Concept Of Rough Sets Research Articles

α-RST: a generalization of rough set theory

The paper presents a transition from the crisp rough set theory to a fuzzy one, called Alpha Rough Set Theory or, in short, α-RST. All basic concepts or rough set theory are extended, i.e., information system, indiscernibility, dependency, reduction, core, definability, approximations and boundary. The resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts. Besides, the control of knowledge granularity is natural in α-RST which is based on a parameterized indiscernibility relation. α-RST is developed to recognize non-deterministic relationships using notions as α-dependency, α-reduct and so forth. On the other hand, we introduce a notion of relative dependency as an alternative of the absolute definibility presented in rough set theory. The extension α-RST leads naturally to the new concept of alpha rough sets which represents sets with fuzzy non-empty boundaries.

Modelling prognostic power of cardiac tests using rough sets

Rough sets (Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data, Dordrecht: Kluwer Academic Publishers, 1991) is a relatively new approach to representing and reasoning with incomplete and uncertain knowledge. This article introduces the basic concepts of rough sets and Boolean reasoning (Brown FM. Boolean Reasoning: The Logic of Boolean Equations, Dordrecht: Kluwer Academic Publishers, 1990). A rough set framework is then set up to investigate the prognosis of cardiac events in a set of patients with chest pain that was earlier studied by Geleijnse et al. (J Am Coll Cardiol 1996;28(2):447–454). That study used logistic regression to find that the single most important independent predictor for future hard cardiac events (cardiac death or non-fatal myocardial infarction) was an abnormal scintigraphic scan pattern. However, performing a scintigraphic scan is a relatively expensive procedure, and may for some patients not really be fully necessary as knowledge of the outcome of the scan may be redundant with respect to making a prognosis. Using an approach based on rough sets, this paper explores how a patient group in need of a scintigraphic scan can be identified for subsequent modelling. Identification of such patients may potentially contribute to lowering the cost of medical care and to improving its quality since, virtually without loss of information, fewer patients may be referred for this procedure.

Interval Regression Analysis with Polynomials and Its Similarity to Rough Sets Concept

This paper proposes interval regression analysis with polynomials. For data sets with crisp inputs and interval outputs, three estimation models called as an upper, a lower, and a possibility estimation models can be formulated from the concepts of the possibility and necessity measures. Always there exists an upper and a possibility estimation model when a linear system with interval coefficients is considered, but it is not assured to attain a solution for a lower estimation model in an interval linear system. If we can not obtain the lower estimation model, it might be caused by adopting a model not fitting to the given data. Thus we consider polynomials to find a regression model which fits well to the given observations. The possibility model is used to check the existence of the lower model. If we can find a proper lower model, the estimated upper and lower models deserve more credit than the previous models in the former studies. We also introduce the measure of fitness to gauge the degree of approximation of the obtained models to the given data. The upper and lower estimation models in interval regression analysis can be considered as the upper and lower approximations in rough sets. The similarity between the interval estimation models and the rough sets concept is also discussed. In order to illustrate our approach, numerical examples are shown.

Rough Set Application to Data Mining Principles in Pavement Management Database

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.

Interpretation preservation of adaptive fuzzy inference systems

The membership functions of an adaptive fuzzy inference system, during the adaptation process, may lose the meaning which was initially assigned to them. In this paper, the concept of rough sets is used to propose a constraint training algorithm. The proposed algorithm maintains the interpretation of the adaptive fuzzy inference systems during the training. The constraints on membership functions are implemented by means of hard or soft limit bounds on the updating parameters of membership functions. An example to illustrate the algorithm is included.

ROUGH CONCEPT ANALYSIS: A SYNTHESIS OF ROUGH SETS AND FORMAL CONCEPT ANALYSIS

The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak [10] with the theory of Formal Concept Analysis pioneered by Rudolf Wille [11]. The central notion in this paper of a rough formal concept combines in a natural fashion the two notions of rough set and formal concept — to use a slogan: “rough set + formal concept = rough formal concept”. This paper is an extension of the paper [5] presented at the international workshop on Rough Sets and Knowledge Discovery (RSKD'93). A related paper [8] using distributed constraints provides a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis, and Entity-Relationship database modeling. A follow-up paper [9] will extend rough concept analysis from formal contexts to distributed constraints.

