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Fuzzy Relational Compositions Based on Generalized Quantifiers

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 443))

Abstract

Fuzzy relational compositions have been extensively studied by many authors. Especially, we would like to highlight initial studies of the fuzzy relational compositions motivated by their applications to medical diagnosis by Willis Bandler and Ladislav Kohout. We revisit these types of compositions and introduce new definitions that directly employ generalized quantifiers. The motivation for this step is twofold: first, the application needs for filling a huge gap between the classical existential and universal quantifiers and second, the already existing successful implementation of generalized quantifiers in so called divisions of fuzzy relations, that constitute a database application counterpart of the theory of fuzzy relational compositions. Recall that the latter topic is studied within fuzzy relational databases and flexible querying systems for more than twenty years. This paper is an introductory study that should demonstrate a unifying theoretical framework and introduce that the properties typically valid for fuzzy relational compositions are valid also for the generalized ones, yet sometimes in a weaken form.

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References

  1. Pedrycz, W.: Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data. Fuzzy Sets and Systems 16, 163–175 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Štěpnička, M., De Baets, B., Nosková, L.: Arithmetic fuzzy models. IEEE Transactions on Fuzzy Systems 18, 1058–1069 (2010)

    Article  Google Scholar 

  3. Bandler, W., Kohout, L.J.: Fuzzy relational products and fuzzy implication operators. In: Proc. Int. Workshop on Fuzzy Reasoning Theory and Applications. Queen Mary College, London (1978)

    Google Scholar 

  4. Bandler, W., Kohout, L.J.: Relational-product architectures for information processing. Information Sciences 37, 25–37 (1985)

    Article  Google Scholar 

  5. Bělohlávek, R.: Fuzzy relational systems: Foundations and principles. Kluwer Academic, Plenum Press, Dordrecht, New York (2002)

    Book  Google Scholar 

  6. De Baets, B., Kerre, E.: Fuzzy relational compositions. Fuzzy Sets and Systems 60, 109–120 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Běhounek, L., Cintula, P.: Fuzzy class theory 154(1), 34–55 (2005)

    Google Scholar 

  8. Běhounek, L., Daňková, M.: Relational compositions in fuzzy class theory. Fuzzy Sets and Systems 160(8), 1005–1036 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bandler, W., Kohout, L.J.: Fuzzy relational products as a tool for analysis and synthesis of the behaviour of complex natural and artificial systems. In: Wang, S.K., Chang, P.P. (eds.) Fuzzy Sets: Theory and Application to Policy Analysis and Information Systems, pp. 341–367. Plenum Press, New York (1980)

    Chapter  Google Scholar 

  10. Pivert, O., Bosc, P.: Fuzzy preference queries to relational databases. Imperial College Press, London (2012)

    Book  MATH  Google Scholar 

  11. Dubois, D., Prade, H.: Semantics of quotient operators in fuzzy relational databases. Fuzzy Sets and Systems 78, 89–93 (1996)

    Article  MathSciNet  Google Scholar 

  12. Delgado, M., Sanchez, D., Vila, M.A.: Fuzzy cardinality based evaluation of quantified sentences. International Journal of Approximate Reasoning 23, 23–66 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Bosc, P., Liétard, L., Pivert, O.: Flexible database querying and the division of fuzzy relations. Scientia Iranica 2, 329–340 (1996)

    Google Scholar 

  14. Baczyński, M., Jayaram, B.: Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  15. Dvořák, A., Holčapek, M.: L-fuzzy quantifiers of type 〈1〉 determined by fuzzy measures. Fuzzy Sets and Systems 160(23), 3425–3452 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. Novák, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets and Systems 159(22), 2939–2969 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  17. Bosc, P., Liétard, L., Pivert, O.: Sugeno fuzzy integral as a basis for the interpretation of flexible queries involving monotonic aggregates. Information Processing & Management 39(2), 287–306 (2003)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Centre of Excellence IT4Innovations, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Martin Štěpnička & Michal Holčapek

Authors
  1. Martin Štěpnička
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  2. Michal Holčapek
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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. LIRMM, UMR CNRS/Universite Montpellier II, 161 rue Ada, 34392, Montpellier cedex 5, France

    Olivier Strauss

  3. UPMC Univ. Paris 06, CNRS UMR 7606, LIP6, 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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© 2014 Springer International Publishing Switzerland

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Štěpnička, M., Holčapek, M. (2014). Fuzzy Relational Compositions Based on Generalized Quantifiers. 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 443. Springer, Cham. https://doi.org/10.1007/978-3-319-08855-6_23

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  • DOI: https://doi.org/10.1007/978-3-319-08855-6_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08854-9

  • Online ISBN: 978-3-319-08855-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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