论文信息 - A new algebraic approach to L-fuzzy relations convenient to study crispness

A new algebraic approach to L-fuzzy relations convenient to study crispness

Abstract The aim of this paper is to develop a suitable calculus of L -fuzzy relations. We show that for this purpose the theory of Dedekind categories is too weak. Therefore, we introduce the notion of a Goguen category as a suitable algebraic definition and show several properties of this kind of a relational category.

Michael Winter | M. Winter

[1] Lotfi A. Zadeh,et al. Fuzzy Sets , 1996, Inf. Control..

[2] A. Tarski,et al. Boolean Algebras with Operators , 1952 .

[3] Dany Serrato,et al. Squares and rectangles in relation categories. Three cases: semilattice, distributive lattice and Boolean non-unitary , 1995 .

[4] Michael Winter,et al. Heterogeneous Relation Algebra , 1997, Relational Methods in Computer Science.

[5] Yasuo Kawahara,et al. Crispness and Representation Theorem in Dedekind Categories , 1997 .

[6] A. Tarski,et al. Boolean Algebras with Operators. Part I , 1951 .

[7] Hitoshi Furusawa,et al. Algebraic Formalisations of Fuzzy Relations and Their Representation Theorems , 1997 .

[8] Alfred Tarski,et al. Distributive and Modular Laws in the Arithmetic of Relation Algebras , 1953 .

[9] J. Goguen. L-fuzzy sets , 1967 .