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With regard to element uncertainty in a hesitant fuzzy element (HFE), the probabilistic hesitant fuzzy element (PHFE) was developed.
A fuzzy element has a degree of membership or compatibility with the set and its negation.
This definition was extended and formalized with the concept of hesitant fuzzy element (HFE) by Xia and Xu [40].
Conversion of the crisp indicator into a fuzzy element using fuzzification method to obtain the membership values of each linguistic quantifier.
To calculate each non-diagonal fuzzy element (e.g., x ˜ 13 ), the dominance of one alternative or criterion over another is determined by the division of two TFNs.
Therefore, in this study, we propose the uncertain probabilistic hesitant fuzzy element (UPHFE), a generalized fuzzy number, which includes four types of HFEs.
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There can be warm, fuzzy elements amid the concrete and scrap metal.
In this paper, inconsistency of pair-wise comparison matrix with fuzzy elements is investigated.
Firstly, we take into account the loss functions of DTRSs with dual hesitant fuzzy elements (DHFEs) and propose a dual hesitant fuzzy DTRS model.
Towards this end, the impact matrix is used (criteria/alternatives matrix), incorporating scores that can take the following forms: crisp numbers, stochastic elements, fuzzy elements and linguistic elements (such as 'good', 'moderate' etc).
Concretely speaking, this paper considers that the membership degree and the non-membership degree of PFSs are expressed as hesitant fuzzy elements.
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