Study on Generalized Soft Lattice and Soft Valuation

Abstract

A soft set is a generalization of a fuzzy set and is an efficient tool for modelling imprecise and vague data. The mathematical structures partially ordered sets and lattices play an important role in mathematics as well as in other disciplines such as computer science, engineering, cryptography, etc. Here we apply soft set theory to lattice theory and introduce the concept of a soft partial ordering and more concepts related to it. Mainly we introduce the concept of a generalized soft lattice(gs lattice) and investigate some of its fundamental properties. Further, we define a soft real valued function called soft valuation on a gs lattice and study its major properties. Moreover, we discuss the notion of a soft distance function in terms of soft valuation and using that function we discuss the conditions under which a gs lattice becomes a soft metric lattice. We conclude this study by defining a soft topological lattice and describe that when a gs lattice with a soft valuation becomes a soft topological lattice.