The X-μ approach: in theory and practice

D. J. Lewis, T. P. Martin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.
Original languageEnglish
Title of host publicationInformation Processing and Management of Uncertainty in Knowledge-Based Systems
Subtitle of host publication15th International Conference, IPMU 2014, Montpellier, France, July 15-19, 2014, Proceedings, Part III
EditorsAnne Laurent, Oliver Strauss, Bernadette Bouchon-Meunier, Ronald R. Yager
PublisherSpringer
Pages406-415
Number of pages10
Volume444
ISBN (Electronic)978-3-319-08852-5
ISBN (Print)978-3-319-08851-8
Publication statusPublished - 2014
Event15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems - Montpellier, France
Duration: 15 Jul 201419 Jul 2014

Conference

Conference15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems
Abbreviated titleIPMU'2014
Country/TerritoryFrance
CityMontpellier
Period15/07/1419/07/14

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