Roughness in Orthomodular Lattices

Abstract

In this paper, we define the rough approximation operators in an algebra using its congruence relations and study some of their properties. Further, we consider the rough approximation operators in orthomodular lattices. We introduce the notion of rough ideal (filter) with respect to a p-ideal in an orthomodular lattice. We show that the upper approximation of an ideal J with respect to a pideal I of an orthomodular lattice is the smallest ideal containing I and J. Further we study the homomorphic images of the rough approximation operators.

WITHDRAWN: Roughness in L-algebras

“…Since Apr θ (h)(u) ≤ Apr θ (h)(u), then β(Apr θ (h), Apr θ (h))(u) = (Apr θ (h)(u), Apr θ (h)(u)) ∈ I [2] . If u ∈ S, then Apr θ (h)(u) = Apr θ (h)(u) yields β(Apr θ (h), Apr θ (h))(u) ∈ ∆ I .…”

“…In [16], Xin et al defined rough approximation operators by a congruence relation on effect algebras and thus induced rough structure of effect algebras. In [2], Nagarajan et al defined the rough approximation operators in orthomodular lattices using its congruence relations and studied some of their properties. In [14], SanJuan investigated Heyting algebras with Boolean operators for rough sets, and presented an algebraic formalism for reasoning on finite increasing sequences over Boolean algebras in general and on generalizations of rough set concepts in particular.…”