Interaction-Aware Hamacher-Choquet Aggregation for Generalized Disc Circular Intuitionistic Fuzzy Information
DOI:
https://doi.org/10.32350/sir.103.02Keywords:
choquet integral, circular intuitionistic fuzzy set, fuzzy measure, generalized disc uncertainty, hamacher operator, intuitionistic fuzzy set, multi-criteria decision-making, renewable energyAbstract
Multi-criteria decision-making (MCDM) problems often contain three simultaneous sources of difficulty: incomplete expert assessments, nonlinear aggregation requirements, and dependence among criteria. This paper develops an interaction-aware aggregation framework for generalized disc circular intuitionistic fuzzy numbers (GDCIFNs). A GDCIFN augments an intuitionistic fuzzy pair (µ, ν) with an element-dependent radius r, subject to a geometric admissibility condition. The main methodological contribution is a consistent coupling of the two dual Hamacher generators with a discrete Choquet integral: the membership component is aggregated through the Hamacher t-conorm generator, the non-membership component through the Hamacher t-norm generator, and the radius through a bounded generator followed by an admissibility projection. This construction avoids treating the same generator as both a t-norm and a t-conorm. We establish well-definedness, closure, idempotency, monotonicity of the membership and non-membership components, boundedness, and permutation consistency. A renewable-energy selection example is computed after correctly normalizing the cost criterion. Sensitivity experiments show that the ranking A3 > A2 > A1 > A4 is stable for . The interaction-aware model produces modest score changes (maximum difference: 0.0073), while preserving ranking stability. The paper explicitly positions the contribution against recent circular-intuitionistic Hamacher aggregation, Hamacher-Choquet aggregation for complex intuitionistic fuzzy information, and disc-intuitionistic Choquet models.
Downloads
References
1. Zadeh LA. Fuzzy sets. Inf Control. 1965;8(3):338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
2. Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986;20(1):87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
3. Pratama D, Yusoff B, Abdullah L, Kilicman A, Kamis NH. Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: exploring a domain radius. AIMS Math. 2024;9(5):12259–12286. https://doi.org/10.3934/math.2024599
This study explores extension operators for circular intuitionistic fuzzy sets using triangular norms and conorms, focusing on the role of domain radius in refining fuzzy set operations and improving their mathematical applicability.
4. Bozyiğit MC, Ünver M. Solar panel selection using extended WASPAS with disc intuitionistic fuzzy Choquet integral operators: CASPAS methodology. arXiv. Preprint posted January 21, 2025. https://doi.org/10.48550/arXiv.2501.12251
5. Liu P, Ali Z. Hamacher interaction aggregation operators for complex intuitionistic fuzzy sets and their applications in green supply chain management. Complex Intell Syst. 2024;10:3853–3871. https://doi.org/10.1007/s40747-023-01329-4
6. Klement EP, Mesiar R, Pap E. Triangular Norms. Kluwer Academic Publishers; 2000. https://doi.org/10.1007/978-94-015-9540-7
7. Choquet G. Theory of capacities. Ann Inst Fourier (Grenoble). 1954;5:131–295. https://doi.org/10.5802/aif.53
8. Grabisch M. The application of fuzzy integrals in multicriteria decision making. Eur J Oper Res. 1996;89(3):445–456. https://doi.org/10.1016/0377-2217(95)00176-X
9. Grabisch M, Labreuche C. A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Ann Oper Res. 2010;175(1):247–286. https://doi.org/10.1007/s10479-009-0655-8
10. Fahmi A, Khan A, Maqbool Z, Abdeljawad T. Circular intuitionistic fuzzy Hamacher aggregation operators for multi-attribute decision-making. Sci Rep. 2025;15(1):5618. https://doi.org/10.1038/s41598-025-88845-0
11. Tehreem, Garg H, Ayaz K, Emam W. Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information. AIMS Math. 2024;9(12):35860–35884. https://doi.org/10.3934/math.20241700
This study proposes multi-attribute decision-making algorithms based on Hamacher Choquet-integral operators under complex intuitionistic fuzzy information. The developed methods support the aggregation of complex fuzzy data and help address decision-making problems involving multiple criteria and uncertain information.
12. Al-Qubati AAQ, Zedam L, Ullah K, Al-Qahtani HF. Choquet-integral aggregation operators based on Hamacher t-norm and t-conorm for complex intuitionistic fuzzy TOPSIS technique to deal with socio-economic problems. IEEE Access. 2024;12:3098–3113. https://doi.org/10.1109/ACCESS.2023.3346499
13. Zimmermann HJ. Fuzzy Set Theory—and Its Applications. 4th ed. Kluwer Academic Publishers; 2001. https://doi.org/10.1007/978-94-010-0646-0
14. Atanassov KT, Kahraman C. Circular intuitionistic fuzzy sets. J Intell Fuzzy Syst. 2020;39(5):5981–5986. https://doi.org/10.3233/JIFS-189072
15. Kadian S, Kumar S. Circular intuitionistic fuzzy sets: A review and future directions. Int J Fuzzy Syst. 2024;26(4):1123–1140.
16. Murofushi T, Sugeno M. An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy Sets Syst. 1989;29(2):201–227. https://doi.org/10.1016/0165-0114(89)90194-2
17. Marichal JL. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Trans Fuzzy Syst. 2000;8(6):800–807. https://doi.org/10.1109/91.890347
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 shahid Shehzad
This work is licensed under a Creative Commons Attribution 4.0 International License.
