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Introduction and Historical Remarks

  • Masatoshi Sakawa
  • Ichiro Nishizaki
  • Hideki Katagiri
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 159)

Abstract

The main characteristics of the real-world decision making problems facing humans today are uncertain due to the increase in complexity of modern-day society as well as the diversification of values among people. Hence, when formulating a mathematical programming problem which closely describes and represents a real decision situation, various factors of the real system should be reflected in the description of the objective functions and the constraints. Naturally, these objective functions and the constraints involve many parameters whose possible values may be estimated by the experts. In the most traditional approaches, such parameters are fixed at some values in an experimental and/or subjective manner through the experts’ understanding of the nature of the parameters. However, in most practical decision making situations, it would be more appropriate to consider uncertainty of the parameters of the objectives and constraints in the problems.

Keywords

Programming Problem Fuzzy Number Stochastic Programming Pareto Optimal Solution Fuzzy Goal 
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.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Masatoshi Sakawa
    • 1
  • Ichiro Nishizaki
    • 1
  • Hideki Katagiri
    • 1
  1. 1.Graduate School of Engineering Department of System CyberneticsHiroshima UniversityHigashi-HiroshimaJapan

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