Abstract
All the existing probabilistic hesitant fuzzy element (P-HFE) comparison techniques are directly based on the possible membership degree of an element together with its probability of occurring. Here, we are going to propose a class of P-HFE comparison techniques which are indirectly based on the ingredients of a P-HFE. Indeed, the proposed P-HFE comparison techniques are mainly related to the multiplying and exponential deformation formulas of each pair of possible membership degree and its associated probability. The proposed P-HFE comparison techniques are classified into three categories: (i) the element-based processes for comparing P-HFEs, (ii) the step-based processes for comparing P-HFEs, and (iii) the step-based processes for comparing P-HFEs. These indirect P-HFE comparison techniques provide us with more insights into the ways to increase the applicability of the P-HFE comparison algorithms, and enable us to deal with the comparison step in multiple criteria decision making problems from a different viewpoint.
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Farhadinia, B., Xu, Z. Developing the comparison techniques of probabilistic hesitant fuzzy elements in multiple criteria decision making. Soft Comput 25, 331–342 (2021). https://doi.org/10.1007/s00500-020-05144-8
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DOI: https://doi.org/10.1007/s00500-020-05144-8