SOFT BOOLEAN ALGEBRA AND ITS PROPERTIES

摘要

Molodtsov [21] introduced the concept of soft theory which can be used as a generic mathematical tool for dealing with uncertainty. In this paper, we apply the notion of the soft set theory of Molodtsov to the theory of Boolean algebras which is a well-known algebraic structure. We introduce the concepts of soft filter and soft ideal on the soft Boolean algebra as well as notions of a soft Boolean algebra and soft Boolean homomorphism, and investigate basic properties as intersection, union and product of the soft Boolean algebras. Also we give several illustrative examples.