Showing papers on "Rough set published in 2003"

Probabilistic approaches to rough sets

Abstract: This paper reviews probabilistic approaches to rough sets in granulation, approximation, and rule induction. The Shannon entropy function is used to quantitatively characterize partitions of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approximations are defined in a decision-theoretic framework. The problem of rule induction, a major application of rough set theory, is studied in probabilistic and information-theoretic terms. Two types of rules are analyzed, the local, low order rules, and the global, high order rules.

Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge

Abstract: Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets, enriching the latter with extra features to represent uncertainty (on top of vagueness). Unfortunately, the various tentative definitions of the concept of an ‘intuitionistic fuzzy rough set’ that were raised in their wake are a far cry from the original objectives of rough set theory. We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlak's original concept of rough sets.

Mining stock price using fuzzy rough set system

Abstract: In this study of mining stock price data, we attempt to predict the stronger rules of stock prices. To address this problem, we proposed an effective method, a fuzzy rough set system to predict a stock price at any given time. Our system has two agents: one is a visual display agent that helps stock dealers monitor the current price of a stock and the other is a mining agent that helps stock dealers make decisions about when to buy or sell stocks. To demonstrate that our system is effective, we used it to predict the stronger rules of stock price and achieved at least 93% accuracy after 180 trials.

On generalizing rough set theory

Abstract: This paper summarizes various formulations of the standard rough set theory It demonstrates how those formulations can be adopted to develop different generalized rough set theories The relationships between rough set theory and other theories are discussed

A New Rough Sets Model Based on Database Systems

Abstract: Rough sets theory was proposed by Pawlak in the early 1980s and has been applied successfully in a lot of domains. One of the major limitations of the traditional rough sets model in the real applications is the inefficiency in the computation of core and reduct, because all the intensive computational operations are performed in flat files. In order to improve the efficiency of computing core attributes and reducts, many novel approaches have been developed, some of which attempt to integrate database technologies. In this paper, we propose a new rough sets model and redefine the core attributes and reducts based on relational algebra to take advantages of the very efficient set-oriented database operations. With this new model and our new definitions, we present two new algorithms to calculate core attributes and reducts for feature selections. Since relational algebra operations have been efficiently implemented in most widely-used database systems, the algorithms presented in this paper can be extensively applied to these database systems and adapted to a wide range of real-life applications with very large data sets. Compared with the traditional rough set models, our model is very efficient and scalable.

Rough reduction in algebra view and information view

Abstract: Rough set (RS) is a valid theory to deal with imprecise, uncertain, and vague information. It has been applied successfully since it was developed by Professor Z. Pawlak in 1982 in such fields as machine learning, data mining, intelligent data analyzing, control algorithm acquiring, etc. The greatest advantage of the RS is its great ability to compute the reductions of information systems. Many researchers have done a lot of work in developing efficient algorithms to compute useful reductions of information systems. There also are some researchers working on the relationship between rough entropy and information entropy. They have developed some efficient reduction algorithms based on conditional information entropy. In this article, the relationship of the definitions of rough reduction in algebra view and information view is studied. Some relationships such as inclusion relationship under some conditions and equivalence relationship under some other conditions are presented. The inclusion relationship between the attribute importance defined in algebra view and information view is presented also. Some efficient heuristic reduction algorithms can be developed further using these results. © 2003 Wiley Periodicals, Inc.

