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Ślęzak D., Synak P., Wojna A., Wróblewski J.

Fundamenta Informaticae

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2013

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Vol. 127, nr 1-4

445--459

EN

We present analytic data processing technology derived from the principles of rough sets and granular computing. We show how the idea of approximate computations on granulated data has evolved toward complete product supporting standard analytic database operations and their extensions. We refer to our previous works where our query execution algorithms were described in terms of iteratively computed rough approximations. We explain how to interpret our data organization methods in terms of classical rough set notions such as reducts and generalized decisions.

2

On Stability and Classification Tools for Genetic Algorithms

Kotowski S., Kosiński W., Michalewicz Z., Synak P., Brocki Ł.

Fundamenta Informaticae

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2009

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Vol. 96, nr 4

477-491

EN

Convergence of genetic algorithms in the form of asymptotic stability requirements is discussed. Some tools to measure convergence properties of genetic algorithms are introduced. A classification procedure is proposed that is based on the following conjecture: the entropy and the fractal dimension of trajectories of genetic algorithms produced by them are quantities that can characterize the algorithms. The role of these quantities as invariants of the algorithm classes is discussed together with the compression ratio of points of genetic algorithms.

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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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Reasoning in Information Maps

Skowron A., Synak P.

Fundamenta Informaticae

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2004

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Vol. 59, nr 2,3

241--259

EN

We investigate patterns over information maps. Such patterns can represent information changes (e.g., in time or space) across information maps. Any map is defined by some transition relation on states. Each state is a pair consisting of a label and information related to the label. Introduced concepts are illustrated by examples. We also discuss searching problems for relevant patterns extracted from data stored in information maps. Some patterns can be expressed by temporal formulas. Then, searching is reduced to searching for relevant temporal formulas. We generalise association rules over information systems to association rules over information maps. Approximate reasoning methods based on information changes are important for many applications (e.g., related to spatio-temporal reasoning). We introduce basic concepts for approximate reasoning about information changes across information maps. We measure degree of changes using information granules. Any rule for reasoning about information changes specifies how changes of information granules from the rule premise influence changes of information granules from the rule conclusion. Changes in information granules can be measured, e.g., using expressions analogous to derivatives. Illustrative examples are also presented.

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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.