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Approximation Operators, Binary Relation and Basis Algebra in L-fuzzy Rough Sets

Wu Z., Li T., Qin K., Ruan D.

Fundamenta Informaticae

2011

Vol. 111, nr 1

47-63

Approximation operators play a vital role in rough set theory. Their three elements, namely, binary relation in the universe, basis algebra and properties, are fundamental in the study of approximation operators. In this paper, the interrelations among the three elements of approximation operators in L-fuzzy rough sets are discussed under the constructive approach, the axiomatic approach and the basis algebra choosing approach respectively. In the constructive approach, the properties of the approximation operators depend on the basis algebra and the binary relation. In the axiomatic approach, the induced binary relation is influenced by the axiom set and the basis algebra. In the basis algebra choosing approach, the basis algebra is constructed by properties of approximation operators and specific binary relations.

A Note on Axiom System for SBL-algebras

Halaš R.

Fundamenta Informaticae

2009

Vol. 90, nr 1-2

87-92

In the paper we resolve an open problem posed by D.Ciucci in [1] on the independence of axioms for SBL-algebras. The main aim is to present its solution which is, in contrast to the one presented in [4], simple, transparent and easily verifiable.

Algebraic Structures Related to Many Valued Logical Systems. Part 1, Heyting Wajsberg Algebras

Cattaneo G., Ciucci D., Giuntini R., Konig M.

Fundamenta Informaticae

2004

Vol. 63, nr 4

331--355

A bottom-up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This characteristic is helpful in the study of abstract rough approximations.