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Ranking methodology of induced Pythagorean trapezoidal fuzzy aggregation operators based on Einstein operations in group decision making

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Abstract

The Pythagorean fuzzy number is a new tool for uncertainty and vagueness. It is a generalization of fuzzy numbers and intuitionistic fuzzy numbers. In this paper, we define some Einstein operations on Pythagorean trapezoidal fuzzy set and develop two averaging aggregation operators, which is an induced Pythagorean trapezoidal fuzzy Einstein ordered weighted averaging operator and an induced Pythagorean trapezoidal fuzzy Einstein hybrid averaging (I-PTFEHA) operator. We presented some new methods to deal with the multi-attribute group decision-making problems under the Pythagorean trapezoidal fuzzy environment. Finally, we used some practical examples to illustrate the validity and feasibility of the proposed methods by comparing with existing method. It shows that the proposed I-PTFEHA operator is much better and reliable than the existing one.

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Acknowledgements

Saleem Abdullah and Muhammad Aslam extended their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Research Group Program under grant number R-G.P. 1/76/40.

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Authors and Affiliations

  1. Department of Mathematics, Hazara University Mansehra, Dhodial, KPK, Pakistan

    Muhammad Shakeel

  2. Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan

    Saleem Abdullah

  3. Department of Mathematics, King Khalid University, Abha, Saudi Arabia

    Muhammad Aslam

  4. Department of Mathematics and Statistic, Riphah International University, Islamabad, Pakistan

    Muhammad Jamil

Authors
  1. Muhammad Shakeel
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  2. Saleem Abdullah
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  3. Muhammad Aslam
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  4. Muhammad Jamil
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Correspondence to Muhammad Shakeel.

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Shakeel, M., Abdullah, S., Aslam, M. et al. Ranking methodology of induced Pythagorean trapezoidal fuzzy aggregation operators based on Einstein operations in group decision making. Soft Comput 24, 7319–7334 (2020). https://doi.org/10.1007/s00500-019-04356-x

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