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An innovative unification process for probabilistic hesitant fuzzy elements and its application to decision making

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  • Bahram Farhadinia

    (Quchan University of Technology)

Abstract

The probabilistic hesitant fuzzy element (PHFE) is a worthwhile extension of hesitant fuzzy element (HFE) which is a means of allowing the decision makers more flexibility in expressing their preferences by the use of hesitant information in practical decision making process. To derive a more realistic expression of decision information, it is necessary to unify the arrangement of elements in PHFEs without imposing artificial elements. Up to now, several processes concerning the unification and arrangement of elements in PHFEs have been proposed, and while, most suffer from different drawbacks being critically discussed in the present study. The main aim of this study is to propose a PHFE unification process which does not have the shortcomings of existing processes, and does not change the inherent characteristic of PHFE probabilities. Based on the proposed unification process, the current study seeks to extend the theory of arithmetic operations on PHFEs by proposing and developing novel types of PHFS division and subtraction. Finally, the proposed PHFE unification process is applied to a number of multiple criteria decision-making (MCDM) problems for illustrating its vast range of applicability.

Suggested Citation

  • Bahram Farhadinia, 2022. "An innovative unification process for probabilistic hesitant fuzzy elements and its application to decision making," Fuzzy Optimization and Decision Making, Springer, vol. 21(3), pages 335-382, September.
    • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:3:d:10.1007_s10700-021-09369-6
    DOI: 10.1007/s10700-021-09369-6
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    References listed on IDEAS

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    1. Huchang Liao & Xiaomei Mi & Zeshui Xu, 2020. "A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 81-134, March.
    2. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
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