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On the Relation of Probability, Fuzziness, Rough and Evidence Theory

  • Conference paper
Intelligence in the Era of Big Data (ICSIIT 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 516))

Abstract

Since the appearance of the first article on fuzzy sets proposed by Zadeh in 1965, the relationship between probability and fuzziness in representing uncertainty has been an object of debate among many people. The question is whether probability theory by itself is sufficient for dealing with uncertainty. This paper again discusses the question to simply understand the relationship between probability and fuzziness using the process of perception. It is obviously seen that probability and fuzziness work in different areas of uncertainty. By fuzzy set, an ill-defined event, called fuzzy event, can be described in the presence of probability theory providing probability of fuzzy event in which fuzzy event might be regarded as a generalization of crisp event. Similarly, by rough set theory, a rough event is proposed representing two approximate events, namely lower and upper approximate events, in the presence of probability theory providing probability of rough event. Finally, the paper shows and discusses relation among belief-plausibility measures (evidence theory), lower-upper approximate probability (probability of rough events), classical probability measures, probability of fuzzy events and probability of generalized fuzzy-rough events.

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Author information

Authors and Affiliations

  1. Department of Informatics Engineering, Petra Christian University, Surabaya, Indonesia

    Rolly Intan

Authors
  1. Rolly Intan
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Correspondence to Rolly Intan .

Editor information

Editors and Affiliations

  1. Informatics, Petra Christian University, Surabaya, Indonesia

    Rolly Intan

  2. CSIRO, Hobart, Tasmania, Australia

    Chi-Hung Chi

  3. Informatics, Petra Christian University, Surabaya, Indonesia

    Henry N. Palit

  4. Informatics, Petra Christian University, Surabaya, Indonesia

    Leo W. Santoso

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Intan, R. (2015). On the Relation of Probability, Fuzziness, Rough and Evidence Theory. In: Intan, R., Chi, CH., Palit, H., Santoso, L. (eds) Intelligence in the Era of Big Data. ICSIIT 2015. Communications in Computer and Information Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46742-8_1

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  • DOI: https://doi.org/10.1007/978-3-662-46742-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46741-1

  • Online ISBN: 978-3-662-46742-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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