Skip to main content
SpringerLink
Log in

Comparison of Methodologies for Multicriteria Feasibility — Constrained Fuzzy and Multiple-Objective Stochastic Linear Programming

  • Chapter
Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 310))

Abstract

Methods for solving a multicriteria linear program with coefficients of the objective functions and the constraints being flat fuzzy numbers and those dealing with a stochastic multicriteria linear program where imprecision of some data is modelled by probability distributions are surveyed.

The methodologies are compared and evaluated. Some ideas of future research are emphasized.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BASS S.M. and KWAKERNAAK H. Rating and ranking of multiple aspect alternatives using fuzzy sets, Automatica 13(1977) 47–58.

    Article  Google Scholar 

  2. BALDWIN J.F. and GUILD N.C.F. Comparison of fuzzy sets on the same decision space, Fuzzy Sets and Systems 2(1979) 213–233.

    Article  Google Scholar 

  3. BELLMAN R. and ZADEH L.A. Decision making in a fuzzy environment, Management Sciences 17(1970), 141–164.

    Article  Google Scholar 

  4. BORTOLAN G. and DEGANI R. A review of some methods for ranking fuzzy subsets, Fuzzy Sets and Systems 15 (1985) 1–19.

    Article  Google Scholar 

  5. CHANG W. Ranking of fuzzy utilities with triangular membership functions, Proc. Int. Conf. on Policy Anal. and Inf. Systems (1981) 263–272.

    Google Scholar 

  6. CHARNES A. and COOPER W.W. Programming with linear fractional functionals, Nav. Res. Logistics Quart. 9(1962) 181–196.

    Article  Google Scholar 

  7. CHARNES A. and COOPER W.W. Response to decision problems under risk and chance constrained programming: dilemmas in the transition. Man. Science, 29, 6 (1983), 150–153.

    Google Scholar 

  8. CHEN S.H. Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, 17 (1985) 113–129.

    Article  Google Scholar 

  9. CONTINI B. A stochastic approach to goal programming. Operations Research 16, 3(1968), 576–586.

    Article  Google Scholar 

  10. DANTZIG G.B. Reminiscences about the origins of Linear Programming in Eds Bachern, Grötschel and Korte “Mathematical programming: the state of the art”. Springer Verlag (1983).

    Google Scholar 

  11. dubois d. Modèles mathématiques de l’imprécis et de l’incertain en vue d’applications aux techniques d’aide à la décision, Thèse, Institut National Polytechnique de Grenoble (1983).

    Google Scholar 

  12. DUBOIS D. Linear Programming with fuzzy data, to appear in “The Analysis of Fuzzy Information”, J.C. Bezdek (Ed.), CRC Press, Boca Raton, Fl.

    Google Scholar 

  13. DUBOIS D. and PRADE H. Systems of linear fuzzy constraints, Fuzzy Sets and Systems 3 (1980), 37–48.

    Article  Google Scholar 

  14. DUBOIS D. and PRADE H. Fuzzy Sets and Systems (Academic Press, New York, 1980).

    Google Scholar 

  15. DUBOIS D. and PRADE H. Ranking of fuzzy numbers in the setting of possibility theory, Inform. Sci. 30 (1983) 183–224.

    Article  Google Scholar 

  16. EFSTATHIOU J. and TONG R.M. Ranking Fuzzy sets: a decision theoretic approach, IEEE Trans. Systems, Man and Cybernetics, SMC - 12 (1982) 665–659.

    Google Scholar 

  17. GOICOECHA A., HANSEN D.R. and DUCKSTEIN L. Multiobjective decision analysis with engineering and business applications. John Wiley and Sons (1982).

    Google Scholar 

  18. HANSEN E. Topics in Interval Analysis (Oxford University Press, London and New York, 1969).

    Google Scholar 

  19. HOGAN A.J., MORRIS J.G. and THOMPSON H.E. Decision problems under risk and chance constrained programming: dilemmas in the transition. Man Sciences 27, 6 (1981), 698–716.

