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Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

Author

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  • Zeeshan Ali

    (Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan
    KERMIT, Department of Mathematical Modeling, Statistics and Bioinformatics, Ghent University, Coupure Links 653, Ghent 9000, Belgium)

  • Tahir Mahmood

    (Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan)

  • Miin-Shen Yang

    (Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan 32023, Taiwan)

Abstract

Complex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the unit interval. In this paper, we first derive the Frank operational laws for CIF information and then examine the prioritized aggregation operators based on Frank operational laws for managing the theory of CIF information. These are the CIF Frank prioritized averaging (CIFFPA) operator, the CIF Frank prioritized ordered averaging (CIFFPOA) operator, the CIF Frank prioritized geometric (CIFFPG) operator, and the CIF Frank prioritized ordered geometric (CIFFPOG) operator with properties of idempotency, monotonicity, and boundedness. Furthermore, we derive the WASPAS (weighted aggregates sum product assessment) under the consideration or presence of the CIF information and try to justify it with the help of a suitable example. Additionally, we illustrate some numerical examples in the presence of the MADM (multi-attribute decision-making) procedures for evaluating the comparison between the proposed operators with some well-known existing operators to show the validity and worth of the proposed approaches.

Suggested Citation

  • Zeeshan Ali & Tahir Mahmood & Miin-Shen Yang, 2023. "Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2058-:d:1133719
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    References listed on IDEAS

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    1. Miin-Shen Yang & Zahid Hussain & Mehboob Ali, 2020. "Belief and Plausibility Measures on Intuitionistic Fuzzy Sets with Construction of Belief-Plausibility TOPSIS," Complexity, Hindawi, vol. 2020, pages 1-12, August.
    2. Zeeshan Ali & Tahir Mahmood & Muhammad Aslam & Ronnason Chinram, 2021. "Another View of Complex Intuitionistic Fuzzy Soft Sets Based on Prioritized Aggregation Operators and Their Applications to Multiattribute Decision Making," Mathematics, MDPI, vol. 9(16), pages 1-29, August.
    3. Stoyan Poryazov & Velin Andonov & Emiliya Saranova & Krassimir Atanassov, 2022. "Two Approaches to the Traffic Quality Intuitionistic Fuzzy Estimation of Service Compositions," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
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    Cited by:

    1. A. S. Wungreiphi & Fokrul Alom Mazarbhuiya & Mohamed Shenify, 2023. "On Extended L r -Norm-Based Derivatives to Intuitionistic Fuzzy Sets," Mathematics, MDPI, vol. 12(1), pages 1-19, December.

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