In this note we introduce a variational problem with respect to an integrable fuzzy set f . The energy functional is maximized over a deleted σ -algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f . Finally an special case is considered where the variational problem can be transformed into a one dimensional se...

Monads can be used to model term rewriting systems by generalising the well-known equivalence between universal algebra and monads on the category Set. In [Lü96], this semantics was used to give a purely categorical proof of the modularity of confluence for the disjoint union of term rewriting systems. This paper provides further support for monadic semantics of rewriting by giving a categorica...

In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by several key results from the theory of quantaloid-enriched categories, this paper develops all needed ingredients purely in order-theoretic languages for the rea...

based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called the...

The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...

We establish a close and previously unknown relation between quantales and groupoids, in terms of which the notion of étale groupoid is subsumed in a natural way by that of quantale. In particular, to each étale groupoid, either localic or topological, there is associated a unital involutive quantale. We obtain a bijective correspondence between localic étale groupoids and their quantales, whic...

Each divisible and unital quantale is associated with two quantaloids. Categories enriched over these two quantaloids can be regarded respectively as crisp sets endowed with fuzzy preorders and fuzzy sets endowed with fuzzy preorders. This paper deals with the relationship between these two kinds of enriched categories. This is a special case of the change-base issue in enriched category theory...

A C∞-Hopf algebra is a C∞-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C∞-Hopf algebras which are given by the algebra C∞(G) of smooth functions on some compact Lie group G, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

The purpose of this paper is study the relationship between the categories of fuzzy multialgebras and crisp algebras. In this regards first we briefly study the categories of multialgebras and fuzzy multialgebras and then by using the fundamental relation of multialgebras we construct a functor from category of fuzzy multialgebras to the category of fuzzy algebras and hence. Hence it can be der...

We consider locales B as algebras in the tensor category s` of sup-lattices. We show the equivalence between the Joyal-Tierney descent theorem for open localic surjections shB q −→ E in Galois theory and a Tannakian recognition theorem over s` for the s`-functor Rel(E) Rel(q ∗) −→ Rel(shB) ∼= (B-Mod)0 into the s`-category of discrete B-modules. Thus, a new Tannaka recognition theorem is obtaine...