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Approximation Spaces in Rough–Granular Computing

Skowron A., Stepaniuk J.

Fundamenta Informaticae

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2010

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Vol. 100, nr 1/4

141-157

EN

We discuss some generalizations of the approximation space definition introduced in 1994 [24, 25]. These generalizations are motivated by real-life applications. Rough set based strategies for extension of such generalized approximation spaces from samples of objects onto their extensions are discussed. This enables us to present the uniform foundations for inducing approximations of different kinds of granules such as concepts, classifications, or functions. In particular, we emphasize the fundamental role of approximation spaces for inducing diverse kinds of classifiers used in machine learning or data mining.

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Rough Set Approach to Behavioral Pattern Identification

Bazan J.G., Bazan-Socha S., Pietrzyk J.J., Kruczek P., Skowron A.

Fundamenta Informaticae

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2007

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Vol. 75, nr 1-4

27-47

EN

The problem considered is how to model perception and identify behavioral patterns of objects changing over time in complex dynamical systems. An approach to solving this problem has been found in the context of rough set theory and methods. Rough set theory introduced by Zdzisaw Pawlak during the early 1980s provides the foundation for the construction of classifiers, relative to what are known as temporal pattern tables. Temporal patterns can be treated as features that make it possible to approximate complex concepts. This article introduces some rough set tools for perception modeling that are developed for a system for modeling networks of classifiers. Such networks make it possible to identify behavioral patterns of objects changing over time. They are constructed using an ontology of concepts delivered by experts that engage in approximate reasoning about concepts embedded in such an ontology. We also present a method that we call a method for on-line elimination of non-relevant parts (ENP). This method was developed for on-line elimination of complex object parts that are irrelevant for identifying a given behavioral pattern. The article includes results of experiments that have been performed on data from a vehicular traffic simulator and on medical data obtained from Neonatal Intensive Care Unit in the Department of Pediatrics, Collegium Medicum, Jagiellonian University. The contribution of this article is the introduction of a network of classifiers that make it possible to identify the behavioral patterns of objects that change over time.

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Concept Approximation in Mathematics and Computer Science. An Essay in Homage to Zdzisaw Pawlak

Polkowski L.

Fundamenta Informaticae

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2007

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Vol. 75, nr 1-4

435-451

EN

This article is conceived as a homage to the life and work of Professor Zdzisaw Pawlak. Intended as a mark to His 80th birthday, it turns out to be a homage to His memory. On such occasions, one is drawn into a whirl of memories, in this case reaching back to about 92', when the author met Zdzisaw because of being interested in rough sets. That theory was created in 1982 by Zdzisaw Pawlak as a vehicle to carry out Concept Approximation and a fortiori, Decision Making, Data Mining, Knowledge Discovery and other activities. The creation of rough set theory, in my opinion then and now, was a single act, ignited and facilitated by Zdzisaw's deep knowledge of ideas going back to Frege, Russell, ukasiewicz, Popper, and others. This attitude to the tradition, was certainly a strong factor that attracted to Him creative folks. Rough sets owe this attitude the intrinsic clarity of ideas, elegant simplicity (not to be confused with easy triviality), and a fortiori a wide spectrum of applications. This essay is intended as a panoramic view also on those applications. Any creation of a theory that gains recognition, many followers, and enters the standard repertoire of researchers is, in itself, an event worthy of analysis. Such analysis is not the subject of this essay; we are satisfied with presenting some views on the nature of Concept Approximation, and with outlining against this background the main features of rough sets and their extensions. In words of Cyprian Kamil Norwid: "... a few ideas that are not new...". This essay owes much to a lecture presented by the author at the Lateran University in Rome in January 2005 at the Conference Series: Scienza e Fede sull'Interpretazione del Reale; in that lecture main ideas exposed in this essay were presented. In the present exposition, some metaphysical ideas discussed in the original lecture were omitted. Nevertheless, the author takes liberty of the essay form in order to encapsulate in this text some more refined ideas than those usually inserted in technical works. The author is grateful to Professors Giandomenico Boffi and Alberto Pettorossi for invitation to Rome. On this occasion the author wishes also to invoke with personal gratitude the memory of the late Professor Helena Rasiowa who, in addition to many deep results, created much of the logical theory of rough sets.

4

Approximation Spaces Based on Relations of Similarity and Dissimilarity of Objects

Gomolińska A.

