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Cubic Bipolar Fuzzy-VIKOR Method Using New Distance and Entropy Measures and Einstein Averaging Aggregation Operators with Application to Renewable Energy

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Abstract

A cubic bipolar fuzzy set (CBFS) is a robust model which has the ability to simultaneously deal with bipolarity and vagueness by taking into account both interval-valued bipolar fuzzy sets (IVBFSs) and bipolar fuzzy sets (BFSs). Motivated by this innovative model, in the present article, some novel distance and entropy measures for CBFSs are proposed. Some operations on cubic bipolar fuzzy numbers (CBFNs) are also presented under P(R)-order by utilizing Einstein t-norm and t-conorm. For information fusion of CBFNs, several novel averaging aggregation operators are introduced based on Einstein operations named as P(R)-order cubic bipolar fuzzy (CBF) Einstein weighted averaging operator (P(R)-CBFEWAO), P(R)-order CBF Einstein ordered weighted averaging operator (P(R)-CBFEOWAO), and P(R)-order CBF Einstein hybrid weighted averaging operator (P(R)-CBFEHWAO). A new hybrid technique with Einstein averaging aggregation operators and CBF-VIKOR method is developed for multi-attribute group decision-making (MAGDM). A practical application of the suggested MAGDM technique towards the best renewable energy resource selection is presented. The applicability and feasibility of the newly proposed technique is analyzed by a comparative analysis of suggested technique with the already existing techniques.

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments in improving the presentation of this paper. This work was supported in part by the Ministry of Science and Technology, Taiwan, under Grant MOST 110-2118-M-033-003.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Lahore, 54590, Pakistan

    Muhammad Riaz & Anam Habib

  2. School of Mathematics, Northwest University, Xi’an, 710127, China

    Muhammad Saqlain

  3. Department of Mathematics, Lahore Garrison University, Lahore, 54000, Pakistan

    Muhammad Saqlain

  4. Department of Applied Mathematics, Chung Yuan Christian University, Taoyuan, 32023, Taiwan

    Miin-Shen Yang

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  1. Muhammad Riaz
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Correspondence to Miin-Shen Yang.

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Riaz, M., Habib, A., Saqlain, M. et al. Cubic Bipolar Fuzzy-VIKOR Method Using New Distance and Entropy Measures and Einstein Averaging Aggregation Operators with Application to Renewable Energy. Int. J. Fuzzy Syst. 25, 510–543 (2023). https://doi.org/10.1007/s40815-022-01383-z

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