Binary Relation, Basis Algebra, Approximation Operator Form and Its Property in L-Fuzzy Rough Sets

The rough set theory usually is used in datamining. At this time, we will suppose the approximation operator to satisfy some wonderful properties. It need us to think about the basis algebra, the binary relation and the approximation operator’s form in the rough set model. Lfuzzy rough approximation operator is a general fuzzy rough approximation operator. Comparing with the others rough approximation operator, it is more clearly for the Lfuzzy rough approximation operator that not only the binary relation and the basis algebra, but also the form of approximation operator influence its properties. To inhibit the relations between binary relation on the universe, basis algebra, the approximation operators’ properties and its form in the L-fuzzy rough set, we introduce some basis algebra(residuated lattice, MTL algebra and IMTL algebra) and some binary relations(the reflexive, symmetric, ⊗-transitive, L-similar, Lindistinguishable fuzzy binary relation) into three types Lfuzzy rough approximation operators and proof some Lfuzzy rough approximation operators’ properties as its properties. As usual, we discuss the approximation operator in the constructive approach and axiomatic approach. This paper focus on the basis algebra and the form of the approximation operators. As the preliminaries, we use some spaces to discuss the properties of the non-classic logic algebra.