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Open Access Research Article

Categorical accommodation of various notions in generalized multidimensional fuzzy sets

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pp. 1955–1971Vol. 28Issue 5August 2025DOI: 10.47974/JIM-2183XML
Received:
07 Aug 2024
Published Online:
14 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2183
Pages:
1955–1971

Abstract

This paper investigates the categorical framework for generalized multi-dimensional fuzzy sets, extending Zadeh’s original theory. We introduce a generalized variant where the co-domain is a partially ordered set. Fundamental categorical notions such as initial and terminal objects, separators, co-separators, and various morphisms (e.g., mono-, epi-, iso-, section, and retraction) are explored. We prove the category is complete and co-complete by identifying equalizers, co-equalizers, products, and co-products using new union and intersection operations for these sets.

Keywords

Subject Classifications

18A0518A2094D05

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