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Cardinality and Entropy for Bifuzzy Sets

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 80))

Abstract

In this paper, one presents entropy and cardinality measure for bifuzzy sets. All these are constructed in the framework of a penta-valued representation. This representation uses the following five indexes: index of truth, index of falsity, index of incompleteness, index of inconsistency and index of indeterminacy. Also a new metric distance for bounded real interval is defined.

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References

  1. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barrenechea, E., Bustince, H., Pagola, M., Fernandez, J., Sanz, J.: Generalized Atanassov’s Intuitionistic Fuzzy Index. Construction method. In: Proceedings of IFSA-EUSFLAT Conference, Lisbon (July 2009)

    Google Scholar 

  3. Bhattacharyya, A.: On a measure of divergence between two statistical populations defined by their probability distributions. Bulletin of the Calcutta Mathematical Society 35, 99–109 (1943)

    MathSciNet  MATH  Google Scholar 

  4. Belnap, N.: A useful four-valued logic. In: Reidel, D. (ed.) Modern uses of multiple-valued logics, Dordrecht-Boston, pp. 8–37 (1977)

    Google Scholar 

  5. Burillo, P., Bustince, H.: Entropy of intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems 78, 305–316 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cornelis, C., Deschrijver, G., Kerre, E.: Square and Triangle: Reflections on Two Prominent Mathematical Structures for the Representation of Imprecision. Notes on Intuitionistic Fuzzy Sets 9, 11–21 (2003)

    MathSciNet  MATH  Google Scholar 

  7. Frank, M.J.: On the simultaneous associativity of f(x,y) and x+y-f(x,y). Aeq. Math. 19, 194–226 (1979)

    Google Scholar 

  8. Grzegorzewski, P., Mrówka, E.: On the Entropy of Intuitionistic Fuzzy Sets, and Interval-Valued Fuzzy Sets. In: Proceedings of IPMU 2004 Conference, Perugia, Italy, July 4-9 (2004)

    Google Scholar 

  9. Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets. Acad. Press, New York (1975)

    MATH  Google Scholar 

  10. Kosko, B.: Fuzzy entropy and conditioning. Information sciences 40, 165–174 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. De Luca, A., Termini, S.: A definition of nonprobabilistic entropy in the setting of fuzzy theory. Information and Control 20, 301–312 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pătraşcu, V.: A New Penta-valued Logic Based Knowledge Representation. In: Proceedings of IPMU 2008 Conference, Malaga, Spain, June 22-27, pp. 17–22 (2008)

    Google Scholar 

  13. Szmidt, E., Kacprzyk, J.: Similarity of Intuitionistic Fuzzy Sets and the Jaccard Coefficient. In: IPMU 2004 Conference, Perugia, Italy, July 4-9 (2004)

    Google Scholar 

  14. Szmidt, E., Kacprzyk, J.: A new measure of entropy and its connection with a similarity measure for intuitionistic fuzzy sets. In: EUSFLAT-LFA 2005 Conference, Barcelona, Spain, pp. 461–466 (2005)

    Google Scholar 

  15. Smarandache, F.: Neutrosophic set. A generalization of the intuitionistic fuzzy set. Intern. J. Pure Appl. Math. 24, 287–297 (2005)

    MathSciNet  MATH  Google Scholar 

  16. Yager, R.R.: On measures of fuzziness and negation. Part I: Membership in the unit interval. Int. J. Gen. syst. 5, 221–229 (1997)

    Article  MathSciNet  Google Scholar 

  17. Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Informatics Technology, Tarom Company, Bucharest, Romania

    Vasile Pătraşcu

Authors
  1. Vasile Pătraşcu
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Frank Hoffmann

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Pătraşcu, V. (2010). Cardinality and Entropy for Bifuzzy Sets. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_69

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  • DOI: https://doi.org/10.1007/978-3-642-14055-6_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14054-9

  • Online ISBN: 978-3-642-14055-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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