Abstract
Hesitant fuzzy linguistic (HFL) term set, as a very flexible tool to represent the judgments of decision makers, has attracted the attention of many researchers. In recent years, some HFL aggregation operators have been developed to aggregate the HFL information. However, most of these operators are proposed based on the Algebraic product and Algebraic sum. In this paper, we presented some HFL aggregation operators to handle HFL information based on Hamacher triangle norms. We first define new operational laws on the HFL element according to Hamacher triangle norms. Then we present a family of HFL Hamacher aggregation operators, including the HFL Hamacher weighted averaging, HFL Hamacher weighted geometric, HFL Hamacher power weighted averaging and HFL Hamacher power weighted geometric operators and their generalized forms. We also investigate some special cases and properties of these operators in detail. Furthermore, we develop two approaches based on the proposed operators to deal with the multi-criteria decision-making problem with HFL information. Finally, a numerical example with regard to choosing a suitable city to release sharing car is provided to illustrate the feasibility of the proposed method, and the advantages of the proposed methods are shown by conducting a sensitivity and comparative analysis.
Highlights
Multi-criteria decision-making (MCDM) problems with different kinds of fuzzy information is handled by utilizing Zadeh’s fuzzy set [1] and their various extensions, including the interval-valued fuzzy set [2], intuitionistic fuzzy set [3,4], Pythagorean fuzzy set [5,6], Type-2 fuzzy set [7,8], fuzzy multi set [9], and hesitant fuzzy set (HFS) [10,11]
We present a hesitant fuzzy linguistic Hamacher weighted averaging (HFLHWA) and a hesitant fuzzy linguistic Hamacher weighted geometric (HFLHWG), a generalized hesitant fuzzy linguistic Hamacher weighted averaging (GHFLHWA) and a generalized hesitant fuzzy linguistic
Based on the above analyses, we can see that the best city and the ranking order of alternatives obtained by the HFLWA and HFL weighted geometric (HFLWG) operators are the same for Methods 1 and 2, which illustrate the validity of Methods 1 and 2
Summary
Multi-criteria decision-making (MCDM) problems with different kinds of fuzzy information is handled by utilizing Zadeh’s fuzzy set [1] and their various extensions, including the interval-valued fuzzy set [2], intuitionistic fuzzy set [3,4], Pythagorean fuzzy set [5,6], Type-2 fuzzy set [7,8], fuzzy multi set [9], and hesitant fuzzy set (HFS) [10,11]. Liu et al [28] developed the HFLWA, HFLWG, and HFL harmonic operators and their order weighted and hybrid weighted forms; (4) Based on the equivalent transformation function between HFLE and hesitant fuzzy element (HFE), Zhang and Qi [29] presented the HFLWA and HFLWG operators, and applied to solve a production strategy decision-making problem; Gou et al [30] introduced the Bonferroni mean operator into the HFLTS environment and defined the HFL Bonferroni mean and HFL weighted Bonferroni mean operators. According to the analysis above, this paper extends the Hamacher t-norm and t-conorm to an HFL environment and presents several new HFL aggregation operators to handle MCDM problem with.
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