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Complex Cubic Fuzzy Einstein Averaging Aggregation Operators: Application to Decision-making Problems

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Abstract

Different complex fuzzy sets are reported in the literature as the generalizations of fuzzy sets. Complex cubic fuzzy sets are also among those complex fuzzy sets, extensions of cubic sets. The main task is using complex cubic fuzzy sets in decision-making problems, and we propose some aggregation operators. We introduce the concept of complex cubic fuzzy ordered and hybrid weighted averaging operators using Einstein’s sum, product, scalar, and exponential multiplication. We discuss some algebraic operations of complex cubic fuzzy sets (CCFS) and their structural properties. We develop three arithmetic averaging operators: complex cubic fuzzy Einstein weighted averaging (CCFEWA), complex cubic fuzzy Einstein ordered weighted averaging (CCFEOWA), and complex cubic fuzzy Einstein hybrid weighted averaging (CCFEHWA) operators. The CCFEHWA operator generalizes both the CCFEWA and CCFEOWA operators. We apply the CCFEHWA operator to multiple attribute decision-making with complex cubic fuzzy data. In the end, we discuss a numerical example with comparative analysis.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University Mansehra, Mansehra, KP, Pakistan

    Muhammad Naeem Khan Tanoli, Muhammad Gulistan, Fazli Amin & Zahid Khan

  2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada

    Muhammad Gulistan

  3. Faculty of Science and Arts, Department of Mathematics, King Khalid University, Muhayl Asser, Abha, Saudi Arabia

    Mohammed M. Al-Shamiri

  4. Faculty of Science, Department of Mathematics and Computer, Ibb University, Ibb, Yemen

    Mohammed M. Al-Shamiri

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  1. Muhammad Naeem Khan Tanoli
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  2. Muhammad Gulistan
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  3. Fazli Amin
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  4. Zahid Khan
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  5. Mohammed M. Al-Shamiri
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All authors contribute equally to the preparation of this manuscript.

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Correspondence to Muhammad Gulistan.

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Tanoli, M.N.K., Gulistan, M., Amin, F. et al. Complex Cubic Fuzzy Einstein Averaging Aggregation Operators: Application to Decision-making Problems. Cogn Comput 15, 869–887 (2023). https://doi.org/10.1007/s12559-022-10100-9

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