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Fractional programming under uncertainty

  • Conference paper
Generalized Convexity

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 405))

Abstract

The purpose of the paper is to present some approaches for multiobjective fractional programming with set coefficients in the objective functions. Among other cases, we discuss for linear fractional multiobjective programming some conservative and nonconservative approaches related to Soyster’s mathematical programming with set-inclusive constraints and Dantzig’s generalized linear programming, respectively. The vectorial max-min optimization will be also used as a conservative approach for inexact multiobjective programming. In particular, the conservative approach will be applied to mathematical programming with nondecreasing objectives with respect to the inexact coefficients. Linear-fractional objective functions will be studied from both points of view (conservative and nonconservative). Also, some applications to the fuzzy linear-fractional multiobjective programming will be suggested.

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References

  1. Chadha, S. S., Duality theorems for a generalized linear and linear fractional program, Cahiers C.E.R.O., 15 (2) (1973), 167–173.

    Google Scholar 

  2. Dantzig, G. B., Linear Programming and Extensions, Princeton Univ. Press, Princeton, New-Jersey, (1963).

    Google Scholar 

  3. Dragusin C., Min-max pour des critères multiples, RAIRO, Récherche Opérationnelle, 12, 2 (1978).

    Google Scholar 

  4. Falk, E. J., Exact solutions of inexact and generalized linear programs, Oper. Res., 24 (4) (1976), 783–787.

    Article  Google Scholar 

  5. Kaur, S., Inexact fractional programming with set-inclusive constraints, Cahiers C.E.R.O., 26 (1–2) (1984), 33–41.

    Google Scholar 

  6. Kornbluth, J.S.H., Steuer, R. E., Goal programming with linear-fractional criteria, European J. Oper. Res., 8 (1) (1981), 58–65.

    Article  Google Scholar 

  7. Luhandjula, M. K., Fuzzy approaches for multiple objective linear fractional optimization, Fuzzy Sets and Systems, 13 (1984), 11–23.

    Article  Google Scholar 

  8. Lyall, V., Duality theory in inexact multiobjective programming, J. Inf. Op-tim. Sci., (India), 9 (2) (1988), 199–206.

    Google Scholar 

  9. Negoita, C. V., Flondor, P. and Sularia, M., On fuzzy environment in optimization problems, Econom. Comput. Econom. Cybernet. Stud. Res., 1 (1977), 13–24.

    Google Scholar 

  10. Schaible, S., Fractional programming with several ratios, Methods of Operations Research, 49 (1985), 77–83.

    Google Scholar 

  11. Singh, C., Convex programming with set-inclusive constraints and its applications to generalized linear and fractional programming, J. Optim. Theory Appl., 38 (1) (1982), 33–42.

    Article  Google Scholar 

  12. Soyster, A. L., Convex programming with set-inclusive constraints and its applications to inexact linear programming, Oper. Res., 21 (5) (1973), 1154–1157.

    Article  Google Scholar 

  13. Soyster, A. L., A duality theory for convex programming with set inclusive constraints, Oper. Res., 22 (4) (1974), 892–898.

    Article  Google Scholar 

  14. Soyster, A. L., Inexact linear programming with generalized resource sets, European J. Oper. Res., 3 (4) (1979), 316–321.

    Article  Google Scholar 

  15. Soyster, A. L., Lev, B., Di Toof, Conservative linear programming with mixed multiple objectives, Omega, 5 (2) (1977), 193–205.

    Article  Google Scholar 

  16. Stancu-Minasian, I. M., Stochastic Programming with Multiple Objective Functions, Editura Academiei Române, Bucuresti and D. Reidel Publishing Company, Dordrecht, Boston, Lancester, (1984).

    Google Scholar 

  17. Stancu-Minasian, I. M., Tigan, S., I.exact mathematical programming, Cluj-Napoca Univ., Seminar of Optimization Theory, Report no. 8, (1987), 99–116.

    Google Scholar 

  18. Stancu-Minasian, I. M., Tigan, S., A stochastic approach to some linear fractional goal programming problems, Kybernetika, 24 (1988), No. 2, 139–149.

    Google Scholar 

  19. Stancu-Minasian I. M., Tigan S., Multiobjective mathematical Programming with inexact data, R. Slowinski and I. Teghem (eds.), Stochastic versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, 395–418, Kluwer Academic Publishers (1990).

    Google Scholar 

  20. Thuente, D., Duality theory for generalized programs with computational methods, Oper. Res., 28 (4) (1980), 1005–1011.

    Article  Google Scholar 

  21. Tigan, S., Sur une méthode pour la résolution d’un problème d’optimization fractionnaire par segments, Analyse Numér. Théor. Approx., 4 (1) (1975), 87–97.

    Google Scholar 

  22. Tigan, S., Surun problème de programmation mathèmatique nonlinéaire avec contraintes de type inclusion, Analyse Numér. Théor. Approx., 5 (2) (1976), 219–224.

    Google Scholar 

  23. Tigan, S., Goal programming with inexact data, Cluj-Napoca University, Report no. 5, (1985), 95–106.

    Google Scholar 

  24. Tigan, S., On some procedures for solving fractional max-min problems, Analyse Numér. Théor. Approx., 17 (1), (1988), 73–91.

    Google Scholar 

  25. Tigan, S., Stancu-Minasian, I. M., Fractional goal programming with inexact data, Itinerant Seminar of Functional Equations, Approximation and Convexity, (Cluj-Napoca, 1989 ), 311–318, Preprint, 89–6, Univ. Babes-Bolyain, Cluj-Napoca, 1989.

    Google Scholar 

  26. Tigan S., Stancu-Minasian I. M., On a bicriterion max-min fractional problem, Analyse Numér. Théor. Approx., 20, 1–2 (1991), 117–125.

    Google Scholar 

  27. Yano H., Sakawa M., Interactive fuzzy decision making for generalized multiobjective linear fractional programming with fuzzy parameters, Fuzzy Sets and Systems, 32 (1989), 245–261.

    Article  Google Scholar 

  28. Zimmermann, H. J., Fuzzy programming with several objective functions, Fuzzy Sets and Systems, 1 (1978), 45–55.

    Article  Google Scholar 

  29. Warburton A. R., Parametric Solution of Bicriterion Linear Fractional Programs, Oper. Res., 33, 1 (1985), 74–84.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Center of Mathematical Statistics, Bucharest, Romania

    I. M. Stancu-Minasian & S. Tigan

  2. University of Medicine and Pharmacy, Cluj-Napoca, Romania

    I. M. Stancu-Minasian & S. Tigan

Authors
  1. I. M. Stancu-Minasian
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  2. S. Tigan
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Editor information

Editors and Affiliations

  1. Faculty of Economics, Janus Pannonius University, Rákóczi út 80, H-7621, Pécs, Hungary

    Sándor Komlósi

  2. Computer and Automation Institute, Hungary Academy of Sciences, P.O. Box 63, Kende u. 13-17, H-1518, Budapest, Hungary

    Tamás Rapcsák

  3. Graduate School of Management, University of California, 92521, Riverside, CA, USA

    Siegfried Schaible

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© 1994 Springer-Verlag Berlin Heidelberg

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Stancu-Minasian, I.M., Tigan, S. (1994). Fractional programming under uncertainty. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_25

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  • DOI: https://doi.org/10.1007/978-3-642-46802-5_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57624-2

  • Online ISBN: 978-3-642-46802-5

  • eBook Packages: Springer Book Archive

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