Fuzzy Stochastic Multiobjective Programming
Fuzzy Stochastic Multiobjective Programming
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DOI：
10.1007/978-1-4419-8402-9
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
M. Sakawa;I. Nishizaki;H. Katagiri
中科院分区：
文献类型：
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作者：
M. Sakawa;I. Nishizaki;H. Katagiri
虽然人们对不确定性多目标数学规划的研究已经积累了很多，也出版了几本关于不确定性多目标数学规划的书（例如Stancu-Minasian（1984）; Slowinski和Teghem（1990）; Sakawa（1993）; Lai和Hwang（1994）; Sakawa（2000）），似乎没有一本书同时关注多目标决策问题中与环境相关的事件的随机性和人类判断的模糊性。在这本书中，作者关注的是介绍在该领域的最新进展，在这两个模糊性和随机性的基础上，作者继续研究工作。特别强调互动决策方面的模糊随机多目标规划的以人为中心的系统在最现实的情况下，在不确定性的模糊性和随机性处理。每章的组织简要总结如下：第2章专门介绍数学术语，这将在本书的其余部分使用。从多目标规划的基本概念和方法入手，介绍了交互式模糊多目标规划和模糊多目标规划。在第三章中，考虑到多目标问题中决策者对随机目标函数和/或约束条件的判断不精确，提出了模糊多目标随机规划。在第四章中，我们不仅考虑了目标函数和约束中参数的随机性，而且考虑了专家对随机参数实现值的模糊理解，建立了模糊随机变量多目标规划问题。在第五章中，我们讨论了两个决策者具有不同决策优先级的层次管理型组织或公共组织中的决策冲突问题，即两层规划问题。最后，第六章对未来的研究方向进行了展望。
Although studies on multiobjective mathematical programming under uncertainty have been accumulated and several books on multiobjective mathematical programming under uncertainty have been published (eg, Stancu-Minasian (1984); Slowinski and Teghem (1990); Sakawa (1993); Lai and Hwang (1994); Sakawa (2000)), there seems to be no book which concerns both randomness of events related to environments and fuzziness of human judgments simultaneously in multiobjective decision making problems. In this book, the authors are concerned with introducing the latest advances in the field of multiobjective optimization under both fuzziness and randomness on the basis of the authors’ continuing research works. Special stress is placed on interactive decision making aspects of fuzzy stochastic multiobjective programming for human-centered systems under uncertainty in most realistic situations when dealing with both fuzziness and randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is devoted to mathematical preliminaries, which will be used throughout the remainder of the book. Starting with basic notions and methods of multiobjective programming, interactive fuzzy multiobjective programming as well as fuzzy multiobjective programming is outlined. In Chapter 3, by considering the imprecision of decision maker’s (DM’s) judgment for stochastic objective functions and/or constraints in multiobjective problems, fuzzy multiobjective stochastic programming is developed. In Chapter 4, through the consideration of not only the randomness of parameters involved in objective functions and/or constraints but also the experts’ ambiguous understanding of the realized values of the random parameters, multiobjective programming problems with fuzzy random variables are formulated. In Chapter 5, for resolving conflict of decision making problems in hierarchical managerial or public organizations where there exist two DMs who have different priorities in making decisions, two-level programming problems are discussed. Finally, Chapter 6 outlines some future research directions.