Fundamenta Informaticae

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2007

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Vol. 79, nr 3-4

319-333

EN

In this article, we aim at extension of similarity-based approximation spaces to the case, where both similarity and dissimilarity of objects are taken into account. Apart from the well-known notions of lower rough approximation, upper rough approximation, and variable-precision positive regions of concepts, adapted to our case, the notions of exterior, possibly negative region, and ignorance region of concepts are introduced and investigated.

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Calculi of Approximation Spaces

Skowron A., Stepaniuk J., Peters J., Swinarski R.

Fundamenta Informaticae

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2006

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Vol. 72, nr 1-3

363-378

EN

This paper considers the problem of how to establish calculi of approximation spaces. Approximation spaces considered in the context of rough sets were introduced by Zdzisaw Pawlak more than two decades ago. In general, a calculus of approximation spaces is a system for combining, describing, measuring, reasoning about, and performing operations on approximation spaces. An approach to achieving a calculus of approximation spaces that provides a basis for approximating reasoning in distributed systems of cooperating agents is considered in this paper. Examples of basic concepts are given throughout this paper to illustrate how approximation spaces can be beneficially used in many settings, in particular for complex concept approximation. The contribution of this paper is the presentation of a framework for calculi of approximation spaces useful for approximate reasoning by cooperating agents.

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Behavioral Pattern Identification Through Rough Set Modeling

Bazan J.G.

Fundamenta Informaticae

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2006

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Vol. 72, nr 1-3

37-50

EN

This paper introduces an approach to behavioral pattern identification as a part of a study of temporal patterns in complex dynamical systems. Rough set theory introduced by Zdzisaw Pawlak during the early 1980s provides the foundation for the construction of classifiers relative to what are known as temporal pattern tables. It is quite remarkable that temporal patterns can be treated as features that make it possible to approximate complex concepts. This article introduces what are known as behavior graphs. Temporal concepts approximated by approximate reasoning schemes become nodes in behavioral graphs. In addition, we discuss some rough set tools for perception modeling that are developed for a system for modeling networks of classifiers. Such networks make it possible to recognize behavioral patterns of objects changing over time. They are constructed using an ontology of concepts delivered by experts that engage in approximate reasoning about concepts embedded in such an ontology. We also present a method that we call a method for on-line elimination of non-relevant parts (ENP). This method was developed for on-line elimination of complex object parts that are irrelevant for identifying a given behavioral pattern. The article includes results of experiments that have been performed on data from a vehicular traffic simulator useful in the identification of behavioral patterns by drivers.

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Spatio-Temporal Approximate Reasoning over Complex Objects

Synak P., Bazan J.G., Skowron A., Peters J.F.

Fundamenta Informaticae

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2005

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Vol. 67, nr 1-3

249-269

EN

We discuss the problems of spatio-temporal reasoning in the context of hierarchical information maps and approximate reasoning networks (AR networks). Hierarchical information maps are used for representations of domain knowledge about objects, their parts, and their dynamical changes. AR networks are patterns constructed over sensory measurements and they are discovered from hierarchical information maps and experimental data. They make it possible to approximate domain knowledge, i.e., complex spatio-temporal concepts and reasonings represented in hierarchical information maps. Experiments with classifiers based on AR schemes using a road traffic simulator are also briefly presented.

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Rough Set Approach to Domain Knowledge Approximation

Nguyen T.T.

Fundamenta Informaticae

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2004

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Vol. 59, nr 2,3

261--270

EN

Classification systems working on large feature spaces, despite extensive learning, often perform poorly on a group of atypical samples. The problem can be dealt with by incorporating domain knowledge about samples being recognized into the learning process. We present a method that allows to perform this task using a rough approximation framework. We show how human expert's domain knowledge expressed in natural language can be approximately translated by a machine learning recognition system. We present in details how the method performs on a system recognizing handwritten digits from a large digit database. Our approach is an extension of ideas developed in the rough mereology theory.

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Complex Patterns

Skowron A., Synak P.

Fundamenta Informaticae

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2004

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Vol. 60, nr 1-4

351--366

EN

We outline some results of our current research on developing a methodology for solving problems of spatio-temporal reasoning. We consider classifiers for complex concepts in spatio-temporal reasoning that are constructed hierarchically. We emphasise the fact that the construction of such hierarchical classifiers should be supported by domain knowledge. Approximate reasoning networks (AR networks) are proposed for approximation of reasoning schemes expressed in natural language. Such reasoning schemes are extracted from knowledge bases representing domain knowledge. This approach makes it possible to induce classifiers for complex concepts by constructing them along schemes of reasoning extracted from domain knowledge.