Rough Set Data Analysis

Introduction

Rule-induction methods are classified into two categories, induction of deterministic rules and of probabilistic ones [4,5,7,10].

On one hand, deterministic rules are described as if-then rules, which can be viewed as propositions. From theset-theoretical point of view, a set of examples supporting the conditional part of a deterministic rule, denoted by C, is a subset of a set whose examples belong to the consequence part, denoted by D. That is, the relation ${ C \subseteq D }$ holds and deterministic rules are supported only by positive examples in a data set.

On the other hand, probabilistic rules are if-then rules with probabilistic information [10].

When a classical proposition will not hold for C and D,C is not a subset of D but closely overlapped with D. That is, the relations ${ C \cap D \ne \phi }$ and ${ |C \cap D|/|C| \geq \delta }$will hold in this case, where the threshold d is the degree of closeness of overlapping sets, which willbe given by...