Tolerance Approximation Spaces

Skowron, Andrzej; Stepaniuk, Jarosław

doi:10.3233/fi-1996-272311

Cited by 821 publications

(164 citation statements)

References 12 publications

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“…The theory and practice of such systems is to come in future. In (Polkowski and Skowron 2000) ideas of rough-neurocomputing based on approximation spaces (Skowron and Stepaniuk 1996;Stepaniuk 2000) are proposed.…”

Section: A Neural Model Of Rough Mereological Computationmentioning

confidence: 99%

Rough Mereological Calculi of Granules: A Rough Set Approach To Computation

Polkowski

Skowron

2001

Computational Intelligence

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Rough Mereology is a paradigm allowing for a synthesis of main ideas of two potent paradigms for reasoning under uncertainty: Fuzzy Set Theory and Rough Set Theory. Approximate reasoning is based in this paradigm on the predicate of being a part to a degree. We present applications of Rough Mereology to the important theoretical idea put forth by Lotfi Zadeh (1996, 1997), i.e., Granularity of Knowledge: We define granules of knowledge by means of the operator of mereological class and we extend the idea of a granule over complex objects like decision rules as well as decision algorithms. We apply these notions and methods in the distributed environment discussing complex problems of knowledge and granule fusion. We express the mechanism of complex granule formation by means of a formal grammar called Synthesis Grammar defined over granules of knowledge, granules of classifying rules, or over granules of classifying algorithms. We finally propose hybrid rough-neural schemes bridging rough and neural computations. 1

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Section: A Neural Model Of Rough Mereological Computationmentioning

confidence: 99%

Rough Mereological Calculi of Granules: A Rough Set Approach To Computation

Polkowski

Skowron

2001

Computational Intelligence

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“…Extension of granules defined by tolerance relation. Now we present examples of granules obtained by application of a tolerance relation (i.e., reflexive and symmetric relation; for more information see, e.g., Skowron and Stepaniuk 1996). Example 6.…”

Section: Syntax and Semantics Of Information Granulesmentioning

confidence: 99%

“…Example 7. Let us consider granules defined by rules of tolerance information systems (Skowron and Stepaniuk 1996). Let IS = U A be an information system and let be a tolerance relation on elementary granules of IS.…”

Section: Syntax and Semantics Of Information Granulesmentioning

confidence: 99%

“…In the standard rough set model Pawlak 1991 elementary granules describe indiscernibility classes with respect to some subsets of attributes. In a more general setting (see, e.g., Skowron and Stepaniuk 1996) tolerance (similarity) classes are described.…”

Section: Granule Inclusion and Closenessmentioning

confidence: 99%

“…We adopt some basic ideas developed in rough mereological approach (see e.g., Polkowski and Skowron 1996Komorowski, Pawlak, Polkowski, and Skowron, 1999). In our approach a crucial role play the rough set approach (Pawlak, 1991;Komorowski, Pawlak, Polkowski, and Skowron 1999) especially the approximation operations in generalized approximation spaces (Skowron and Stepaniuk 1996).…”

Section: Introductionmentioning

confidence: 99%

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Granular Computing: a Rough Set Approach

Nguyen

Skowron

Stepaniuk

2001

Computational Intelligence

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We discuss information granule calculi as a basis of granular computing. They are defined by constructs like information granules, basic relations of inclusion and closeness between information granules as well as operations on them. The exact interpretation between granule languages of different information sources (agents) often does not exist. Hence (rough) inclusion and closeness of granules are considered instead of their equality. Examples of all the basic constructs of information granule calculi are presented. The construction of more complex information granules is described by expressions called terms. We discuss the synthesis problem of robust terms, i.e., descriptions of information granules, satisfying a given specification in a satisfactory degree. We also present a method for synthesis of information granules represented by robust terms (approximate schemes of reasoning) by means of decomposition of specifications for such granules. The discussed problems of granular computing are of special importance for many applications, in particular related to spatial reasoning as well as to knowledge discovery and data mining.

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Computational Intelligence

Pedrycz¹

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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Tolerance Approximation Spaces

Cited by 821 publications

References 12 publications

Rough Mereological Calculi of Granules: A Rough Set Approach To Computation

Rough Mereological Calculi of Granules: A Rough Set Approach To Computation

Granular Computing: a Rough Set Approach

Computational Intelligence

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