Attribute Reduction in Interval and Set-Valued Decision Information Systems

Hong Wang, Hong-Bo Yue, Xi-E Chen

College of Mathematics and Computer Science, Shan’xi Normal University, Linfen, China.
Shanxi Coal Mining Adminstrators College, Taiyuan, China.

DOI: 10.4236/am.2013.411204                

Abstract

In many practical situation, some of the attribute values for an object may be interval and set-valued. This paper introduces the interval and set-valued information systems and decision systems. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories: disjunctive (Type 1) and conjunctive (Type 2) systems. In this paper, we mainly focus on semantic interpretation of Type 1. Then, we define a new fuzzy preference relation and construct a fuzzy rough set model for interval and set-valued information systems. Moreover, based on the new fuzzy preference relation, the concepts of the significance measure of condition attributes and the relative significance measure of condition attributes are given in interval and set-valued decision information systems by the introduction of fuzzy positive region and the dependency degree. And on this basis, a heuristic algorithm for calculating fuzzy positive region reduction in interval and set-valued decision information systems is given. Finally, we give an illustrative example to substantiate the theoretical arguments. The results will help us to gain much more insights into the meaning of fuzzy rough set theory. Furthermore, it has provided a new perspective to study the attribute reduction problem in decision systems.

Keywords

Interval and Set-Valued Information Systems; Fuzzy Preference Relation; Interval and Set-Valued Decision Information Systems; Fuzzy Positive Region; Dependency Degree; Significance Measure

Conflicts of Interest

The authors declare no conflicts of interest.

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