Abstract
As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.
Highlights
Since the fuzzy set (FS) was introduced by Zadeh [1], it has received much attention for its applicability
By means of Hamacher operations on hesitant fuzzy element (HFE), we propose a family of hesitant fuzzy Hamacher power-aggregation operators that allow decision-makers to have more choices in multiple-attribute decision-making (MADM) problems
1 − ∏ 1 − γσλ(i) where ui (i = 1, 2, . . . , n) is a collection of weights satisfying the condition (29), and if ζ = 2, the GHFHPOWA operator reduces to the generalized hesitant fuzzy Einstein power-ordered weighted average (GHFEPOWA) operator [18]: GHFHPOWA2 (h1, h2, . . . , hn )
Summary
Since the fuzzy set (FS) was introduced by Zadeh [1], it has received much attention for its applicability. Compared to most aggregation operators, the PA and POWA operators have the advantage of incorporating information about the relationship between argument values that are combined These operators have received a lot of attention from researchers in recent years, Xu and Yager [25], Zhou et al [26] and Zhang [15] introduced some new power-aggregation operators, including the weighted generalizations of these operators. By means of Hamacher operations on HFEs, we propose a family of hesitant fuzzy Hamacher power-aggregation operators that allow decision-makers to have more choices in MADM problems.
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