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This paper deals with categories of L-fuzzy structures, such as L-fuzzy closure and interior operators, L-fuzzy pretopologies and co-pretopologies, L-fuzzy relations, or spaces with L-fuzzy partitions and transformations of these categories into the categories of L-fuzzy topological spaces. Unlike traditional approaches that use mappings in the category of L fuzzy topological spaces as morphisms, continuous L-fuzzy relations are used, aligning with the actual trends in fuzzy set theory. Functors transforming the categories of the above-mentioned structures into the category of L-fuzzy topological spaces with a continuous L-fuzzy relation are presented, and some properties of these functors are investigated.

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Functors from Fuzzy Structures Categories into Categories of Fuzzy Topological Spaces with Continuous Fuzzy Relations

  • 会议论文

  • 发表日期：

    2025年

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  • Jiří Močkoř

摘要

This paper deals with categories of L-fuzzy structures, such as L-fuzzy closure and interior operators, L-fuzzy pretopologies and co-pretopologies, L-fuzzy relations, or spaces with L-fuzzy partitions and transformations of these categories into the categories of L-fuzzy topological spaces. Unlike traditional approaches that use mappings in the category of L fuzzy topological spaces as morphisms, continuous L-fuzzy relations are used, aligning with the actual trends in fuzzy set theory. Functors transforming the categories of the above-mentioned structures into the category of L-fuzzy topological spaces with a continuous L-fuzzy relation are presented, and some properties of these functors are investigated.