Inconsistent Decision Systems Research Articles

Topological reduction approaches for relation decision systems

In this study, we use topological methods to investigate attribute reduction problems for relation decision systems. We propose the notions of topological consistent and inconsistent relation decision systems. Then, we propose the concept of the consistent topological reduction of topological consistent relation decision systems. To enlarge the scope of application, we define the general topological reduction of relation decision systems, which is a further generalization of consistent topological reduction. Moreover, we develop corresponding reduction algorithms for these two types of reductions. To demonstrate that our algorithms cannot be unified by the general reduction algorithm, we discuss the relationship between the consistent topological reducts and the reducts identified by the general reduction algorithm. We conduct numerical experiments on 11 UCI datasets to verify our theoretical results. The experimental results demonstrate that the proposed reduction algorithms are effective and practicable.

Attribute reduction in inconsistent grey decision systems based on variable precision grey multigranulation rough set model

This paper mainly deals with attribute reduction of inconsistent grey decision systems (IGDSs) based on the variable precision grey multigranulation rough set (VP-GMGRS). Firstly, we present two transformation models to transform IGDS into consistent decision confidence system. One is the consistent decision system transformation model, based on which, an IGDS can be transformed into a VP-GMGRS approximate distribution consistent decision system. The other is the decision confidence system transformation model, which can be degenerated to a classical group decision system. Meanwhile, we educe related judgement theorems of approximation distribution consistent set in IGDS. Following that, a theoretical attribute reduction approach is presented by employing discernibility attribute sets and function based on VP-GMGRS approximate distributions. In addition, algorithms and illustrative examples with IGDS are employed and assisted to understand and explain the mechanism of attribute reduction theoretical approaches. Finally, comparison experiments are organized to verify the validity and feasibility of the proposed reduction method.

Attribute reduction approaches for general relation decision systems

This paper proposes the concept of general relation decision systems and studies attribute reduction algorithms for relation decision systems, which are generalization of decision tables. In our relation decision systems, both condition and decision attribute sets consist of general binary relations. Novel attribute reduction algorithms for consistent and inconsistent relation decision systems are derived, respectively. A data set from the UCI machine learning databases is used in the empirical study, the experimental results verify the effectiveness of the proposed algorithms. The results unify the earlier attribute reduction algorithms for decision tables.

A Rough Set-Based Method for Updating Decision Rules on Attribute Values’ Coarsening and Refining

Rule induction method based on rough set theory (RST) has received much attention recently since it may generate a minimal set of rules from the decision system for real-life applications by using of attribute reduction and approximations. The decision system may vary with time, e.g., the variation of objects, attributes and attribute values. The reduction and approximations of the decision system may alter on Attribute Values' Coarsening and Refining (AVCR), a kind of variation of attribute values, which results in the alteration of decision rules simultaneously. This paper aims for dynamic maintenance of decision rules w.r.t. AVCR. The definition of minimal discernibility attribute set is proposed firstly, which aims to improve the efficiency of attribute reduction in RST. Then, principles of updating decision rules in case of AVCR are discussed. Furthermore, the rough set-based methods for updating decision rules in the inconsistent decision system are proposed. The complexity analysis and extensive experiments on UCI data sets have verified the effectiveness and efficiency of the proposed methods.

Fast assignment reduction in inconsistent incomplete decision systems

This paper focuses on fast algorithm for computing the assignment reduct in inconsistent incomplete decision systems. It is quite inconvenient to judge the assignment reduct directly according to its definition. We propose the judgment theorem for the assignment reduct in the inconsistent incomplete decision system, which greatly simplifies judging this type reduct. On such basis, we derive a novel attribute significance measure and construct the fast assignment reduction algorithm(FARA), intended for computing the assignment reduct in inconsistent incomplete decision systems. Finally, we make a comparison between FARA and the discernibility matrixbased method by experiments on 13 University of California at Irvine(UCI) datasets, and the experimental results prove that FARA is efficient and feasible.

