TITLE:
Attribute Reduction in Interval and Set-Valued Decision Information Systems
AUTHORS:
Hong Wang, Hong-Bo Yue, Xi-E Chen
KEYWORDS:
Interval and Set-Valued Information Systems; Fuzzy Preference Relation; Interval and Set-Valued Decision Information Systems; Fuzzy Positive Region; Dependency Degree; Significance Measure
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11,
November
5,
2013
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.