    Google Scholar 

  20. JAHN K.V. Eine Theorie der Gleichungesysteme mit Intervall-Koeffizienten, Z. Angew. Math. Mech. 54 (1974), 405–412.

    Article  Google Scholar 

  21. KALL P. Stochastic programming. E.J.O.R. 10 (1982), 125–130.

    Article  Google Scholar 

  22. NADEAU R. La programmation linéaire stochastique. Document du Lamsade 26 (1983). Univ. Paris-Dauphine.

    Google Scholar 

  23. NEGOITA C.V. Management applications of systems theory (Birkaüser Verlag, Basel, 1978).

    Google Scholar 

  24. OVCHINNIKOV S. and MIGDAL M. On ranking Fuzzy Sets, to appear in Fuzzy Sets and Systems.

    Google Scholar 

  25. RAMÍK J. and RÍMÁNEK Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems, 16 (1985), 123–138.

    Article  Google Scholar 

  26. ROUBENS M. Comparison of flat fuzzy numbers. Bucefal 24 (1985) 41–55 and “Recent Developments in the Theory and Applications of Fuzzy Sets” W. Bandler and A. Kandel (Eds) Proceedings of Nafips ’86.

    Google Scholar 

  27. ROUBENS M. and VINCKE P. Fuzzy possibility Graphs and their use in ranking fuzzy numbers, T.R. Faculté Polytechnique de Mons (1986),submitted for publication.

    Google Scholar 

  28. SLOWINSKI R. A Multicriteria Fuzzy Linear Programming Method for Water Supply System Development Planning, Fuzzy Sets and Systems 19(1986) 217–237.

    Article  Google Scholar 

  29. SLOWINSKI R. and TEGHEM J. Jr. Fuzzy vs stochastic approaches to multicriteria linear programming under uncertainty. T.R. Technical University of Poznan (1986), submitted for publication.

    Google Scholar 

  30. SOYSTER A.L. Convex programming with set-inclusive constraints. Application to inexact linear programming, Operations Research 21 (1973), 1154–1157.

    Article  Google Scholar 

  31. STANCU-MINASIAN I.M. and WETS M.J. A research bibliography in stochastic programming, 1955–1975. Operations Research 24 (1976), 1078–1119.

    Article  Google Scholar 

  32. STANCU-MINASIAN I.M. Stochastic programming with multiple objective functions. D. Reidel Publ. Company (1984).

    Google Scholar 

  33. STANCU-MINASIAN I.M. and TIGAN S.T. The vectorial minimum risk problem in“Proceedings of the Colloquium on approximation and optimization”Cluj Napoca (1984), 321–328.

    Google Scholar 

  34. STEUER R. Algorithms for linear programming problems with interval objective function coefficients. Mathematics of O.R., 6 (1981), 333–348.

    Article  Google Scholar 

  35. TANAKA H. and ASAI K. Fuzzy Linear Programming Based on Fuzzy Functions, Bulletin of University of Osaka Prefecture, Serie A, 29 (1980), 113–125.

    Google Scholar 

  36. TEGHEM J. Jr. Multiobjective and stochastic linear programming. Foundations of Control Engineering, 8, 3–4 (1983), 225–232.

    Google Scholar 

  37. TEGHEM J. Jr., DUFRANE D., THAUVOYE M. and KUNSCH P. STRANGE: an interactive method for multiobjective linear programming under uncertainty. E.J.O.R., 26, 1 (1986), 65–82.

    Article  Google Scholar 

  38. TONG R.M. and BONISSONE P.P. A linguistic Approach to Decisionmaking with Fuzzy Sets, IEEE Transactions on Systems, Man and Cybernetics, SMC-10 (1980) 716–723.

    Article  Google Scholar 

  39. YAGER R.R. A procedure for ordering fuzzy subsets of the unit interval, Inform.Sci. 24 (1981) 143–161.

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculté polytechnique de Mons, 9, rue de Houdain, 7000, Mons, Belgium

    Marc Roubens & Jacques Teghem Jr.

Authors
  1. Marc Roubens
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacques Teghem Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Institute of Informatics, University of Trento, Via Verdi 26, 38100, Trento, Italy

    Mario Fedrizzi

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Roubens, M., Teghem, J. (1988). Comparison of Methodologies for Multicriteria Feasibility — Constrained Fuzzy and Multiple-Objective Stochastic Linear Programming. In: Kacprzyk, J., Fedrizzi, M. (eds) Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46644-1_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-46644-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50005-6

  • Online ISBN: 978-3-642-46644-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation