Showing papers on "Rough set published in 1997"

Principles and Applications

Abstract: From the Publisher: This volume presents the results of approximately 15 years of work from researchers around the world on the use of fuzzy set theory to represent imprecision in databases. The maturity of the research in the discipline and the recent developments in commercial/industrial fuzzy databases provided an opportunity to produce this survey. Fuzzy Databases: Principles and Applications is self-contained providing background material on fuzzy sets and database theory. It is comprehensive covering all of the major approaches and models of fuzzy databases that have been developed including coverage of commercial/industrial systems and applications. Background and introductory material are provided in the first two chapters. The major approaches in fuzzy databases comprise the second part of the volume. This includes the use of similarity and proximity measures as the fuzzy techniques used to extend the relational data modeling and the use of possibility theory approaches in the relational model. Coverage includes extensions to the data model, querying approaches, functional dependencies and other topics including implementation issues, information measures, database security, alternative fuzzy data models, the IFO model, and the network data models. A number of object-oriented extensions are also discussed. The use of fuzzy data modeling in geographical information systems (GIS) and use of rough sets in rough and fuzzy rough relational data models are presented. Major emphasis has been given to applications and commercialization of fuzzy databases. Several specific industrial/commercial products and applications are described. These include approaches to developing fuzzy front-end systems and special-purpose systems incorporating fuzziness.

Incomplete Information: Rough Set Analysis

Abstract: Introduction: What You Always Wanted to Know about Rough Sets.- Rough Sets and Decision Rules: Synthesis of Decision Rules for Object Classification On the Lower Boundaries in Learning Rules from Examples On the Best Search Method in the LEM1 and LEM2 Algorithms.- Algebraic Structure of Rough Set Systems: Rough Sets and Algebras of Relations Rough Set Theory and Logic-Algebraic Structures.- Dependence Spaces: Dependence Spaces of Information Systems Applications of Dependence Spaces.- Reasoning About Constraints: Indiscernibility-Based Formalization of Dependencies in Information Systems Dependencies between Many-Valued Attributes.- Indiscernibility-Based Reasoning: Logical Analysis of Indiscernibility Some Philosophical Aspects of Indiscernibility Rough Mereology and Anayltical Morphology.- Similarity-Based Reasoning: Similarity Versus Preference in Fuzzy-Based Logics A Logic for Reasoning about Similarity Information Systems, Similarity Relations and Modal Logics.- Extended Rough Set-Based Deduction Methods: Axiomatization of Logics Based on Kripke Models with Relative Accessibility Relations Rough Logics: A Survey with Further Directions On the Logic with Rough Quantifier.

A Review of Rough Set Models

Abstract: Since introduction of the theory of rough set in early eighties, considerable work has been done on the development and application of this new theory. The paper provides a review of the Pawlak rough set model and its extensions, with emphasis on the formulation, characterization, and interpretation of various rough set models.

Combination of Rough and Fuzzy Sets Based on α-Level Sets

Abstract: A fuzzy set can be represented by a family of crisp sets using its α-level sets, whereas a rough set can be represented by three crisp sets. Based on such representations, this paper examines some fundamental issues involved in the combination of rough-set and fuzzy-set models. The rough-fuzzy-set and fuzzy-rough-set models are analyzed, with emphasis on their structures in terms of crisp sets. A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space, and a fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a crisp set in a fuzzy approximation space. The approximation of a fuzzy set in a fuzzy approximation space leads to a more general framework. The results may be interpreted in three different ways.

Statistical evaluation of rough set dependency analysis

Abstract: Rough set data analysis (RSDA) has recently become a frequently studied symbolic method in data mining. Among other things, it is being used for the extraction of rules from databases; it is, however, not clear from within the methods of rough set analysis, whether the extracted rules are valid.In this paper, we suggest to enhance RSDA by two simple statistical procedures, both based on randomization techniques, to evaluate the validity of prediction based on the approximation quality of attributes of rough set dependency analysis. The first procedure tests the casualness of a prediction to ensure that the prediction is not based on only a few (casual) observations. The second procedure tests the conditional casualness of an attribute within a prediction rule.The procedures are applied to three data sets, originally published in the context of rough set analysis. We argue that several claims of these analyses need to be modified because of lacking validity, and that other possibly significant results were overlooked.

Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices)

Abstract: The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (“indiscernibility”) relation R \( \subseteq\) U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.

