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Transactions on Rough Sets IX pp 14–34Cite as

Modified Indiscernibility Relation in the Theory of Rough Sets with Real-Valued Attributes: Application to Recognition of Fraunhofer Diffraction Patterns

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Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5390))

Abstract

The goal of the paper is to present the modification of classical indiscernibility relation, dedicated for rough set theory in a real-valued attributes space. Contrary to some other known generalizations, indiscernibility relation modified here, remains an equivalence relation and it is obtained by introducing a structure into collection of attributes. It defines real-valued subspaces, used in a multidimensional cluster analysis, partitioning the universe in a more natural way, as compared to one-dimensional discretization, iterated in classical model. Since the classical model is a special, extreme case of our modification, the modified version can be considered as more general. But more importantly, it allows for natural processing of real-valued attributes in a rough-set theory, broadening the scope of applications of classical, as well as variable precision rough set model, since the latter can utilize the proposed modification, equally well. In a case study, we show a real application of modified relation, a hybrid, opto-electronic recognizer of Fraunhofer diffraction patterns. Modified rough sets are used in an evolutionary optimization of the optical feature extractor implemented as a holographic ring-wedge detector. The classification is performed by a probabilistic neural network, whose error, assessed in an unbiased way is compared to earlier works.

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Authors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

    Krzysztof A. Cyran

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  1. Krzysztof A. Cyran
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institute of Computer Science, Warsaw University of Technology, Nowowoiejska 15/19, 00-665, Warsaw, Poland

    Henryk Rybiński

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Cyran, K.A. (2008). Modified Indiscernibility Relation in the Theory of Rough Sets with Real-Valued Attributes: Application to Recognition of Fraunhofer Diffraction Patterns. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_2

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  • DOI: https://doi.org/10.1007/978-3-540-89876-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89875-7

  • Online ISBN: 978-3-540-89876-4

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