On (M,N)-S I (implicative) filters in R₀-algebras

Abstract

Molodtsov's soft set theory provides a general mathematical framework for dealing with uncertainty. This paper aims to put forward a new soft set–(M,N)-soft intersection set, which is a generalization of soft intersection sets. We introduce (M, N)-S I (implicative) filters of R₀-algebras. Some characterizations of these kinds of filters are established. In particular, we discuss the properties of (M,N)-soft congruences in R₀-algebras. It can lay a foundation for providing a new soft algebraic tool in considering many problems that contain uncertainties.

Keywords:

• Soft set
• R₀-algebras
• filter
• implicative filter
• (M,N)-soft congruence
• (M,N)-S I implicative(Boolean) filter