Rough Set Theory and Granular Computing

Abstract: Bayes' Theorem - the Rough Set Perspective.- 1 Introduction.- 2 Bayes' Theorem.- 3 Information Systems and Approximation of Sets.- 4 Decision Language.- 5 Decision Algorithms.- 6 Decision Rules in Information Systems.- 7 Properties of Decision Rules.- 8 Decision Tables and Flow Graphs.- 9 Illustrative Example.- 10 Conclusion.- References.- Approximation Spaces in Rough Neurocomputing.- 1 Introduction.- 2 Approximation Spaces in Rough Set Theory.- 3 Generalizations of Approximation Spaces.- 4 Information Granule Systems and Approximation Spaces.- 5 Classifiers as Information Granules.- 6 Approximation Spaces for Information Granules.- 7 Approximation Spaces in Rough-Neuro Computing.- 8 Conclusion.- References.- Soft Computing Pattern Recognition: Principles, Integrations and Data Mining.- 1 Introduction.- 2 Relevance of Fuzzy Set Theory in Pattern Recognition.- 3 Relevance of Neural Network Approaches.- 4 Genetic Algorithms for Pattern Recognition.- 5 Integration and Hybrid Systems.- 6 Evolutionary Rough Fuzzy MLP.- 7 Data mining and knowledge discovery.- References.- I. Generalizations and New Theories.- Generalization of Rough Sets Using Weak Fuzzy Similarity Relations.- 1 Introduction.- 2 Weak Fuzzy Similarity Relations.- 3 Generalized Rough Set Approximations.- 4 Generalized Rough Membership Functions.- 5 An Illustrative Example.- 6 Conclusions.- References.- Two Directions toward Generalization of Rough Sets.- 1 Introduction.- 2 The Original Rough Sets.- 3 Distinction among Positive, Negative and Boundary Elements.- 4 Approximations by Means of Elementary Sets.- 5 Concluding Remarks.- References.- Two Generalizations of Multisets.- 1 Introduction.- 2 Preliminaries.- 3 Infinite Memberships.- 4 Generalization of Membership Sequence.- 5 Conclusion.- References.- Interval Probability and Its Properties.- 1 Introduction.- 2 Interval Probability Functions.- 3 Combination and Conditional Rules for IPF.- 4 Numerical Example of Bayes' Formula.- 5 Concluding Remarks.- References.- On Fractal Dimension in Information Systems.- 1 Introduction.- 2 Fractal Dimensions.- 3 Rough Sets and Topologies on Rough Sets.- 4 Fractals in Information Systems.- References.- A Remark on Granular Reasoning and Filtration.- 1 Introduction.- 2 Kripke Semantics and Filtration.- 3 Relative Filtration with Approximation.- 4 Relative Filtration and Granular Reasoning.- 5 Concluding Remarks.- References.- Towards Discovery of Relevant Patterns from Parameterized Schemes of Information Granule Construction.- 1 Introduction.- 2 Approximation Granules.- 3 Rough-Fuzzy Granules.- 4 Granule Decomposition.- References.- Approximate Markov Boundaries and Bayesian Networks: Rough Set Approach.- 1 Introduction.- 2 Data Based Probabilistic Models.- 3 Approximate Probabilistic Models.- 4 Conclusions.- References.- II. Data Mining and Rough Sets.- Mining High Order Decision Rules.- 1 Introduction.- 2 Motivations.- 3 Mining High Order Decision Rules.- 4 Mining Ordering Rules: an Illustrative Example.- 5 Conclusion.- References.- Association Rules from a Point of View of Conditional Logic.- 1 Introduction.- 2 Preliminaries.- 3 Association Rules and Conditional Logic.- 4 Association Rules and Graded Conditional Logic.- 5 Concluding Remarks.- References.- Association Rules with Additional Semantics Modeled by Binary Relations.- 1 Introduction.- 2 Databases with Additional Semantics.- 3 Re-formulating Data Mining.- 4 Mining Semantically.- 5 Semantic Association Rules.- 6 Conclusion.- References.- A Knowledge-Oriented Clustering Method Based on Indiscernibility Degree of Objects.- 1 Introduction.- 2 Clustering Procedure.- 3 Experimental Results.- 4 Conclusions.- References.- Some Effective Procedures for Data Dependencies in Information Systems.- 1 Preliminary.- 2 Three Procedures for Dependencies.- 3 An Algorithm for Rule Extraction.- 4 Dependencies in Non-deterministic Information Systems.- 5 Concluding Remarks.- References.- Improving Rules Induced from Data Describing Self-Injurious Behaviors by Changing Truncation Cutoff and Strength.- 1 Introduction.- 2 Temporal Data.- 3 Rule Induction and Classification.- 4 Postprocessing of Rules.- 5 Experiments.- 6 Conclusions.- References.- The Variable Precision Rough Set Inductive Logic Programming Model and Future Test Cases in Web Usage Mining.- 1 Introduction.- 2 The VPRS model and future test cases.- 3 The VPRSILP model and future test cases.- 4 A simple-graph-VPRSILP-ESD system.- 5 VPRSILP and Web Usage Graphs.- 6 Experimental details.- 7 Conclusions.- References.- Rough Set and Genetic Programming.- 1 Introduction.- 2 Rough Set Theory.- 3 Genetic Rough Induction (GRI).- 4 Experiments and Results.- 5 Conclusions.- References.- III. Conflict Analysis and Data Analysis.- Rough Set Approach to Conflict Analysis.- 1 Introduction.- 2 Conflict Model.- 3 System with Constraints.- 4 Analysis.- 5 Agents' Strategy Analysis.- 6 Conclusions.- References.- Criteria for Consensus Susceptibility in Conflicts Resolving.- 1 Introduction.- 2 Consensus Choice Problem.- 3 Susceptibility to Consensus.- 4 Conclusions.- References.- L1-Space Based Models for Clustering and Regression.- 1 Introduction.- 2 Fuzzy c-means Based on L1-space.- 3 Mixture Density Model Based on L1-space.- 4 Regression Models Based on Absolute Deviations.- 5 Numerical Examples.- 6 Conclusion.- References.- Upper and Lower Possibility Distributions with Rough Set Concepts.- 1 The Concept of Upper and Lower Possibility Distributions.- 2 Comparison of dual possibility distributions with dual approximations in rough set theory.- 3 Identification of Upper and Lower Possibility Distributions.- 4 Numerical Example.- 6 Conclusions.- References.- Efficiency Values Based on Decision Maker's Interval Pairwise Comparisons.- 1 Introduction.- 2 Interval AHP with Interval Comparison Matrix.- 3 Choice of the Optimistic Weights and Efficiency Value by DEA.- 4 Numerical Example.- 5 Concluding Remarks.- References.- IV. Applications in Engineering.- Rough Measures, Rough Integrals and Sensor Fusion.- 1 Introduction.- 2 Classical Additive Set Functions.- 3 Basic Concepts of Rough Sets.- 4 Rough Measures.- 5 Rough Integrals.- 6 Multi-Sensor Fusion.- 7 Conclusion.- References.- A Design of Architecture for Rough Set Processor.- 1 Introduction.- 2 Outline of Rough Set Processor.- 3 Design of Architecture.- 4 Discussions.- 6 Conclusion.- References.- Identifying Adaptable Components - A Rough Sets Style Approach.- 1 Introduction.- 2 Defining Adaptation of Software Components.- 3 Identifying One-to-one Component Adaptation.- 4 Identifying One-to-many Component Adaptation.- 5 Conclusions.- References.- Analysis of Image Sequences for the UAV.- 1 Introduction.- 2 Basic Notions.- 3 The WITAS Project.- 4 Data Description.- 5 Tasks.- 6 Results.- 7 Conclusions.- References.