A Feature Selection Approach of Inconsistent Decision Systems in Rough Set

Feature selection has been widely discussed as an important preprocessing step in data mining applications since it reduces a model's complexity. In this paper, limitations of several representative reduction methods are analyzed firstly, and then by distinguishing consistent objects form inconsistent objects, decision inclusion degree and its probability distribution function as a new measure are presented for both inconsistent and consistent simplified decision systems. New definitions of distribution reduct and maximum distribution reduct for simplified decision systems are proposed. Many important propositions, properties, and conclusions for reduct are drawn. By using radix sorting and hash techniques, a heuristic distribution reduct algorithm for feature selection is constructed. Finally, compared with other feature selection algorithms on six UCI datasets, the proposed approach is effective and suitable for both consistent and inconsistent decision systems.

On knowledge acquisition in multi-scale decision systems

The key to granular computing is to make use of granules in problem solving. However, there are different granules at different levels of scale in data sets having hierarchical scale structures. Therefore, the concept of multi-scale decision systems is introduced in this paper, and a formal approach to knowledge acquisition measured at different levels of granulations is also proposed, and some algorithms for knowledge acquisition in consistent and inconsistent multi-scale decision systems are proposed with illustrative examples.

Extended rough set-based attribute reduction in inconsistent incomplete decision systems

A systematic study of attribute reduction in inconsistent incomplete decision systems (IIDSs) has not yet been performed, and no complete methodology of attribute reduction has been developed for IIDSs to date. In an IIDS, there are various ways to handle missing values. In this paper, a missing attribute value may be replaced with any known value of a corresponding attribute (such a missing attribute value is called a “do not care” condition). In this way, this paper establishes reduction concepts specifically for IIDSs, mainly by extending related reduction concepts from other types of decision systems into IIDSs, and then derives their relationships and properties. With these derived properties, the extended reducts are divided into two distinct types: heritable reducts and nonheritable reducts, and algorithms for computing them are presented. Using the relationships derived here, the eight types of extended reducts established for IIDSs can be converted to five equivalent types. Then five discernibility function-based approaches are proposed, each for a particular kind of reduct. Each approach can find all reducts of its associated type. The theoretical analysis of the proposed approaches is described in detail. Finally, numerical experiments have shown that the proposed approaches are effective and suitable for handling both numerical and categorical attributes, but that they have different application conditions. The proposed approaches can provide a solution to the reduction problem for IIDSs.

Approaches to Knowledge Reduction of Decision Systems based on Conditional Rough Entropy

Knowledge reduction in rough set theory is an important feature selection method. Since it is an NP-hard problem, it is necessary to investigate fast and effective approximate algorithms. In this paper, to address this issue, by introducing rough entropy in information systems, the novel measures of conditional rough entropy with distinguishing consistent objects form inconsistent objects are presented for both consistent and inconsistent decision systems. Thus, many important propositions, properties, and conclusions for reduct are drawn, and by using decomposition, radix sorting, hash, and input sequence techniques, we construct a forward greedy algorithm for knowledge reduction. Finally, through analyzing the given example, compared with some standard UCI datasets and other knowledge reduction algorithms, the proposed technique is effective and suitable for both consistent and inconsistent decision systems. Thus, it establishes the theoretical basis for seeking efficient algorithm of knowledge acquisition in decision systems.

Feature Selection in Decision Systems Based on Conditional Knowledge Granularity

Feature selection is an important technique for dimension reduction in machine learning and pattern recognition communities. Feature evaluation functions play essential roles in constructing feature selection algorithms. This paper introduces a new notion of knowledge granularity, called conditional knowledge granularity, reflecting relationship between conditional attributes and decision attribute. An evaluation function to measure significance of conditional attributes is proposed and equivalent characterization of attribute reduction is established based on the conditional knowledge granularity. An optimal algorithm for feature selection is developed on the basis of the proposed evaluation function. Furthermore, a novel approach to performing feature selection in an inconsistent decision system is put forward through establishing a rough communication between the inconsistent decision system and a consistent decision system. Simulated experiments verifies feasibility and efficiency of the proposed tech...

