Abstract
Linguistic aggregation operator is a paramount appliance to fix linguistic multiple attribute decision-making (MADM) issues. In the article, the Hamy mean (HM) operator is utilized to fuse hesitant fuzzy linguistic (HFL) information and several novel HFL aggregation operators including the hesitant fuzzy linguistic Hamy mean (HFLHM) operator, weighted hesitant fuzzy linguistic Hamy mean (WHFLHM) operator, hesitant fuzzy linguistic dual Hamy mean (HFLDHM) operator, and weighted hesitant fuzzy linguistic dual Hamy mean (WHFLDHM) operator are proposed. Besides, several paramount theorems and particular cases of these aggregation operators are investigated in detail, and then a novel MADM approach is presented by using the proposed aggregation operators. Ultimately, a practical example is utilized to manifest the effectiveness and practicability of the propounded method.
Highlights
Introduction e essence ofmultiple attribute decision-making (MADM) is the process of sorting a limited number of alternatives under given attributes and selecting the optimal one through the evaluation information provided by experts
By taking into account the merits of the linguistic term set and the Hamy mean (HM) operator, we extend the HM operator to hesitant fuzzy linguistic (HFL) setting to present several HFL aggregation operators for dealing with MADM problems effectively
We present the hesitant fuzzy linguistic Hamy mean (HFLHM) operator, HFLWHM operator, hesitant fuzzy linguistic dual Hamy mean (HFLDHM) operator, and HFLWDHM operator
Summary
We will retrospect several related fundamental definitions including HFS, LTS, HFLS, HM operator, and DHM operator. Where hA(x) is a collection of several possible values in [0, 1] which indicate the possible membership degree that x ∈ X belongs to the linguistic term set sθ(x), and θ(x) ∈ [0, t]. HFLS synthesizes the merits of LTS and HFS, which makes the views expressed by decision makers belong to the corresponding linguistic term. LTS is more in line with the evaluation thinking of individuals, and HFE can allow multiple decision makers to give their own possible value to an alternative. The HFLE can express evaluation information by a linguistic term. Four decision makers give their evaluation value based on the linguistic term (s5) “good” {0.2, 0.3, 0.4, 0.6}, and the evaluation information by the form of HFLE can be indicated as 〈s5, {0.2, 0.3, 0.4, 0.6}〉. In order to compare HFLEs, Lin et al [39] gave the ranking method as follows
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