On Hesitant Fuzzy Subalgebraic Systems in IUP-Algebras

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DOI: https://doi.org/10.28924/2291-8639-23-2025-314
Published: Nov 28, 2025
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Ananya Surat, Nidarat Pansrigern, Amonrat Khokhamram, Aiyared Iampan, On Hesitant Fuzzy Subalgebraic Systems in IUP-Algebras, Int. J. Anal. Appl., 23 (2025), 314.

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Ananya Surat, Nidarat Pansrigern, Amonrat Khokhamram, Aiyared Iampan

Abstract

We introduce hesitant fuzzy sets of algebraic structures in IUP-algebras, including hesitant fuzzy IUP-subalgebras, IUP-filters, IUP-ideals, and strong IUP-ideals. These notions are defined via relaxed set-theoretic and algebraic conditions suitable for hesitant fuzzy membership functions. Their mutual relationships are analyzed, showing how they extend and unify prior definitions in the UP-algebraic setting. Several examples and counterexamples are provided to illustrate essential differences between these classes and to demonstrate that each concept is a proper generalization of its classical or fuzzy counterpart. A diagram of class inclusions is also presented to visualize the structural hierarchy among these hesitant fuzzy sets.

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