Displaying similar documents to “On the L -valued categories of L - E -ordered sets”

On a functional equation connected to the distributivity of fuzzy implications over triangular norms and conorms

Michał Baczyński, Tomasz Szostok, Wanda Niemyska (2014)

Kybernetika

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Distributivity of fuzzy implications over different fuzzy logic connectives have a very important role to play in efficient inferencing in approximate reasoning, especially in fuzzy control systems (see [9, 15] and [4]). Recently in some considerations connected with these distributivity laws, the following functional equation appeared (see [5]) f ( min ( x + y , a ) ) = min ( f ( x ) + f ( y ) , b ) , where a , b > 0 and f : [ 0 , a ] → [ 0 , b ] is an unknown function. In this paper we consider in detail a generalized version of this equation, namely the equation f ( m 1 ( x + y ) ) = m 2 ( f ( x ) + f ( y ) ) , where...

Totality of product completions

Jiří Adámek, Lurdes Sousa, Walter Tholen (2000)

Commentationes Mathematicae Universitatis Carolinae

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Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category 𝒜 by asking the Yoneda embedding 𝒜 → [ 𝒜 o p , 𝒮 e t ] to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion Π 𝒜 of 𝒜 . We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the...

Evaluating many valued modus ponens

Dana Hliněná, Vladislav Biba (2012)

Kybernetika

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This paper deals with many valued case of modus ponens. Cases with implicative and with clausal rules are studied. Many valued modus ponens via discrete connectives is studied with implicative rules as well as with clausal rules. Some properties of discrete modus ponens operator are given.

A categorical concept of completion of objects

Guillaume C. L. Brümmer, Eraldo Giuli (1992)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.