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.

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.

Fuzzy TL-uniform spaces.

Hashem, Khaled A., Morsi, Nehad N. (2006)

International Journal of Mathematics and Mathematical Sciences

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The Formal Construction of Fuzzy Numbers

Adam Grabowski (2014)

Formalized Mathematics

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In this article, we continue the development of the theory of fuzzy sets [23], started with [14] with the future aim to provide the formalization of fuzzy numbers [8] in terms reflecting the current state of the Mizar Mathematical Library. Note that in order to have more usable approach in [14], we revised that article as well; some of the ideas were described in [12]. As we can actually understand fuzzy sets just as their membership functions (via the equality of membership function...

Similarity in fuzzy reasoning.

Frank Klawonn, Juan Luis Castro (1995)

Mathware and Soft Computing

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Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval...