APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS

Abstract

The concept of soft sets, introduced by Molodtsov [20] is a mathematical<br />tool for dealing with uncertainties, that is free from the difficulties<br />that have troubled the traditional theoretical approaches. In this paper, we<br />apply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras.<br />The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras,<br />soft abysms and soft deductive systems are introduced, and their basic properties<br />are investigated. The relations between soft Hilbert algebras, soft Hilbert<br />abysmal algebras and soft Hilbert deductive algebras are also derived.