APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS

The concept of soft sets, introduced by Molodtsov [۲۰] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. In this paper, weapply 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 propertiesare investigated. The relations between soft Hilbert algebras, soft Hilbertabysmal algebras and soft Hilbert deductive algebras are also derived.

Keywords:

Hilbert algebra , Soft set , Soft Hilbert algebra , Soft Hilbert abysmal algebra , Soft Hilbert deductive algebra , (trivial , whole) soft Hilbert algebra , Soft subalgebra , Soft abysm , Soft deductive system