Theory of Fuzzy Quotient Space (Methods of Fuzzy Granular Computing)

Abstract: In this paper, the quotient space model is extended to the fuzzy granular world and two main conclusions are given. First, the following four statements are equivalent: (1) a fuzzy equivalence relation given in universe X, (2) a normalized isosceles distance given in quotient space [X], (3) a hierarchical structure given in X, (4) a fuzzy knowledge base given in X. Second, the whole world with different fuzzy granularities composes a complete semi-order lattice. The results provide a powerful mathematical model and tool for granule computing.

Rough sets bankruptcy prediction models versus auditor signalling rates

Abstract: Both international and US auditing standards require auditors to evaluate the risk of bankruptcy when planning an audit and to modify their audit report if the bankruptcy risk remains high at the conclusion of the audit. Bankruptcy prediction is a problematic issue for auditors as the development of a cause–effect relationship between attributes that may cause or be related to bankruptcy and the actual occurrence of bankruptcy is difficult. Recent research indicates that auditors only signal bankruptcy in about 50% of the cases where companies subsequently declare bankruptcy. Rough sets theory is a new approach for dealing with the problem of apparent indiscernibility between objects in a set that has had a reported bankruptcy prediction accuracy ranging from 76% to 88% in two recent studies. These accuracy levels appear to be superior to auditor signalling rates, however, the two prior rough sets studies made no direct comparisons to auditor signalling rates and either employed small sample sizes or non-current data. This study advances research in this area by comparing rough set prediction capability with actual auditor signalling rates for a large sample of United States companies from the 1991 to 1997 time period. Prior bankruptcy prediction research was carefully reviewed to identify 11 possible predictive factors which had both significant theoretical support and were present in multiple studies. These factors were expressed as variables and data for 11 variables was then obtained for 146 bankrupt United States public companies during the years 1991–1997. This sample was then matched in terms of size and industry to 145 non-bankrupt companies from the same time period. The overall sample of 291 companies was divided into development and validation subsamples. Rough sets theory was then used to develop two different bankruptcy prediction models, each containing four variables from the 11 possible predictive variables. The rough sets theory based models achieved 61% and 68% classification accuracy on the validation sample using a progressive classification procedure involving three classification strategies. By comparison, auditors directly signalled going concern problems via opinion modifications for only 54% of the bankrupt companies. However, the auditor signalling rate for bankrupt companies increased to 66% when other opinion modifications related to going concern issues were included. In contrast with prior rough sets theory research which suggested that rough sets theory offered significant bankruptcy predictive improvements for auditors, the rough sets models developed in this research did not provide any significant comparative advantage with regard to prediction accuracy over the actual auditors' methodologies. The current research results should be fairly robust since this rough sets theory based research employed (1) a comparison of the rough sets model results to actual auditor decisions for the same companies, (2) recent data, (3) a relatively large sample size, (4) real world bankruptcy/non-bankruptcy frequencies to develop the variable classifications, and (5) a wide range of industries and company sizes. Copyright © 2003 John Wiley & Sons, Ltd.

