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

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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.

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Abbreviations

H :

Hesitant fuzzy set (HFS)

h :

Hesitant fuzzy element (HFE)

\(\hbar \) :

The element of h

\({{}^\wp {H}}\) :

Probabilistic hesitant fuzzy set (PHFS)

\({}^\wp {h}\) :

Probabilistic hesitant fuzzy element (PHFE)

\(\langle {\hbar }(x) ,\wp (x)\rangle \) :

The element of \({}^\wp {h}\)

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Authors and Affiliations

  1. Department of Mathematics, Quchan University of Technology, Quchan, Iran

    Bahram Farhadinia

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  1. Bahram Farhadinia
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Correspondence to Bahram Farhadinia.

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Farhadinia, B. An innovative unification process for probabilistic hesitant fuzzy elements and its application to decision making. Fuzzy Optim Decis Making 21, 335–382 (2022). https://doi.org/10.1007/s10700-021-09369-6

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