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A New Algorithm to Compute Low T-Transitive Approximation of a Fuzzy Relation Preserving Symmetry. Comparisons with the T-Transitive Closure

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3571))

Abstract

It is given a new algorithm to compute a lower T-transitive approximation of a fuzzy relation that preserves symmetry. Given a reflexive and symmetric fuzzy relation, the new algorithm computes a T-indistinguishability that is contained in the fuzzy relation. It has been developed a C++ program that generates random symmetric fuzzy relations or random symmetric and reflexive fuzzy relations and computes their T-transitive closure and the new low T-transitive approximation. Average distances of the fuzzy relation with the T-transitive closure are similar than the average distances with the low T-transitive approximation.

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References

  1. Garmendia, L., Campo, C., Cubillo, S., Salvador, A.: A Method to Make Some Fuzzy Relations T-Transitive. International Journal of Intelligence Systems 14(9), 873–882 (1999)

    Article  MATH  Google Scholar 

  2. Garmendia, L., Salvador, A.: On a new method to T-transitivize fuzzy relations. In: Information Processing and Management of Uncertainty in Knowledge - based Systems, IPMU 2000, pp. 864 – 869 (2000)

    Google Scholar 

  3. Garmendia, L., Salvador, A.: On a new method to T-transitivize fuzzy relations. In: Bouchon-Meunier, B., Gutierrez-Rios, J., Magdalena, L., Yager, R.R. (eds.) Technologies for Constructing Intelligent Systems, vol. 2, pp. 251–260. Springer, Heidelberg (2000)

    Google Scholar 

  4. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall, New Jersey (1995)

    MATH  Google Scholar 

  5. Hashimoto, H.: Transitivity of generalized fuzzy matrices. Fuzzy Sets and Systems 17(1), 83–90 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  6. Montero, F., Tejada, J.: On fuzzy transitivity. Instituto Nacional de Estadística 111, 49–58 (1986)

    Google Scholar 

  7. Naessens, H., De Meyer, H., De Baets, B.: Algorithms for the Computation of T-Transitive Closures. IEEE Trans Fuzzy Systems 10(4), 541–551 (2002)

    Article  Google Scholar 

  8. Ovchinnikov, S.: Representations of Transitive Fuzzy Relations. In: Skala, H.J., Termini, S., Trillas, E. (eds.) pp. 105–118. Reidel Pubs. (1984)

    Google Scholar 

  9. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, New York (1983)

    MATH  Google Scholar 

  10. Trillas, E., Alsina, C., Terricabras, J.M.: Introducción a la lógica borrosa, Ariel Matemática (1995)

    Google Scholar 

  11. Lee, H.-S.: An optimal algorithm for computing the max–min transitive closure of a fuzzy similarity matrix. Fuzzy Sets and Systems 123, 129–136 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Xiao, X.: An algorithm for calculating fuzzy transitive closure. Fuzzy Math 5(4), 71–73 (1985)

    Google Scholar 

  13. Zadeh, L.A.: Fuzzy sets. Inform. and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhao, Z.: An improved algorithm for fuzzy classification analysis. J. Lanzhou Univ. 19(3), 160–163 (1983)

    Google Scholar 

  15. Potoczny, H.B.: On similarity relations in fuzzy relational databases. Fuzzy Sets and Systems 12(3), 231–235 (1984)

    Article  MATH  Google Scholar 

  16. Jacas, J., Recasens, J.: Fuzzy T-transitive relations: eigenvectors and generators. Fuzzy Sets and Systems 72, 147–154 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  17. Jacas, J., Recasens, J.: Decomposable indistinguishability operators. In: Proceedings of the Sixth IFSA Congress, Sao Paulo (1995)

    Google Scholar 

  18. Valverde, L.: On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17, 313–328 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zadeh, L., Similarity, A.: relations and fuzzy orderings. Inform. Sci. 3, 177–200 (1971)

    Article  MATH  Google Scholar 

  20. Boixader, D.: On the relationship between T-transitivity and approximate equality. Fuzzy Sets and Systems 33, 6–69 (2003)

    Google Scholar 

  21. Wagenknecht, M.: On transitive solutions of fuzzy equations, inequalities and lower approximation of fuzzy relations. Fuzzy Sets and Systems 75, 229–240 (1995)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Facultad de Informática, Dpto. de Lenguajes y Sistemas Informáticos, Universidad Complutense of Madrid, 28040, Madrid, Spain

    Luis Garmendia

  2. E.T.S.I. Caminos Canales y Puertos, Dpto. de Matemática Aplicada, Technical University of Madrid, 28040, Madrid, Spain

    Adela Salvador

Authors
  1. Luis Garmendia
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  2. Adela Salvador
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Editor information

Editors and Affiliations

  1. IIIA - CSIC, 08193, Bellaterra, Spain

    Lluís Godo

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© 2005 Springer-Verlag Berlin Heidelberg

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Garmendia, L., Salvador, A. (2005). A New Algorithm to Compute Low T-Transitive Approximation of a Fuzzy Relation Preserving Symmetry. Comparisons with the T-Transitive Closure. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_49

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  • DOI: https://doi.org/10.1007/11518655_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27326-4

  • Online ISBN: 978-3-540-31888-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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