Soft Set Based Approximate Reasoning: A Quantitative Logic Approach

Soft set theory is a newly emerging mathematical approach to vagueness. However, it seems that there is no existing research devoted to the discussion of applying soft sets to approximate reasoning. This paper aims to initiate an approximate reasoning scheme based on soft set theory. We consider proposition logic in the framework of a given soft set. By taking parameters of the underlying soft set as atomic formulas, the concept of (well-formed) formulas over a soft set is defined in a natural way. The semantic meaning of Formulas is then given by taking objects of the underlying soft set as valuation. functions. We propose the notion of decision soft sets and define decision rules as implicative type of formulas in decision soft sets. Motivated by basic ideas from quantitative logic, we also introduce several measures and preorders to evaluate the soundness of formulas and decision rules in soft sets. Moreover, an interesting example is presented to illustrate all the new concepts and the basic ideas initiated here.