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.
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© 2011 Springer Science+Business Media, LLC
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Sakawa, M., Nishizaki, I., Katagiri, H. (2011). Fundamentals. In: Fuzzy Stochastic Multiobjective Programming. International Series in Operations Research & Management Science, vol 159. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8402-9_2
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DOI: https://doi.org/10.1007/978-1-4419-8402-9_2
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-8401-2
Online ISBN: 978-1-4419-8402-9
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