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Possibilistic Optimization Tasks with Mutually T-Related Parameters: Solution Methods and Comparative Analysis

  • Alexander Yazenin
  • Ilia Soldatenko
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 254)

Abstract

The problems of possibilistic linear programming are studied in the article. Unlike in other known related publications, t-norms are used to describe the interaction (relatedness) of fuzzy parameters. Solution methods are proposed, models of possibilistic optimization are compared for different t-norms.

Keywords

Fuzzy Number Feasible Region Identical Left Fuzzy Variable Crossover Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Dubois, D., Prade, H.: Possibility theory. Tr. from french. Moskva. Radio i svyaz (1990) (in Russian)Google Scholar
  2. 2.
    Ermolyev, Y.M.: Methods of stochastic programming. — M.: Nauka, in Russian (1976) (in Russian)Google Scholar
  3. 3.
    Soldatenko, I.S.: On weighted sum of mutually T W-related fuzzy variables. Vestnik of Tver State University. Applied Mathematics 5(33), 63–77 (2007) (in Russian)Google Scholar
  4. 4.
    Yazenin, A.V.: To the problem of fuzzy goal achievement level maximization. Izvestia RAN. Theory and Systems for Control 4, 120–123 (1999) (in Russian)MathSciNetGoogle Scholar
  5. 5.
    Yazenin, A.V.: Fuzzy variables and fuzzy mathematical programming. In: Proceedings of inter-republican scientific conference “Models of alternatives choosing in a fuzzy environment”, pp. 57–59. Riga polytechnical institute, Riga (1984) (in russian)Google Scholar
  6. 6.
    Yazenin, A.V.: Models of fuzzy mathematical programming. In: Proceedings of inter-republican scientific conference “Models of alternatives choosing in a fuzzy environment”, pp. 51–53. Riga polytechnical institute, Riga (1984)Google Scholar
  7. 7.
    Yazenin, A.V.: Fuzzy mathematical programming. Kalinin State University, Kalinin (1986) (in Russian)Google Scholar
  8. 8.
    De Baets, B., Marková-Stupňanová, A.: Analytical expressions for the addition of fuzzy intervals. Fuzzy Sets and Systems 91, 203–213 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Dubois, D., Prade, H.: Additions of interactive fuzzy numbers. IEEE Trans. Automat. Control 26, 926–936 (1981)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Dubois, D., Prade, H.: Fuzzy numbers: an overview. In: Bezdek, J. (ed.) Analysis of Fuzzy Information, vol. 2, pp. 3–39. CRC-Press, Boca Raton (1988)Google Scholar
  11. 11.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)zbMATHGoogle Scholar
  12. 12.
    Hong, D.H.: Parameter estimations of mutually T-related fuzzy variables. Fuzzy Sets and Systems 123, 63–71 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper I: basic analytical and algebraic properties. Fuzzy Sets and Systems 143, 5–26 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper II: general constructions and parameterized families. Fuzzy Sets and Systems 145, 411–438 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper III: continuous t-norms. Fuzzy Sets and Systems 145, 439–454 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Liu, B.: Uncertain programming. Wiley and Sons, New York (1999)Google Scholar
  17. 17.
    Mesiar, R.: A note to the T-sum of L − R fuzzy numbers. Fuzzy Sets and Systems 79, 259–261 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Mesiar, R.: Computation of L − R-fuzzy numbers. In: Proc. 5th Internat. Workshop on Current Issues in Fuzzy Technologies, Trento, Italy, pp. 165–176 (1995)Google Scholar
  19. 19.
    Mesiar, R.: Shape preserving additions of fuzzy intervals. Fuzzy Sets and Systems 86, 73–78 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Mesiar, R.: Triangular-norm-based addition of fuzzy intervals. Fuzzy Sets and Systems 91, 231–237 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Nahmias, S.: Fuzzy Variables. Fuzzy Sets and Systems 1, 97–110 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Nguyen, H.T., Walker, E.A.: A first cours in fuzzy logic. CRC Press, Boca Raton (1997)Google Scholar
  23. 23.
    Rao, M., Rashed, A.: Some comments on fuzzy variables. Fuzzy Sets and Systems 6, 285–292 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Yazenin, A.V.: Fuzzy and stochastic programming. Fuzzy Sets and Systems 22, 171–180 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Yazenin, A.V.: On the problem of possibilistic optimization. Fuzzy Sets and Systems 81, 133–140 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Yazenin, A.V., Wagenknecht, M.: Possibilistic optimization. Brandenburgische Technische Universitat, Cottbus, Germany (1996)Google Scholar
  27. 27.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexander Yazenin
    • 1
  • Ilia Soldatenko
    • 1
  1. 1.Department of Information TechnologiesTver State UniversityTverRussia

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