Applications of soft sets in Hilbert algebras

Abstract. The concept of soft sets, introduced by Molodtsov [20] is a math-ematical tool for dealing with uncertainties, that is free from the difficulties that have troubled the traditional theoretical approaches. In this paper, we apply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras. The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras, soft abysms and soft deductive systems are introduced, and their basic proper-ties are investigated. The relations between soft Hilbert algebras, soft Hilbert abysmal algebras and soft Hilbert deductive algebras are also derived. 1