SOFT SETS - AN ORDINAL FORMULATION OF VAGUENESS WITH SOME APPLICATIONS TO THE THEORY OF CHOICE

In the theory of fuzzy sets, it is usual to represent the 'degree of belongingness' by a number lying between 0 and 1. This paper develops an alternative framework which dispenses with such cardinal numerical representations of the degree of belongingness, and relies, instead, on an ordinal formulation. The ordinal notion of a vague set is called a soft set. Soft sets are shown to have a tight logical relation with the concept of L-sets introduced earlier by Goguen. The paper also discusses applications of the framework of soft sets to several problems in the theory of choice.