Skip to main content

Fuzzy Multi-Objective Decision-Making Models and Approaches

  • Chapter

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 16))

Abstract

Multi-objective linear programming (MOLP) techniques are widely used to model many organizational decision problems. Referring to the imprecision inherent in human judgments, uncertainty may be incorporated in some parameters of an established MOLP model that is also called a fuzzy MOLP (FMOLP) problem. This chapter first reviews the development of fuzzy multi-objective decision-making (FMODM) models and approaches and then proposes an effective way for an optimal solution in the FMOLP problem. By introducing an adjustable satisfactory degree α, a new concept of FMOLP and a solution transformation theorem are given in this chapter. This chapter thus develops an interactive fuzzy goal multi-objective decision-making method, which provides an interactive fashion with decision makers during their solution process and allows decision makers to give their fuzzy goals in any form of membership function. An illustrative example shows the details of the proposed method.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bellman, R.E., and Zadeh, L.A., 1970, Decision-making in a fuzzy environment, Management Science, 17: 141-164.

    Article  MathSciNet  Google Scholar 

  • Carlsson, C., and Fuller, R., 1996, Fuzzy multiple criteria decision making: recent developments, Fuzzy Sets and Systems, 78: 139-152.

    Article  MATH  MathSciNet  Google Scholar 

  • Charnes, A., and Cooper, W.W., 1977, Goal programming and multiple objective optimizations, European Journal of Operational Research, 1: 39-54.

    Article  MATH  MathSciNet  Google Scholar 

  • Hwang, C.L., and Masud, A.S., 1979, Multiple Objective Decision Making: Methods and Applications, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Inuiguchi, M., and Ramik, J., 2000, Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets and Systems, 111: 3-28.

    Article  MATH  MathSciNet  Google Scholar 

  • Kuwano, H., 1996, On the fuzzy multi-objective linear programming problem: goal programming approach, Fuzzy Sets and Systems, 82: 57-64.

    Article  MATH  MathSciNet  Google Scholar 

  • Lai, Y.J., and Hwang, C.L., 1994, Fuzzy Multiple Objective Decision Making: Methods and Applications. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Lai, Y.J., and Hwang, C.L., 1992, A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49: 121-133.

    Article  MathSciNet  Google Scholar 

  • Luhandjula, M.K., 1987, Multiple objective programming problems with possibilistic coefficients, Fuzzy Sets and Systems, 21: 135-145.

    Article  MATH  MathSciNet  Google Scholar 

  • Ramik, J., 2000, Fuzzy goals and fuzzy alternatives in goal programming problems, Fuzzy Sets and Systems, 111: 81-86.

    Article  MATH  MathSciNet  Google Scholar 

  • Ramik, J., and Rommelfanger, H., 1996, Fuzzy mathematical programming based on some new inequality relations, Fuzzy Sets and Systems, 81: 77-87.

    Article  MATH  MathSciNet  Google Scholar 

  • Ramik, J., and Rommelfanger, H., 1993, A single- and a multi-valued order on fuzzy numbers and its use in linear programming with fuzzy coefficients, Fuzzy Sets and Systems, 57: 203-208.

    Article  MATH  MathSciNet  Google Scholar 

  • Rommelfanger, H., 1990, FULPAL - an interactive method for solving (Multiobjective) fuzzy linear programming problems, in: Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, Slowinski, R., and Teghem, J., eds. pp. 279-299, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Rommelfanger, H., 1989, Interactive decision making in fuzzy linear optimization problems, European Journal of Operational Research, 41: 210-217.

    Article  MATH  MathSciNet  Google Scholar 

  • Sakawa, M., 1993a, Fuzzy Sets and Interactive Multiobjective Optimization, Plenum Press, New York.

    MATH  Google Scholar 

  • Sakawa, M., 1993b, Interactive multiobjective linear programming with fuzzy parameters, in: Fuzzy Sets and Interactive Multiobjective Optimization, Plenum Press New York.

    Google Scholar 

  • Sakawa, M., and Yano, H., 1990, Interactive decision making for multiobjective programming problems with fuzzy parameters, in: Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, Slowinski, R., and Teghem, J., eds. pp. 191-229, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Sakawa, M., and Nishizaki, I., 2000, Solutions based on fuzzy goals in fuzzy linear programming games, Fuzzy Sets and Systems, 115: 105-119.

    Article  MATH  MathSciNet  Google Scholar 

  • Slowinski, R., 1990, ‘FLIP’: an interactive method for multiobjective linear programming with fuzzy coefficients, in: Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, Slowinski, R., and Teghem, J., eds. pp. 249-262, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Tanaka, H., and Asai, K., 1984, Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems, 13: 1-10.

    Article  MATH  MathSciNet  Google Scholar 

  • Lu, J., Wu, F., and Zhang G.Q., 2007, On a generalized fuzzy goal optimization for solving fuzzy multi-objective linear programming problems, Journal of Intelligent and Fuzzy Systems, 18(1): 83-97.

    MATH  MathSciNet  Google Scholar 

  • Lu, J., Ruan, D., Wu, J., and Zhang, G., 2006, An Į-fuzzy goal approximate algorithm for solving fuzzy multiple objective linear programming problems, Soft Computing—A Fusion of Foundations, Methodologies and Applications, 11(3): 259-267.

    Google Scholar 

  • Wu, F., Lu, J., and Zhang, G.Q., 2004a, An Į-fuzzy goal approximate algorithm for fuzzy multiple objective linear programming problems, Proceedings of The Third International Conference on Information, Tokyo, Japan, pp. 261-264.

    Google Scholar 

  • Wu, F., Lu, J., and Zhang, G.Q., 2004b, A fuzzy goal approximate algorithm for solving multiple objective linear programming problems with fuzzy parameters, Proceedings of FLINS 2004: 6th International Conference on Applied Computational Intelligence, Blankenberghe, Belgium, pp. 304-307.

    Chapter  Google Scholar 

  • Wu, F., Lu, J., and Zhang, G.Q., 2003, A new approximate algorithm for solving multiple objective linear programming with fuzzy parameters, Proceedings of The Third International Conference on Electronic Business (ICEB 2003), Singapore, pp. 532-534.

    Google Scholar 

  • Wu, F., Lu, J., and Zhang, G.Q., 2006, A new approximate algorithm for solving multiple objective linear programming problems with fuzzy parameters, Applied Mathematics and Computation, 174(1): 524-544.

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang, G.Q., Wu, Y., Remias, M., and Lu, J., 2002, An a-fuzzy max order and solution of linear constrained fuzzy optimization problems, East-West Journal of Mathematics, Special Volume, 84.

    Google Scholar 

  • Zhang, G.Q., Wu, Y., Remias, M., and Lu, J., 2003, Formulation of fuzzy linear programming problems as four-objective constrained optimization problems, Applied Mathematics and Computation, 39: 383-399.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science + Business Media, LLC

About this chapter

Cite this chapter

Lu, J., Zhang, G., Da Ruan (2008). Fuzzy Multi-Objective Decision-Making Models and Approaches. In: Kahraman, C. (eds) Fuzzy Multi-Criteria Decision Making. Springer Optimization and Its Applications, vol 16. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76813-7_19

Download citation

Publish with us

Policies and ethics