Linear Programming with Words

  • Stefan Chanas
  • Dorota Kuchta
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 34)


Linear programming is the part of operational research, which is most widely used in practical applications. There are many classical algorithms in this domain (the most important one is the well known simplex method) and many new ones, together with corresponding software, are being developed for specific applications, which often solve problems of enormous dimensions.


Decision Maker Membership Function Fuzzy Number Verbal Statement Linear Programming Problem 


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  1. 1.
    G. Bortolan, R. Degani, A review of some methods for ranking fuzzy subsets, Fuzzy Sets and Systems 15 (1985) 1–19.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Chen, S.J., Hwang, C.L., Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer Verlag, Berlin, Heidelberg, 1992Google Scholar
  3. 3.
    D. Dubois, H. Prade, Operations on fuzzy numbers, Int. J. Systems Sci. 30 (1978) 613–626.MathSciNetCrossRefGoogle Scholar
  4. 4.
    D. Dubois, H. Prade, Fuzzy sets in approximate reasoning, Part 1: inference with possibility distributions, Fuzzy Sets and Systems 40 (1991) 143–202.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    M. Locke, Fuzzy modelling in expert for process control, Syst. Anal. Model. Simul 7 (1990) 715–719.MathSciNetGoogle Scholar
  6. 6.
    S. Tong, Interval number and fuzzy number linear programmings, Fuzzy Sets and Systems 66 (1994) 301–306.MathSciNetCrossRefGoogle Scholar
  7. 7.
    I. B. Turksen, Approximate reasoning for production planning, Fuzzy Sets and Systems 4 (1988) 23–27.MathSciNetCrossRefGoogle Scholar
  8. 8.
    I. B. Turksen, Measurement of membership function and their acquisition, Fuzzy Sets and Systems 4 (1991) 5–38.MathSciNetCrossRefGoogle Scholar
  9. 9.
    S.R. Watson, J.J. Weiss and M.L. Donnell Fuzzy decision analysis, IEEE Trans. on Syst., Man and Cyber. SMC-9(1) (1979) 1–9.Google Scholar
  10. 10.
    F. Wenstop, Quantitative analysis with linguistic values, Fuzzy Sets and Systems 4 (1980) 99–115.MATHCrossRefGoogle Scholar
  11. 11.
    M.R. Wilhelm and H.R. Parsaei, A fuzzy linguistic approach to implementing a strategy for computer integrated manufacturing, Fuzzy Sets and Systems 42 (1991) 191–204.CrossRefGoogle Scholar
  12. 12.
    L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning I,II,III, Inform. Sci. 8 (1975) 199–249; 301–357; 9 43–80.Google Scholar
  13. 13.
    L. A. Zadeh, Fuzzy sets as a basis for theory of possibility, Fuzzy Sets and Systems 1 (1978) 3–29.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Stefan Chanas
    • 1
  • Dorota Kuchta
    • 1
  1. 1.Institute of Industrial Engineering and ManagementWroclaw University of TechnologyWroclawPoland

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