Rough Set Approach to Multi-Attribute Choice and Ranking Problems

Abstract: We propose an original way of applying the rough set theory to the analysis of multi-attribute preference systems in the choice (Pa) and ranking (Py) decision problematics. From the viewpoint of rough set theory, this approach implies to consider a pairwise comparison table, i.e. an information table whose objects are pairs of actions instead of single actions, and whose entries are binary relations instead of attribute values. From the viewpoint of multi-attribute decision methodology, this approach allows both representation of decision maker’s (DM’s) preferences in terms of “if …then…” rules and their use for recommendation in Pa and Py problematics, without assessing such preference parameters as importance weights and substitution rates. The rule representation of DM’s preferences is alternative to traditionally decision support models. The rough set approach to (Pα) and (Pβ) is explained in detail and illustrated by a didactic example.

GRANULAR COMPUTING: From Rough Sets and Neighborhood Systems to Information Granulation and Computing with Words

Abstract: Rough set methodology relevant to granular computing are formulated and generalized to other schemes of granulation that are based on neighborhood systems and their fuzzification.

Data Mining: Trends in Research and Development

Abstract: Data mining is an interdisciplinary research area spanning several disciplines such as database systems, machine learning, intelligent information systems, statistics, and expert systems. Data mining has evolved into an important and active area of research because of theoretical challenges and practical applications associated with the problem of discovering (or extracting) interesting and previously unknown knowledge from very large real-world databases. Many aspects of data mining have been investigated in several related fields. But the problem is unique enough that there is a great need to extend these studies to include the nature of the contents of the real-world databases. In this chapter, we discuss the theory and foundational issues in data mining, describe data mining methods and algorithms, and review data mining applications. Since a major focus of this book is on rough sets and its applications to database mining, one full section is devoted to summarizing the state of rough sets as related to data mining of real-world databases. More importantly, we provide evidence showing that the theory of rough sets constitutes a sound basis for data mining applications.

Vagueness - a Rough Set View

Abstract: Vagueness for a long time has been studied by philosophers, logicians and linguists. Recently researchers interested in AI contributed essentially to this area.

Analyzing Discretizations of Continuous Attributes Given a Monotonic Discrimination Function

Abstract: This article addresses the problem of analyzing existing discretizations of continuous attributes with regard to their redundancy and minimality properties. The research was inspired by the increasing number of heuristic algorithms created for generating the discretizations using various methodologies, and apparent lack of any direct techniques for examining the solutions obtained as far as their basic properties, e.g., the redundancy, are concerned. The proposed method of analysis fills this gap by providing a test for redundancy and enabling for a controlled reduction of the discretization's size within specified limits. Rough set theory techniques are used as the basic tools in this method. Exemplary results of discretization analyses for some known real-life data sets are presented for illustration.

Decision algorithms: a survey of rough set-theoretic methods

Abstract: In this paper we present some strategies for synthesis of decision algorithms studied by us. These strategies are used by systems of communicating agents and lead from the original (input) data table to a decision algorithm. The agents are working with parts of data and they compete for the decision algorithm with the best quality of object classification. We give examples of techniques for searching for new features and we discuss some adaptive strategies based on the rough set approach for the construction of a decision algorithm from a data table. We also discuss a strategy of clustering by tolerance.

Information-based algorithm for reduction of knowledge

Abstract: In Rough Set (RS) theory, it has been proved that finding the minimal reduct of an information system is an NP-complete problem. Because of this, it is hard to obtain the set of the most concise rules by existing algorithm in RS for reduction of knowledge. In this paper, an information-based algorithm for reduction of knowledge is proposed, and its time complexity is analyzed. Through an example, we show that the proposed algorithm is effective for dealing with relatively large-scale databases.

Synthesis of Decision Systems from Data Tables

Abstract: We discuss two basic questions related to the synthesis of decision algorithms The first question can be formulated as follows: what strategies can be used in order to discover the decision rules from experimental data? Answering this question, we propose to build these strategies on the basis of rough set methods and Boolean reasoning techniques We present some applications of these methods for extracting decision rules from decision tables used to represent experimental data The second question can be formulated as follows: what is a general framework for approximate reasoning in distributed systems? Answering this question, we assume that distributed systems are organized on rough mereological principles in order to assembly (construct) complex objects satisfying a given specification in a satisfactory degree We discuss how this approach can be used for building the foundations for approximate reasoning Our approach is based on rough mereology, the recently developed extension of mereology of Lesniewski

Maintenance of Reducts in the Variable Precision Rough Set Model

Abstract: Definitions of a reduct for a single object, decision class and all objects of decision table for the variable precision rough set model are introduced. The definitions have a property that the set of prime implicants of minimal disjunctive normal form of a discernibility function is equal to the set of reducts. Thus the problem of reducts maintenance in dynamically extended information systems is equivalent to the problem of discernibility function maintenance. We prove that the problem can be stated in the form of a Boolean equation: g ⋀ h = f ⋀ k, where f, h and k are given monotonic Boolean functions and g is a function to be determined in minimal disjunctive normal form. An incremental algorithm finding the solution of the above equation is proposed.

