Displaying similar documents to “Some Remarks on the Category Set(l), Part II”

Information systems in categories of valued relations.

Vladimir B. Gisin (1994)

Mathware and Soft Computing

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The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment 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.

On the notion of Fuzzy Set.

Nando Prati (1992)

Stochastica

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Many discussions have been made on the problem of (i) What are Fuzzy Sets? since the origin of the theory. Due to the structure of Fuzzy Sets the first impression that many people have is that Fuzzy Sets are the distribution of a probability. Recent developments of many theories of uncertainty measures (belief functions, possibility and fuzzy measures, capacities) can make also think that a Fuzzy Set is the distribution of an uncertainty measure. Other problems...

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.