On Possibilistic/Fuzzy Optimization

  • Masahiro Inuiguchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4529)


We focus on possibilistic/fuzzy optimality in the framework of mathematical programming problem with a possibilistic objective function. We observe the interaction between possibilistic objective function values. Two optimality concepts, possible and necessary optimalities are reviewed. The necessary soft optimality is investigated.


Membership Function Fuzzy Number Linear Programming Problem Reasonable Solution Fuzzy Linear Programming Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Inuiguchi, M., Ramík, J.: Possibilistic linear programming. Fuzzy Sets and Systems 111(1), 3–28 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Inuiguchi, M., Kume, Y.: Extensions of fuzzy relations considering interaction between possibility distributions and an application to fuzzy linear program (in Japanese). Trans. of ISCIE 3(4), 93–102 (1990)Google Scholar
  3. 3.
    Inuiguchi, M., Sakawa, M.: Possible and necessary optimality tests in possibilistic linear programming problems. Fuzzy Sets and Systems 67(1), 29–46 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Inuiguchi, M.: Enumeration of all possibly optimal vertices with possible optimality degrees in linear programming problems with a possibilistic objective function. Fuzzy Optimization and Decision Making 3(4), 311–326 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Inuiguchi, M., Sakawa, M.: Robust optimization under softness in a fuzzy linear programming problem. International Journal of Approximate Reasoning 18(1-2), 21–34 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Inuiguchi, M., Tanino, T., Tanaka, H.: Optimization approaches to possibilistic linear programming problems. In: Proc. of Joint 9th IFSA Congress and 20th NAFIPS International Conference, pp. 2724–2729 (2001)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Masahiro Inuiguchi
    • 1
  1. 1.Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, Osaka 560-8531Japan

Personalised recommendations