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Granular Rough Mereological Logics with Applications to Dependencies in Information and Decision Systems

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Transactions on Rough Sets XII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 6190))

Abstract

We are concerned with logical formulas induced from data sets, in particular, with decision rules. Contrary to the standard practice of many–valued logics in which formulas are semantically interpreted as their states /values of truth and logical calculi consist essentially in finding functional interpretations of logical functors, in the considered by us case, the semantic interpretation takes place in the universe of entities/objects and formulas are interpreted as their meanings, i.e., subsets of the object universe. Yet, the final evaluation of a formula should be its state of truth. In search of an adequate formal apparatus for this task, we turn to rough mereology and to the idea of intensionality vs. extensionality. Rough mereology allows for similarity measures (called rough inclusions) which in turn form a basis for the mechanism of granulation of knowledge. Granules of knowledge, defined as classes of satisfactorily similar objects, can be regarded as worlds in which properties of entities are evaluated as extensions of logical formulas. Obtained in this way granular rough mereological intensional logics reveal essential properties of rough set based reasoning.

This article extends the contribution “Reasoning about Concepts by Rough Mereological Logics” by the authors at RSKT 2008, May 2008 at Chengdu, Sichuan, China.

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Author information

Authors and Affiliations

  1. Polish–Japanese Institute of Information Technology, Koszykowa 86, 02008, Warsaw, Poland

    Lech Polkowski

  2. Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolnierska 14, 10560, Olsztyn, Poland

    Lech Polkowski

  3. Chair of Formal Linguistics, Warsaw University, Browarna 8/12, 00650, Warsaw, Poland

    Maria Semeniuk–Polkowska

Authors
  1. Lech Polkowski
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  2. Maria Semeniuk–Polkowska
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Editor information

Editors and Affiliations

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

    James F. Peters

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

    Andrzej Skowron

  3. Insitute of Computing Science, Laboratory of Intelligent Decision Support Systems, Poznań University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Roman Słowiński

  4. Department of Mathematics and Computing Science, Saint Mary’s University, B3H 3C3, Halifax, NS, Canada

    Pawan Lingras

  5. School of Electronics and Information Engineering, Tongji University, 201804, Shanghai, P.R. China

    Duoqian Miao

  6. Faculty of Medicine, Department of Medical Informatics, 89-1 Enya-cho, Shimane University, 693-8501, Izumo, Japan

    Shusaku Tsumoto

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Polkowski, L., Semeniuk–Polkowska, M. (2010). Granular Rough Mereological Logics with Applications to Dependencies in Information and Decision Systems. In: Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds) Transactions on Rough Sets XII. Lecture Notes in Computer Science, vol 6190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14467-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-14467-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14466-0

  • Online ISBN: 978-3-642-14467-7

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