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A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

Author

Listed:
  • Muhammad Riaz

    (Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan)

  • Wojciech Sałabun

    (Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland)

  • Hafiz Muhammad Athar Farid

    (Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan)

  • Nawazish Ali

    (Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan)

  • Jarosław Wątróbski

    (Department of Information Systems Engineering, Faculty of Economics, Finance and Management University of Szczecin, Mickiewicza 64, 71-101 Szczecin, Poland)

Abstract

A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real-world circumstances. The intention of this article is to introduce several aggregation operators in the framework of q-rung orthopair fuzzy numbers (q-ROFNs). The key feature of q-ROFNs is to deal with the situation when the sum of the q th powers of membership and non-membership grades of each alternative in the universe is less than one. The Einstein operators with their operational laws have excellent flexibility. Due to the flexible nature of these Einstein operational laws, we introduce the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator, q-rung orthopair fuzzy Einstein ordered weighted averaging (q-ROFEOWA) operator, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator, and q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG) operator. We discuss certain properties of these operators, inclusive of their ability that the aggregated value of a set of q-ROFNs is a unique q-ROFN. By utilizing the proposed Einstein operators, this article describes a robust multi-criteria decision making (MCDM) technique for solving real-world problems. Finally, a numerical example related to integrated energy modeling and sustainable energy planning is presented to justify the validity and feasibility of the proposed technique.

Suggested Citation

  • Muhammad Riaz & Wojciech Sałabun & Hafiz Muhammad Athar Farid & Nawazish Ali & Jarosław Wątróbski, 2020. "A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management," Energies, MDPI, vol. 13(9), pages 1-39, May.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:9:p:2155-:d:352829
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