Decision-making algorithm based on Pythagorean fuzzy environment with probabilistic hesitant fuzzy set and Choquet integral

Misbah Rasheed; ElSayed Tag-Eldin; Nivin A. Ghamry; Muntazim Abbas Hashmi; Muhammad Kamran; Umber Rana; Misbah Rasheed; ElSayed Tag-Eldin; Nivin A. Ghamry; Muntazim Abbas Hashmi; Muhammad Kamran; Umber Rana

doi:10.3934/math.2023624

AIMS Mathematics

2023, Volume 8, Issue 5: 12422-12455. doi: 10.3934/math.2023624

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Decision-making algorithm based on Pythagorean fuzzy environment with probabilistic hesitant fuzzy set and Choquet integral

1.
Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan
2.
Future University in Egypt New Cairo 11835, Egypt
3.
Cairo university, Faculty of Computers and Artificial intelligence, Giza, Egypt
4.
Department of Mathematics, Thal university Bhakkar, 30000, Punjab, Pakistan

Received: 12 January 2023 Revised: 11 February 2023 Accepted: 23 February 2023 Published: 24 March 2023
MSC : 03B52, 03E72

The Pythagorean Probabilistic Hesitant Fuzzy (PyPHF) Environment is an amalgamation of the Pythagorean fuzzy set and the probabilistic hesitant fuzzy set that is intended for some unsatisfactory, ambiguous, and conflicting situations where each element has a few different values created by the reality of the situation membership hesitant function and the falsity membership hesitant function with probability. The decision-maker can efficiently gather and analyze the information with the use of a strategic decision-making technique. In contrast, ambiguity will be a major factor in our daily lives while gathering information. We describe a decision-making technique in the PyPHF environment to deal with such data uncertainty. The fundamental operating principles for PyPHF information under Choquet Integral were initially established in this study. Then, we put up a set of new aggregation operator names, including Pythagorean probabilistic hesitant fuzzy Choquet integral average and Pythagorean probabilistic hesitant fuzzy Choquet integral geometric aggregation operators. Finally, we explore a multi-attribute decision-making (MADM) algorithm based on the suggested operators to address the issues in the PyPHF environment. To demonstrate the work and contrast the findings with those of previous studies, a numerical example is provided. Additionally, the paper provides sensitivity analysis and the benefits of the stated method to support and reinforce the research.
- Pythagorean fuzzy information,
- aggregation operators,
- decision-making
Citation: Misbah Rasheed, ElSayed Tag-Eldin, Nivin A. Ghamry, Muntazim Abbas Hashmi, Muhammad Kamran, Umber Rana. Decision-making algorithm based on Pythagorean fuzzy environment with probabilistic hesitant fuzzy set and Choquet integral[J]. AIMS Mathematics, 2023, 8(5): 12422-12455. doi: 10.3934/math.2023624

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Abstract

The Pythagorean Probabilistic Hesitant Fuzzy (PyPHF) Environment is an amalgamation of the Pythagorean fuzzy set and the probabilistic hesitant fuzzy set that is intended for some unsatisfactory, ambiguous, and conflicting situations where each element has a few different values created by the reality of the situation membership hesitant function and the falsity membership hesitant function with probability. The decision-maker can efficiently gather and analyze the information with the use of a strategic decision-making technique. In contrast, ambiguity will be a major factor in our daily lives while gathering information. We describe a decision-making technique in the PyPHF environment to deal with such data uncertainty. The fundamental operating principles for PyPHF information under Choquet Integral were initially established in this study. Then, we put up a set of new aggregation operator names, including Pythagorean probabilistic hesitant fuzzy Choquet integral average and Pythagorean probabilistic hesitant fuzzy Choquet integral geometric aggregation operators. Finally, we explore a multi-attribute decision-making (MADM) algorithm based on the suggested operators to address the issues in the PyPHF environment. To demonstrate the work and contrast the findings with those of previous studies, a numerical example is provided. Additionally, the paper provides sensitivity analysis and the benefits of the stated method to support and reinforce the research.

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