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Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

Bushra Batool (Department of Mathematics, University of Sargodha, Sargodha, Pakistan)
Saleem Abdullah (Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan)
Shahzaib Ashraf (Department of Mathematics and Statistics, Bacha Khan University, Charsadda, Pakistan)
Mumtaz Ahmad (Department of Mathematics, University of Sargodha, Sargodha, Pakistan)

Kybernetes

ISSN: 0368-492X

Article publication date: 15 June 2021

Issue publication date: 3 March 2022

279

Abstract

Purpose

This is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.

Design/methodology/approach

PyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.

Findings

In addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

Originality/value

Paper is original and not submitted elsewhere.

Keywords

Acknowledgements

This study work was supported by Higher Education Commission (HEC), Pakistan under National Research Program for University (NRPU), Project title: Fuzzy Mathematical Modeling for Decision Support Systems and Smart Grid Systems (No. 10701/KPK/NRPU/R and D/HEC/2017).

Citation

Batool, B., Abdullah, S., Ashraf, S. and Ahmad, M. (2022), "Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making", Kybernetes, Vol. 51 No. 4, pp. 1626-1652. https://doi.org/10.1108/K-11-2020-0747

Publisher

:

Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

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