Year: 2025
Type: article
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.
DOI: 10.47974/jim-2183
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4413802811