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Operators with N-threshold for uncertainty management

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Abstract

In this paper we present a pair of operators (t-norm, t-conorm) dual with a strong negation with n-thresholda 1, …,a n ∈(0, 1),a 1<a 2< …<a n . In this way we obtain an extension of operators with threshold, that are obtained forn=1. The new pair is obtained from given one.

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References

  1. H. Akdag and D. Pacholczyk,SEQUI: Un système expert pour le traitement de questionnaires incertaines. Journées or léanaises sur la gestion d'incertitude dans le systèmes decisionnels. September (1987)

  2. C. Alsina, E. Trillas and L. Valverde,On non distributive local connectives for fuzzy theory, BUSEFAL3 (1980), 18–29

    Google Scholar 

  3. J. F. Baldwin,Evidential Support Logic Programming, Fuzzy Sets and Systems24 (1987), 1–26.

    Article  MATH  Google Scholar 

  4. J. C. Fodor,A remark on constructing t-norms, Fuzzy Sets and Systems41 (1991), 195–199

    Article  MATH  MathSciNet  Google Scholar 

  5. I. Iancu,T-norms with threshold, Fuzzy Sets and Systems85 (1997), 83–92

    Article  MATH  MathSciNet  Google Scholar 

  6. I. Iancu,Introduction of a double threshold in uncertainty management, In Proc. of the 7th Int. Conf. Artificial Intelligence and Information-Control Systems of Robots (Editor I. Plander), World Scientific, Singapore (1997), 201–210

    Google Scholar 

  7. I. Iancu,Prosum-Prolog system for uncertainty management, Int. J. Intell. Systems12(9) (1997), 615–627

    Article  MATH  Google Scholar 

  8. I. Iancu,A method for constructing t-norms, J. Appl. Math. & Computing(old:KJCAM)5 (2) (1998), 407–414

    MATH  MathSciNet  Google Scholar 

  9. I. Iancu,Fuzzy connectives with applications in uncertainty management, Proc the 3-rnd annual meeting of the Romanian Society of Mathematical Sciences (1999), 40–47

  10. I. Iancu,On a family of t-operators, Annals of the Univ. of Craiova. Math. and Comp. Sciences Series, Vol XXVI (1999), 84–92

    MathSciNet  Google Scholar 

  11. I. Iancu,On a representation of an uncertain body of evidence, Annals of the Univ. of Craiova, Math. and Comp. Science Series, Vol. XXX,2 (2003), 100–108.

    MathSciNet  Google Scholar 

  12. S. Jenei,Fibred triangular norms, Fuzzy Sets and Systems10 (1999), 3–13

    Google Scholar 

  13. S. Jenei,New family of triangular norms via contrapositive symmetrization of reziduated implications, Fuzzy Sets and Systems110 (2000), 154–174

    Article  MathSciNet  Google Scholar 

  14. E. P. Klement, R. Mesiar and E. PapQuasi-and pseudo-inverses of monotone functions, and the construction of t-norms, Fuzzy Sets and Systems104 (1999), 3–13

    Article  MATH  MathSciNet  Google Scholar 

  15. E. P. Klement, R. Mesiar and E. Pap,Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000

    MATH  Google Scholar 

  16. C. H. Ling,Representation of associative functions, Publ. Math. Debrecen12 (1965), 189–212

    MathSciNet  Google Scholar 

  17. K. Menger,Statistical metrics, Proc. Nat. Acad. Sci. U.S.A.8 (1942), 535–537

    Article  MathSciNet  Google Scholar 

  18. R. Mesiar,On some constructions of new triangular norms, Mathware & Soft Computing2 (1995), 39–45

    MATH  MathSciNet  Google Scholar 

  19. D. Pacholczyk,Introduction d'un seuil dans le calcul d'incertitude en logique floue, BUSEFAL32 (1987), 11–18

    Google Scholar 

  20. B. Schweizer and A. Sklar,Associative functions and statistical triangle inequalities, Publ. Math. Debrecen8 (1961), 169–186

    MATH  MathSciNet  Google Scholar 

  21. B. Schweizer and A. Sklar,Associative functions and abstract semigroups, Publ. Math. Debrecen10 (1963), 69–81

    MathSciNet  Google Scholar 

  22. E. Trillas,Sobre funciones de negation en la teoria de conjuntos difusos, Stochastica1 (1979), 47–59

    MathSciNet  Google Scholar 

  23. P. Vicenik,A note to construction of t-norms based on pseudo—inverses of monotone functions, Fuzzy Sets and Systems104 (1999), 15–18

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Craiova, 13 A.I. Cuza Street, 1100, Craiova, Romania

    Ion Iancu

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  1. Ion Iancu
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Correspondence to Ion Iancu.

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Ion Iancu received his BS in mathematics from University of Craiova and Ph. D at University of Bucharest. He had Tempus and Socrates grants at the Free University of Bruxelles, University of Dijon and University of Athens. He is professor at University of Craiova. His research interests are modeling of uncertainty and imprecision, knowledge representation, approximate reasoning, genetic algorithms.

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Iancu, I. Operators with N-threshold for uncertainty management. JAMC 19, 1–17 (2005). https://doi.org/10.1007/BF02935785

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  • DOI: https://doi.org/10.1007/BF02935785

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