Fundamentals

Masatoshi Sakawa (), Ichiro Nishizaki () and Hideki Katagiri ()
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Masatoshi Sakawa: Hiroshima University
Ichiro Nishizaki: Hiroshima University
Hideki Katagiri: Hiroshima University

Chapter Chapter 2 in Fuzzy Stochastic Multiobjective Programming, 2011, pp 11-47 from Springer

Abstract: Abstract This chapter is devoted to reviewing optimization concepts and the related computational methods that will be used in the remaining chapters. In particular, we deal with three optimization concepts incorporating fuzziness and ambiguity of human judgments, uncertainty of events characterizing decision making problems, and multiplicity of evaluation criteria. Fuzzy programming which is developed in order to take into account fuzziness and ambiguity of human judgments, and this method is first presented together with the basic concepts in fuzzy set theory. Fundamentals of stochastic programming are also provided for decision problems under probabilistic uncertainty. Specifically, two-stage programming and chance constraint programming are covered. To meet expectations of diversified evaluations, multiobjective programming has been investigated.

Keywords: Fuzzy Number; Linear Programming Problem; Pareto Optimal Solution; Satisfactory Degree; Fuzzy Goal (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4419-8402-9_2

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DOI: 10.1007/978-1-4419-8402-9_2

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