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In this article, we apply fuzzy set theory to IUP-algebras, introducing four new concepts: fuzzy IUP-subalgebras, fuzzy IUP-filters, fuzzy IUP-ideals, and fuzzy strong IUP-ideals, and examining their properties and relationships.We also found a relationship between characteristic functions and the four concepts of fuzzy sets.In addition, the concepts of prime subsets and prime fuzzy sets were also applied.The notions of upper t-(strong) level subsets and lower t-(strong) level subsets of a fuzzy set are introduced in IUP-algebras.
Kuntama et al. (Fri,) studied this question.