Topological Rough Algebras

Abstract: It is known ([15]) that the propositional aspect of rough set theory is adequately captured by the modal system S5. A Kripke model gives the approximation space (A,R) in which well formed formulas are interpreted as rough sets. Banejee and Chakraborty ([1]) introduced a new binary connective in S5, the intended interpretation of which was the notion of rough equality, defined by Pawlak in 1982. They called the resulting Lindenbaum-Tarski like algebra a rough algebra. We show here that their rough algebra is a particular case of a quasi-Boolean algebra (as introduced in [4]). It also leads to a definition of the new classes of algebras, called topological quasi-Boolean algebras2 and topological rough algebras. We introduce, following Rasiowa and Bialynicki-Birula’s representation theorem for the quasi-Boolean algebras ([4], [20]), a notion of quasi field of sets and generalize it to a new notion of a topological quasi field of sets. We use it to give the representation theorems for the topological quasi-Boolean algebras and topological rough algebras, and hence to provide a mathematical characterization of the rough algebra.

Rough real functions and rough controllers

Abstract: This paper is an extension of articles Pawlak (1987), where some ideas concerning rough functions were outlined. The concept of the rough function is based on the rough set theory (Pawlak, 1991) and is needed in many applications, where experimental data are processes, in particular as a theoretical basis for rough controllers (Czogala et al., 1994, Mrozek and Plonka, 1994).

Rough set application to data mining principles in pavement management database

Abstract: This paper presents a new approach to rough set theory in pavement rehabilitation and maintenance decision support systems. A rough set-based analysis acts like a knowledge engineer who sits between data and the user. The rough set concept is an effective tool for analysis of information systems in a pavement management system (PMS) database gained by both objective and subjective methods. The rough set approach in a PMS database enables pavement engineers to discover minimal subsets of condition attributes in assessing and describing the pavement conditions, and to derive decision rules in rehabilitation and maintenance decision making. The approach appears to capture information on uncertainty, imprecision, and ambiguity along with precise values in a PMS database.

Incremental learning of probabilistic rules from clinical databases based on rough set theory.

Abstract: Several rule induction methods have been introduced in order to discover meaningful knowledge from databases, including medical domain. However, most of the approaches induce rules from all the data in databases and cannot induce incrementally when new samples are derived. In this paper, a new approach to knowledge acquisition, which induce probabilistic rules incrementally by using rough set technique, is introduced and was evaluated on two clinical databases. The results show that this method induces the same rules as those induced by ordinary non-incremental learning methods, which extract rules from all the datasets, but that the former method requires more computational resources than the latter approach.

Learning maximal generalized decision rules via discretization, generalization and rough set feature selection

Abstract: We present a method to mine maximal generalized decision rules from databases by integrating discretization, generalization and rough sets feature selection. Our method reduces the data horizontally and vertically. In the first phase, discretization and generalization are integrated and the numeric attributes are discretized into a few intervals. Primitive values of symbolic attributes are replaced by high level concepts and some obvious superfluous or irrelevant symbolic attributes are also eliminated. Horizontal reduction is accomplished by merging identical tuples after the substitution of an attribute value by its higher level value in a predefined concept hierarchy for symbolic attributes or the discretization of continuous (or numeric) attributes. In the second phase, a novel context sensitive feature merit measure is used to rank the features, a subset of relevant attributes is chosen based on rough sets theory and the merit values of the features. A reduced table is obtained by removing those attributes which are not in the relevant attributes subset and the data set is further reduced vertically without destroying the interdependence relationships between the classes and the attributes. Rough sets based value reduction is further performed on the reduced table and all redundant condition values are dropped, finally, tuples in the reduced table are transformed into a set of maximal generalized decision rules. The experimental results on UCI data sets and an actual market database shows that our method can dramatically reduce the feature space and improve the learning accuracy.

Rough Control: A Perspective

Abstract: Observing the current state of commercial and industrial AI, control and hybrid systems are said to have the highest potentials for massive practical applications of rough set theory. After a brief description of the control problem and fuzzy systems, the principles of rough control and a scenario of fine temperature control are discussed.

