Rough Set And Vague Set Theory And Their Related Application

Rough set theory, initialized by Professor Pawlak in early 1980's,has been proved to be an excellent mathematical tool dealing with uncertain and vague description of objects, whose basic idea is to derive classification rules of conception by knowledge reduction with the ability of classification unchanged. Vague set theory is a novel fuzzy theory dealing with fuzzy information. A fuzzy set is a class of objects along with a grade of membership function. This membership function assigns each object a grade of membership ranging between zero to one. But this membership function assigns each object a single value. This single value combines the evidence for and the evidence against , without indicating how much there is of each. Therefore, Gau et al. presented the concepts of vague sets in 1993. Vague set theory has been widely used in the areas of artificial intelligence.Firstly, the basic concepts of rough sets and vague sets are introduced in this paper. Then a new approach rough set-based for ordering rules acquisition in vague decision table is presented. An order relation among vague values is constructed according to the degree of suitability that an alternative satisfies the decision-maker's requirement, on the basis of which we transform the vague decision table into the binary decision table. Then optimal rules can be induced using rough set theory. Finally, rules induced in binary decision table are transformed into ordering rules in vague decision table. Simulation results show that the method is effective. At last, a new distance measure and a weighted one between vague sets and vague elements are given. An example is presented to illustrate the application of the distance measure in handling behavior analysis problems.