholars find that in real life, due to insufficiency in available information, it may be difficult for the decision makers to exactly express their opinions with some crisp values or the others, but we can use some interval values within [0,1], it is easier and more reasonable, based on the continuous study of fuzzy sets, Xu [6] proposed the concept of interval-valued hesitant fuzzy sets on the basis of fuzzy sets which permit the membership degree of an element to a given set with several different interval values, adding flexibility to the decision maker's assignment, it can describe the uncertainty of the decision-maker more precisely, and is especially suitable for describing the realistic decision problem with hesitation. So we can use the IVHF sets to describe the attribute of the sensor.…”

Applications of finite interval-valued hesitant fuzzy preference relations in group decision making

“…The study of nitely generated sets, which were rstly considered by Chen et al [5] and de ned in detail by…”

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].…”