Akademik Veri Yönetim Sistemi
Fuzzy Sets and Systems, cilt.533, 2026 (SCI-Expanded, Scopus)
Ω⋆-lax objects, providing a categorical framework for fuzzy sets on structured sets, are generalization of L -fuzzy sets in an abstract category C on the basis of a fixed partially ordered object Ω⋆. One of the main objectives of this paper is to exhibit how they are used to define the notions of fuzzy sets on fuzzy sets, fuzzy sets on sets with fuzzy equalities and fuzzy sets on typed sets and to investigate some categorical properties of Ω⋆-lax objects. Categorical many-valued functions are special Ω⋆-lax objects that enable us to formulate the notions of fuzzy functions between sets with the same kind of structures. It is another main objective of this paper to study them. Referring to a symmetric, partially ordered Ω-monoidal relation system Υ on C having a symmetric, closed monoidal structure, we formalize categorical many-valued functions as Υ-functions and give their some basic properties. Furthermore, the results are applied to fuzzy functions between two sets, two fuzzy sets, two sets with fuzzy equalities, two typed sets.