Strong Interval-Valued Intuitionistic Fuzzy Ideals of Semirings.
Main Article Content
Abstract
This research presents the idea of strong interval-valued intuitionistic fuzzy ideals within semirings and explores their key algebraic characteristics. This concept builds upon the existing theory of interval-valued intuitionistic fuzzy ideals by imposing more stringent conditions on the interval-valued membership and non-membership functions when considering addition and multiplication. To validate this concept, several fundamental properties, examples, and characterizations have been established. Additionally, significant structural findings are demonstrated, such as closure under intersections, behaviour with respect to semiring homomorphisms and isomorphisms, level subset characterizations, and properties related to finite sums and products. These findings lay a robust theoretical groundwork for the exploration of strong interval-valued intuitionistic fuzzy ideals and enhance the field of interval-valued intuitionistic fuzzy algebra, with potential applications in fuzzy algebraic systems, decision-making, and modelling uncertainty....
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
Atanassov, K. T. (1994). Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 64(2), 159–174.
Atanassov, K. T., & Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349.
Alghazzawi, D., Alolaiyan, H., Ashfaq, H., Shuaib, U., Khalifa, H. A. E.-W., Gomaa, H. G., & Xin, Q. (2024). Selecting an optimal approach to reduce energy crises under interval-valued intuitionistic fuzzy environment. Scientific Reports, 14, 8713
Dong, J.-Y., & Wan, S.-P. (2024). Interval-valued intuitionistic fuzzy best-worst method with additive consistency. Expert Systems with Applications, 236, 121213.
Gaketem, T., & Khamrot, P. (2024). Generalized interval-valued fuzzy ideals in semigroups. Journal of Mathematics and Computer Science, 34(2), 116–127.
Gaketem, T., Iampan, A., & Khamrot, P. (2026). Interval-valued intuitionistic (Tⓜ,S)-fuzzy subsemirings in semirings. International Journal of Analysis and Applications, 24, 57.
Khamrot, P., & Gaketem, T. (2024). Spherical interval-valued fuzzy ideals which coincide in semigroups. Journal of Mathematics and Computer Science, 33(1), 42–56.
Rao, M. M. K., & Rafi, N. (2024). On interval-valued fuzzy prime ideals of Γ-semirings. Annals of Communications in Mathematics, 7(1), 10–20.
Su, Y., Gong, Z., & Qin, N. (2024). Complex interval-valued intuitionistic fuzzy sets: Quaternion number representation, correlation coefficient and applications. AIMS Mathematics, 9(8), 19943–19966.
Wu, X., Tan, C., Cayli, G. D., & Liu, P. (2021). On the algebraic structures of the space of interval-valued intuitionistic fuzzy numbers. Fuzzy Optimization and Decision Making, 20(4), 515–540.
Perarasan, K., Vasuki, M., Mishra, A. K., Harif, B. M., Kumar, A. D., & Celestin, M. (2026). Q-Fuzzy JU-Algebras: A Structural Analysis with Respect to ⊗.
Perarasan, K., Vasuki, M., Mishra, A. K., Harif, B. M., Kumar, A. D., & Celestin, M. (2019). An Introduction to HP-Algebras: Axiomatic Foundations and Basic Theory.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
Zimmermann, H.-J. (2010). Fuzzy set theory—and its applications (4th ed.). Springer