Set functors,L-fuzzy set categories,and generalized terms |
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Affiliation: | Dept. Computing Science, Umeå University SE-901 87 Umeå, Sweden;Dept. Matemática Aplicada, Universidad de Málaga P.O. Box 4114, 29080 Málaga, Spain |
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Abstract: | In this work, we generalize previous constructions of fuzzy set categories, introduced in 1], by considering L-fuzzy sets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzy sets are used to define the L-fuzzy categories, which are proven to be rational. In the final part of the paper, the L-fuzzy functors given by the extension principles are provided with a structure of monad which is used, together with the functorial definition of the term monad, to provide monad compositions as a basis for a notion of generalised terms. |
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