Rough Computational Approach to UAR based on Dominance Matrix in IOIS

Abstract

Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. The classical rough set theory based on equivalence relation has made a great progress, while the equivalence relation is too harsh to meet and is extended to dominance relation in real world. It is important to investigate rough computational methods for rough set theory, which is one of the bottleneck problems in the development of rough set theory. In this article, rough computational approach to upper approximation reduction (UAR) is discussed based on dominance matrix in inconsistent ordered information systems (IOIS). The algorithm of upper approximation reduction is obtained, from which we can provide approach to upper approximation reduction operated simply in inconsistent systems based on dominance relations. Finally, an example illustrates the validity of this method, and shows the method is excellent to a complicated information system.

A Distance-Based Method for Attribute Reduction in Incomplete Decision Systems

“…We use the importance of an attribute as heuristic information to design an effective heuristic algorithm to find the best reduct. We prove theoretically that the complexity of our algorithm is less than that of the algorithms in [1,3,4,20].…”

“…Finally, the complexity of Algorithm 5.1 is O(|Attr| 2 |U | 2 ). Consequently, this complexity is better than the complexity of algorithms in [1,3,4,20].…”

“…Derived from the idea of rough set theory [11], Marzena Kryszkiewicz [5] defines a tolerance relation based on the equivalent relation and proposes tolerance rough set. Recently, much research has been undertaken on measures and methods to find reducts in incomplete decision systems [1,3,4,7,8,9,12,13,20]. Though distance has been a popular measure applied to solve some problems in data mining [16,18,19], there is limited reseach on attribute reduction in rough set theory.…”

Analysis of Students’ Misconception Based on Rough Set Theory

“…In addition, rough set theory has fruitful results in many fields, particularly in approximate reasoning [10], mathematical logic analysis and reduct [11][12][13], building of predictive models [14], decision support system [15][16][17][18][19] and other areas. Many studies have shown that the use of rough set theory not only formulate a clear decision-making projects [12], but also enhance the effectiveness of the research while doing optimization [19,20]. Among them, the research related to education of Qu and Wang [16] provided a basis of personalized teaching strategies in distance learning website by analysis of reduct and attribute significance.…”

A New Method of Attribute Reduction Based On Information Quantity in An Incomplete System

“…As the computation complexity is too high, the efficiency is extremely low. Some of these methods can not deal with incomplete information system when there are a lot of null values in information systems, and at the same time the knowledge we get may not be reliable [11][12][13][14]. As the result in contrast with the indirect method, the direct method maintains the original structure of information systems, and avoids human subjectivity.…”