THE PROPERTIES OF ROUGH V-COEXACT SEQUENCE IN ROUGH GROUP

Properties of Rough Approximations

Rough set theory, introduced by Pawlak [10], is a mathematical formalism dealing with uncertainty and to some extent overlapping fuzzy set theory introduced by Zadeh [12]. In fuzzy set theory vagueness is expressed by a membership function. The rough set theory approach is based on indiscernibility relations and approximations. A major advantage of rough set theory is that it needs no prelimina...

Basic Properties of Rough Sets and Rough Membership Function1

(1) For every set X such that ∇X ⊆ idX holds X is trivial. Let A be a relational structure. We say that A is diagonal if and only if: (Def. 1) The internal relation of A ⊆ idthe carrier of A. Let A be a non trivial set. Observe that 〈A,∇A〉 is non diagonal. Next we state the proposition (2) For every reflexive relational structure L holds idthe carrier of L ⊆ the internal relation of L. One can ...

Basic Properties of Rough Sets and Rough Membership Function

Let A be a set. One can verify that 〈A, idA〉 is discrete. The following proposition is true (1) For every set X such that ∇X ⊆ idX holds X is trivial. Let A be a relational structure. We say that A is diagonal if and only if: (Def. 1) The internal relation of A ⊆ idthe carrier of A. Let A be a non trivial set. Observe that 〈A,∇A〉 is non diagonal. We now state the proposition (2) For every refle...

Rough Sets, Rough Relations and Rough Functions

T-Rough Sets Based on the Lattices

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...