Abstract
Let Ω be a complete residuated lattice. By SetF(Ω) we denote a category of sets with similarity relations (A,δ) with values in Ω. We investigate an interpretation of a first order predicate fuzzy logic in a model based on objects of this category SetF(Ω). A notion of a fuzzy set in this category is introduced and interpretation of formulas as fuzzy sets are defined. Characteristic morphisms are defined for such fuzzy sets and relationship between interpretation by fuzzy sets and interpretation defined by characteristic morphisms are investigated.
The paper has been supported by the project MSM 6198898701 of the MŠMT ČR and 1M6798555601.
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Močkoř, J. (2007). Characteristic Morphisms and Models of Fuzzy Logic in a Category of Sets with Similarities. In: Castillo, O., Melin, P., Ross, O.M., Sepúlveda Cruz, R., Pedrycz, W., Kacprzyk, J. (eds) Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. Advances in Soft Computing, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72434-6_84
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DOI: https://doi.org/10.1007/978-3-540-72434-6_84
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