Search results for "Higher category theory"

showing 2 items of 2 documents

Categories of lattice-valued sets as categories of arrows

2006

In this paper we introduce a category X(A) which is a generalization of the category of lattice-valued subsets of sets Set(JCPos) introduced by us earlier. We show the necessary and sufficient conditions for X(A) to be topological over XxA.

Discrete mathematicsHigher category theoryClosed categoryArtificial IntelligenceLogicMathematics::Category TheoryCategoryConcrete categoryCategory of topological spacesCategory of setsTopological category2-categoryMathematicsFuzzy Sets and Systems
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Towards the theory of M-approximate systems: Fundamentals and examples

2010

The concept of an M-approximate system is introduced. Basic properties of the category of M-approximate systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximate systems.

Higher category theoryEquivalence of categoriesLogicbusiness.industryFuzzy setAlgebraMorphismSystems theoryArtificial IntelligenceMathematics::Category TheoryCategoryRough setArtificial intelligenceCategory theorybusinessMathematicsFuzzy Sets and Systems
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