Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)
- Volume 2 Issue 3
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- Pages.17-21
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- 1992
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- 1976-9172(pISSN)
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- 2288-2324(eISSN)
Structures of Fuzzy Relations
Abstract
In this paper we consider the notion of fuzzy relation as a generalization of that of fuzzy set. For a complete Heyting algebra L. the category set(L) of all L-fuzzy sets is shown to be a bireflective subcategory of the category Rel(L) of all L-fuzzy relations and L-fuzzy relation preserving maps. We investigate categorical structures of subcategories of Rel(L) in view of quasitopos. Among those categories, we include the category L-fuzzy similarity relations with respect to both max-min and max-product compositions, respectively, as a cartesian closed topological category. Moreover, we describe exponential objects explicitly in terms of function space.
Keywords