Reduction In Incomplete Information Systems Research Articles

Improved rough approximations based on variable J-containment neighborhoods

Classic generalized rough set model in neighborhood systems provides a more general framework for depicting approximations, while it may meet the non-reflexive situations. Some scholars put forward different neighborhoods, such as adhesion neighborhoods (briefly, P_{j}-neighborhoods), containment neighborhoods (briefly, C_{j}-neighborhoods), and E_{j}-neighborhoods. However, not all of them are reflexive. Moreover, the granularity of P_{j}-neighborhoods and C_{j}-neighborhoods are too fine, and that of E_{j}-neighborhoods too coarse. To solve the problem, we aim to design a novel construction approach of neighborhoods, called variable j-containment neighborhoods (briefly, V_{j}^{beta }-neighborhoods), which satisfies the reflexivity and the granularity so flexible that the neighborhood space can adjust the granularity to meet the needs of problems. We generalize three kinds of rough approximations in V_{j}^{beta }-neighborhood spaces and discuss their properties. What’s more, we analyze the topology structures relying on V_{j}^{beta }-neighborhood spaces and compare our proposed approach with the existing approaches. By selecting the appropriate parameter beta, our neighborhood system is more flexible in adjusting the granularity to fit problem requirements. And illustrative examples demonstrate the advantages of the proposed rough set model to attribute reduction in incomplete information systems.

Generalized binary discernibility matrix for attribute reduction in incomplete information systems

AbstractTo extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.

Dependence space of topology and its application to attribute reduction

Attribute reduction plays an important role in pattern recognition and machine learning. Covering-based rough sets, as a technique of granular computing, can be a useful tool for studying attribute reduction. Topology has a close relationship with rough sets and plays a significant role in attribute reduction in information systems. So it is meaningful to combine topology with rough sets to address the problems of attribute reduction. In this paper, we mainly discuss and address the problem of attribute reduction in incomplete information systems with dependence space induced by topological base. Firstly, we investigate the topological structure induced by covering-based rough sets and some characteristics of the topological structure are presented. Secondly, a new type of dependence space is constructed in terms of the base of topological structure, and some characteristics of the dependence space are investigated. Finally, we apply the obtained results of the space to the attribute reduction in incomplete information systems. Especially, a discernibility matrix is defined for the attribute reduction in incomplete information systems.

Exclusive disjunctive soft sets

Soft sets theory, initiated by Molodtsov, is an emerging tool to deal with uncertain problems and has been studied by scholars in both theory and practice. This paper proposes the notion of exclusive disjunctive soft sets and studies some of its operations, such as, restricted/relaxed AND operations, dependency between exclusive disjunctive soft sets and bijective soft sets, exclusive disjunctive soft decision systems, reduction of exclusive disjunctive soft decision systems, core of exclusive disjunctive soft decision systems, decision rules in exclusive disjunctive decision soft sets. Moreover, this study gives an application of exclusive disjunctive soft sets, which shows that it can be applied to attribute reduction of incomplete information system.

Attribute reduction based on evidence theory in incomplete decision systems

Attribute reduction is a basic issue in knowledge representation and data mining. This paper deals with attribute reduction in incomplete information systems and incomplete decision systems based on Dempster–Shafer theory of evidence. The concepts of plausibility reduct and belief reduct in incomplete information systems as well as relative plausibility reduct and relative belief reduct in incomplete decision systems are introduced. It is shown that in an incomplete information system an attribute set is a belief reduct if and only if it is a classical reduct and a plausibility consistent set must be a classical consistent set. In a consistent incomplete decision system, the concepts of relative reduct, relative plausibility reduct, and relative belief reduct are all equivalent. In an inconsistent incomplete decision system, an attribute set is a relative plausibility reduct if and only if it is a relative reduct, a plausibility consistent set must be a belief consistent set, and a belief consistent set is not a plausibility consistent set in general.