Rough-fuzzy MLP: modular evolution, rule generation, and evaluation

Abstract: A methodology is described for evolving a Rough-fuzzy multi layer perceptron with modular concept using a genetic algorithm to obtain a structured network suitable for both classification and rule extraction. The modular concept, based on "divide and conquer" strategy, provides accelerated training and a compact network suitable for generating a minimum number of rules with high certainty values. The concept of variable mutation operator is introduced for preserving the localized structure of the constituting knowledge-based subnetworks, while they are integrated and evolved. Rough set dependency rules are generated directly from the real valued attribute table containing fuzzy membership values. Two new indices viz., "certainty" and "confusion" in a decision are defined for evaluating quantitatively the quality of rules. The effectiveness of the model and the rule extraction algorithm is extensively demonstrated through experiments alongwith comparisons.

Research on Efficient Algorithms for Rough Set Methods

Abstract: This paper makes an deep study of the reasons of the algorithms' inefficiency, mainly focuses on two important concepts: indiscernibility relation and positive region, analyzes the properties of indiscernibility relation, proposes and proves an equivalent and efficient method for computing positive region. Thus some efficient basic algorithms for rough set methods are introduced with a detailed analysis of the time complexity and comparison with the existing algorithms. Furthermore, this paper researches the incremental computing of positive region. Based on the above results, a complete algorithm for the reduction of attributes is designed. Its completeness is proved. In addition, its time complexity and space complexity are analyzed in detail. In order to test the efficiency of the algorithm, some experiments are made on the data sets in UCI machine learning repository. Theoretical analysis and experimental results show that the reduction algorithm is more efficient than those existing algorithms.

Application of rough sets in the presumptive diagnosis of urinary system diseases

Abstract: The main idea of this article is to prepare the model of the expert system, which will perform the presumptive diagnosis of two diseases of urinary system. This is an example of the rough sets theory application to generate the set of decision rules in order to solve a medical problem. The lower and upper approximations of decision concepts and their boundary regions have been formulated here. The quality and accuracy control for approximations of decision concepts family has been provided as well. Also, the absolute reducts of the condition attributes set have been separated. Moreover, the certainty, support and strength factors for all of the rules have been precisely calculated. At the end of the article, the author has also shown the reverse decision algorithm.

A rough set approach to knowledge reduction based on inclusion degree and evidence reasoning theory

Abstract: The theory of rough sets is an extension of set theory for studying intelligent systems characterized by insufficient and incomplete information. We discuss the basic concept and properties of knowledge reduction based on inclusion degree and evidence reasoning theory, and propose a knowledge discovery approach based on inclusion degree and evidence reasoning theory.

RRIA: A Rough Set and Rule Tree Based Incremental Knowledge Acquisition Algorithm

Abstract: As a special way in which the human brain is learning new knowledge, incremental learning is an important topic in AI. It is an object of many AI researchers to find an algorithm that can learn new knowledge quickly, based on original knowledge learned before, and in such way that the knowledge it acquires is efficient in real use. In this paper, we develop a rough set and rule tree based incremental knowledge acquisition algorithm. It can learn from a domain data set incrementally. Our simulation results show that our algorithm can learn more quickly than classical rough set based knowledge acquisition algorithms, and the performance of knowledge learned by our algorithm can be the same as or even better than classical rough set based knowledge acquisition algorithms. Besides, the simulation results also show that our algorithm outperforms ID4 in many aspects.