Rough Set Theory and Rule Induction Techniques for Discovery of Attribute Dependencies in Medical Information Systems

Abstract: Problems connected with applications of the rough set theory to identify the most important attributes and with induction of decision rules from the medical data set are discussed in this paper. The medical data set concerns patients with multiple injuries. The direct use of the original rough set model leads to finding too many possibilities of reducing the input data. To solve this difficulty, a new approach integrating rough set theory, rule induction and statistical techniques is introduced. First, the Chi-square test is additionally performed in order to reject non-significant attributes. Then, starting from remaining attributes we try to construct such definitions of new attributes that improve finally discovered decision rules. The results have shown that the proposed approach integrating all methods has given better results than those obtained by applying the original rough set method.

A Fusion of Rough Sets, Modified Rough Sets, and Genetic Algorithms for Hybrid Diagnostic Systems

Abstract: A hybrid classification system is a system composed of several intelligent techniques such that the inherent limitations of one individual technique be compensated for by the strengths of another technique. In this paper, we investigate the outline of a hybrid diagnostic system for Attention Deficit Disorder (ADD) in children. This system uses Rough Sets (RS) and Modified Rough Sets (MRS) to induce rules from examples and then uses our modified genetic algorithms to globalize the rules. Also, the classification capability of this hybrid system was compared with the behavior of (a) another hybrid classification system using RS, MRS, and the “dropping condition” approach, (b) the Interactive Dichotomizer 3 (ID3) approach, and (c) a basic genetic algorithm.

Searching for Relational Patterns in Data

Abstract: We consider several basic classes of tolerance relations among objects. These (global) relations are defined from some predefined similarity measures on values of attributes. A tolerance relation in a given class of tolerance relations is optimal with respect to a given decision table A if it contains only pairs of objects with the same decision and the number of such pairs contained in the relation is maximal among all relations from the class. We present a method for (sub-)optimal tolerance relation learning from data (decision table). The presented method is based on rough set approach. We show that for some basic families of tolerance relations this problem can be transformed to a relative geometrical problem in a real affine space. Hence geometrical computations are becoming useful tools for solving the problem of global tolerance relation construction. The complexity of considered problems can be evaluated by the complexity of the corresponding geometrical problems. We propose some efficient heuristics searching for an approximation of optimal tolerance relations in considered families of tolerance relations. The global tolerance relations can be treated as patterns in the cartesian product of the object set. We show how to apply the relational patterns (global tolerance relations) in clustering and classification of objects.

A new approach for fault diagnosis in power systems based on rough set theory

Abstract: This paper proposes a new rough set (RS) based approach for power system fault diagnosis using the information of relays and circuit breakers. The RS approach is developed to deal with the corrupted alarm patterns. The proposed approach has been tested on an example power system. The test results, although preliminary, suggest that the method can handle the imperfect alarm signals effectively. The significant advantage of the new method is that it can discriminate the indispensable alarm signals from dispensable ones that would not affect the correctness of the diagnosis results even if they are missing or erroneous.

Generation of Multiple Knowledge from Databases Based on Rough Sets Theory

Abstract: In this paper we present a new approach to generate multiple knowledge using rough sets theory. The idea is to generate several knowledge bases instead of one knowledge base for the classification of new object, hoping that the combination of answers of multiple knowledge bases result in better performance. Multiple knowledge bases can be formulated precisely and in an unified way within the framework of rough sets theory. Our approach is based on the reducts and decision matrix of the rough set theory. Our method first eliminates the superfluous attributes from the databases, next, the minimal decision rules are obtained through decision matrices. Then a set of reducts which include all the indispensable attributes to the learning task are computed, finally, the minimal decision rules are grouped to the corresponding reducts to form different knowledge bases. We attempt to make a theoretical model by using rough sets theory to explain the generation of multiple knowledge. The distinctive feature of our method over other methods of generating multiple knowledge is that in our method, each knowledge base is as accurate and complete as possible and at the same time as different from the other knowledge bases as possible. The test result shows the higher classification accuracy produced by multiple knowledge bases than that produced by single knowledge base.

Rough Sets as a Tool for Studying Attribute Dependencies in the Urinary Stones Treatment Data Set

Abstract: The medical experience with urolithiasis patients treated by the extracorporeal shock wave lithotripsy (ESWL) is analysed using the rough set approach The evaluation of the significance of attributes for qualifying patients to the ESWL treatment is the most important problem for the clinical practice The use of a simple rough set model gives a high number of possible reducts which are difficult to interpret So, the heuristic strategies based on the rough set theory are proposed to select the most significant attributes All these strategies lead to similar results having a good clinical interpretation