Displaying similar documents to “Information systems in categories of valued relations.”

Some notes on the category of fuzzy implications on bounded lattices

Amin Yousefi, Mashaallah Mashinchi, Radko Mesiar (2021)

Kybernetika

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In this paper, we introduce the product, coproduct, equalizer and coequalizer notions on the category of fuzzy implications on a bounded lattice that results in the existence of the limit, pullback, colimit and pushout. Also isomorphism, monic and epic are introduced in this category. Then a subcategory of this category, called the skeleton, is studied. Where none of any two fuzzy implications are Φ -conjugate.

Complete subobjects of fuzzy sets over M V -algebras

Jiří Močkoř (2004)

Czechoslovak Mathematical Journal

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A subobjects structure of the category Ω - of Ω -fuzzy sets over a complete M V -algebra Ω = ( L , ∧ , ∨ , ⊗ , → ) is investigated, where an Ω -fuzzy set is a pair 𝐀 = ( A , δ ) such that A is a set and δ A × A → Ω is a special map. Special subobjects (called complete) of an Ω -fuzzy set 𝐀 which can be identified with some characteristic morphisms 𝐀 → Ω * = ( L × L , μ ) are then investigated. It is proved that some truth-valued morphisms ¬ Ω Ω * → Ω * , ∩ Ω , ∪ Ω Ω * × Ω * → Ω * are characteristic morphisms of complete subobjects.