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International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2014: Information Processing and Management of Uncertainty in Knowledge-Based Systems pp 406–415Cite as

The X-μ Approach: In Theory and Practice

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Part of the Communications in Computer and Information Science book series (CCIS,volume 444)

Abstract

Criticisms exist for fuzzy set theory which do not reside in classical (or “crisp”) set theory, some such issues exhibited by fuzzy set theory regard the law of excluded middle and law of contradiction. There are also additional complexities in fuzzy set theory for monotonicity, order and cardinality. Fuzzy set applications either avoid these issues, or use them to their advantage. The X-μ approach, however, attempts to solve some of these issues through analysis of inverse fuzzy membership functions. Through the inverse fuzzy membership function it is possible to computationally calculate classical set operations over an entire fuzzy membership. This paper firstly explores how the X-μ approach compares to both classical/crisp set theory and conventional fuzzy set theory, and explores how the problems regarding the laws of excluded middle and contradiction might be solved using X-μ. Finally the approach is implemented and applied to an area of big data over the world-wide-web, using movie ratings data.

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Authors and Affiliations

  1. Intelligent Systems Laboratory, University of Bristol, Woodland Road, Bristol, BS8 1UB, United Kingdom

    Daniel J. Lewis & Trevor P. Martin

Authors
  1. Daniel J. Lewis
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  2. Trevor P. Martin
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Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. Institute for Human Factors and Technology Management, IAT, University of Stuttgart, Nobelstraße 12, 70569, Stuttgart, Germany

    Oliver Strauss

  3. LIP6, UPMC Univ. Paris 06, CNRS UMR 7606, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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Lewis, D.J., Martin, T.P. (2014). The X-μ Approach: In Theory and Practice. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_42

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  • DOI: https://doi.org/10.1007/978-3-319-08852-5_42

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08851-8

  • Online ISBN: 978-3-319-08852-5

  • eBook Packages: Computer ScienceComputer Science (R0)