Fuzzy rough set based attribute reduction for information systems with fuzzy decisions

Fuzzy rough set is a generalization of crisp rough set to deal with data sets with real value attributes. A primary use of fuzzy rough set theory is to perform attribute reduction for decision systems with numerical conditional attribute values and crisp (symbolic) decision attributes. In this paper we define inconsistent fuzzy decision system and their reductions, and develop discernibility matrix-based algorithms to find reducts. Finally, two heuristic algorithms are developed and comparison study is provided with the existing algorithms of attribute reduction with fuzzy rough sets. The proposed method in this paper can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones. Experimental results imply that our algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.

Attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems

Attribute reduction is viewed as an important issue in data mining and knowledge representation. This paper studies attribute reduction in fuzzy decision systems based on generalized fuzzy evidence theory. The definitions of several kinds of attribute reducts are introduced. The relationships among these reducts are then investigated. In a fuzzy decision system, it is proved that the concepts of fuzzy positive region reduct, lower approximation reduct and generalized fuzzy belief reduct are all equivalent, the concepts of fuzzy upper approximation reduct and generalized fuzzy plausibility reduct are equivalent, and a generalized fuzzy plausibility consistent set must be a generalized fuzzy belief consistent set. In a consistent fuzzy decision system, an attribute set is a generalized fuzzy belief reduct if and only if it is a generalized fuzzy plausibility reduct. But in an inconsistent fuzzy decision system, a generalized fuzzy belief reduct is not a generalized fuzzy plausibility reduct in general.

A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets

Efficient attribute reduction in large, incomplete decision systems is a challenging problem; existing approaches have time complexities no less than O(∣ C∣ 2∣ U∣ 2). This paper derives some important properties of incomplete information systems, then constructs a positive region-based algorithm to solve the attribute reduction problem with a time complexity no more than O(∣ C∣ 2∣ U∣log∣ U∣). Furthermore, our approach does not change the size of the original incomplete system. Numerical experiments show that the proposed approach is indeed efficient, and therefore of practical value to many real-world problems. The proposed algorithm can be applied to both consistent and inconsistent incomplete decision systems.

Approaches to knowledge reduction of covering decision systems based on information theory

In this paper, we propose some new approaches for attribute reduction in covering decision systems from the viewpoint of information theory. Firstly, we introduce information entropy and conditional entropy of the covering and define attribute reduction by means of conditional entropy in consistent covering decision systems. Secondly, in inconsistent covering decision systems, the limitary conditional entropy of the covering is proposed and attribute reductions are defined. And finally, by the significance of the covering, some algorithms are designed to compute all the reducts of consistent and inconsistent covering decision systems. We prove that their computational complexity are polynomial. Numerical tests show that the proposed attribute reductions accomplish better classification performance than those of traditional rough sets. In addition, in traditional rough set theory, MIBARK-algorithm [G.Y. Wang, H. Hu, D. Yang, Decision table reduction based on conditional information entropy, Chinese J. Comput., 25 (2002) 1–8] cannot ensure the reduct is the minimal attribute subset which keeps the decision rule invariant in inconsistent decision systems. Here, we solve this problem in inconsistent covering decision systems.

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.

Knowledge reduction in random information systems via Dempster–Shafer theory of evidence

Knowledge reduction is one of the main problems in the study of rough set theory. This paper deals with knowledge reduction in (random) information systems based on Dempster–Shafer theory of evidence. The concepts of belief and plausibility reducts in (random) information systems are first introduced. It is proved that both of belief reduct and plausibility reduct are equivalent to classical reduct in (random) information systems. The relative belief and plausibility reducts in consistent and inconsistent (random) decision systems are then proposed and compared to the relative reduct and relationships between the new reducts and some existing ones are examined.