Multiple criteria linear programming approach to data mining: Models, algorithm designs and software development

Abstract: It is well known that data mining has been implemented by statistical regressions, induction decision tree, neural networks, rough set, fuzzy set and etc. This paper promotes a multiple criteria linear programming (MCLP) approach to data mining based on linear discriminant analysis. This paper first describes the fundamental connections between MCLP and data mining, including several general models of MCLP approaches. Given the general models, it focuses on a designing architecture of MCLP-data mining algorithms in terms of a process of real-life business intelligence. This architecture consists of finding MCLP solutions, preparing mining scores, and interpreting the knowledge patterns. Secondly, this paper elaborates the software development of the MCLP-data mining algorithms. Based on a pseudo coding, two versions of software (SAS- and Linux-platform) will be discussed. Finally, the software performance analysis over business and experimental databases is reported to show its mining and prediction power. As a part of the performance analysis, a series of data testing comparisons between the MCLP and induction decision tree approaches are demonstrated. These findings suggest that the MCLP-data mining techniques have a great potential in discovering knowledge patterns from a large-scale real-life database or data warehouse.

Intelligent remote monitoring and diagnosis of manufacturing processes using an integrated approach of neural networks and rough sets

Abstract: This research develops a methodology for the intelligent remote monitoring and diagnosis of manufacturing processes. A back propagation neural network monitors a manufacturing process and identifies faulty quality categories of the products being produced. For diagnosis of the process, rough set is used to extract the causal relationship between manufacturing parameters and product quality measures. Therefore, an integration of neural networks and a rough set approach not only provides information about what is expected to happen, but also reveals why this has occurred and how to recover from the abnormal condition with specific guidelines on process parameter settings. The methodology is successfully implemented in an Ethernet network environment with sensors and PLC connected to the manufacturing processes and control computers. In an application to a manufacturing system that makes conveyor belts, the back propagation neural network accurately classified quality faults, such as wrinkles and uneven thickness. The rough set also determined the causal relationships between manufacturing parameters, e.g., process temperature, and output quality measures. In addition, rough set provided operating guidelines on specific settings of process parameters to the operators to correct the detected quality problems. The successful implementation of the developed methodology also lays a solid foundation for the development of Internet-based e-manufacturing.

Feature ranking in rough sets

Abstract: The paper proposes a novel feature ranking technique using discernibility matrix. Discernibility matrix is used in rough set theory for reduct computation. By making use of attribute frequency information in discernibility matrix, the paper develops a fast feature ranking mechanism. Based on the mechanism, two heuristic reduct computation algorithms are proposed. One is for optimal reduct and the other for approximate reduct. Empirical results are also reported.

Order based genetic algorithms for the search of approximate entropy reducts

Abstract: We use entropy to extend the rough set based notion of a reduct. We show that the order based genetic algorithms, applied to the search of classical decision reducts, can be used in exactly the same way in case of extracting optimal approximate entropy reducts from data.

Automated extraction of hierarchical decision rules from clinical databases using rough set model

Abstract: One of the most important problems on rule induction methods is that they cannot extract rules, which plausibly represent experts' decision processes. On one hand, rule induction methods induce probabilistic rules, the description length of which is too short, compared with the experts' rules. On the other hand, construction of Bayesian networks generates too lengthy rules. In this paper, the characteristics of experts' rules are closely examined and a new approach to extract plausible rules is introduced, which consists of the following three procedures. First, the characterization of decision attributes (given classes) is extracted from databases and the classes are classified into several groups with respect to the characterization. Then, two kinds of sub-rules, characterization rules for each group and discrimination rules for each class in the group are induced. Finally, those two parts are integrated into one rule for each decision attribute. The proposed method was evaluated on a medical database, the experimental results of which show that induced rules correctly represent experts' decision processes.

Data mining based on rough sets

Abstract: The chapter is focused on the data mining aspect of the applications of rough set theory. Consequently, the theoretical part is minimized to emphasize the practical application side of the rough set approach in the context of data analysis and model-building applications. Initially, the original rough set approach is presented and illustrated with detailed examples showing how data can be analyzed with this approach. The next section illustrates the Variable Precision Rough Set Model (VPRSM) to expose similarities and differences between these two approaches. Then, the data mining system LERS, based on a different generalization of the original rough set theory than VPRSM, is presented. Brief descriptions of algorithms are also cited. Finally, some applications of the LERS data mining system are listed.

A view on rough set concept approximations

Abstract: The concept of approximation is one of the most fundamental in rough set theory. In this work we examine this basic notion as well as its extensions and modifications. The goal is to construct a parameterized approximation mechanism making it possible to develop multi-stage multi-level concept hierarchies that are capable of maintaining acceptable level of imprecision from input to output.