A COMMON ALGEBRAIC FRAMEWORK OF EMPIRICAL LEARNING METHODS BASED ON ROUGH SETS AND MATROID THEORY

In order to acquire knowledge from databases, there have been proposed several methods of inductive learning, such as ID3 family and AQ family. These methods are applied to discover meaningful knowledge from large databases, and their usefulness is ensured. However, since there has been no formal approach proposed to treat these methods, efficiency of each method is only compared empirically. In this paper, we introduce matroid theory and rough sets to construct a common framework for empirical machine learning methods which induce the combination of attribute-value pairs from databases. Combination of the concepts of rough sets and matroid theory gives us an excellent set-theoretical framework and enables us to understand the differences and the similarities between these methods clearly. In this paper, we compare three classical methods, AQ, Pawlak's Consistent Rules and ID3. The results show that there exist the differences in algebraic structure between the former two and the latter and that this causes the differences between AQ and ID3.

Fuzzy rough sets

The purpose of this paper is to introduce and discuss the concept of fuzzy rough sets.

INCREMENTAL LEARNING OF PRODUCTION RULES FROM EXAMPLES UNDER UNCERTAINTY: A ROUGH SET APPROACH

This paper introduces an algorithm, LEM3, for incremental learning of production rules from examples. Based on the concept of rough sets introduced by Pawlak, LEM3 is capable of learning rules from consistent as well as inconsistent examples. In LEM3, rules are generated by using the rule-generating procedure implemented in a nonincremental learning program LEM2. Consequently, the rules learned by LEM3 do not use redundant attribute-value pairs. One major feature of LEM3 is the incorporation of a separate global data structure for storing information learned from new examples. The global data structure is updated on an example by example basis, and it provides all the essential information for the incremental updating of lower and upper approximations of a concept and the generating of rules. This separation of learned knowledge from rule-generating procedures provides a more modular design of learning systems.

Rough sets approach to analysis of data from peritoneal lavage in acute pancreatitis.

Two kinds of information systems composed of data from peritoneal lavage in acute pancreatitis are analysed with the concept of rough sets: system A, classifying patients described by pre-lavage attributes, and system B, classifying patients described by attributes of the course of the multistage lavage. The analysis tends to define subsets which are significant for high quality of classification. These attributes give the best description of the patient's state and are in the closest relationship with the time of lavage. The character of this relationship is shown by decision algorithms derived from decision tables representing the information system.

A methodology of design knowledge acquisition for use in learning expert systems

This paper presents an approach to design conceptual knowledge acquisition. The approach was basically developed for knowledge acquisition in BRZDY1, a learning expert system for conceptual design currently under development. A formal identification of qualitative, conceptual design decisions, based on typology by coverings and the description of design problems by qualitative variables, is discussed. Also, we describe the fundamentals of the method of generating design rules from examples of decisions made by an expert. This method is based on the extended concept of rough set. A comprehensive example of the application of this method to conceptual design of steel members under bending is provided at the end of the paper.

Comparison of rough-set and statistical methods in inductive learning

Quinlan suggested an inductive algorithm based on the statistical theory of information originally proposed by Shannon. Recently Pawlak showed that the principles of inductive learning (learning from examples) can be precisely formulated on the basis of the theory of rough sets. These two approaches are apparently very different, although in both methods objects in the knowledge base are assumed to be characterized by “features” (attributes and attribute values). The main objective of this paper is to show that the concept of “approximate classification” of a set is closely related to the statistical approach. In fact, in the design of inductive programs, the criterion for selecting dominant attributes based on the concept of rough sets is a special case of the statistical method if equally probable distribution of objects in the “doubtful region” of the approximation space is assumed.

Rough Grammars

In the paper we define the notions of the best lower and the best upper approximations of grammar, which are based on the concept of rough set introduced by Pawlak in [4]. Furthermore we give the properties of languages generated by the best lower and the best upper approximations of grammar.