Fuzzy dynamic programming
Fuzzy dynamic programming
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DOI：
10.1007/978-1-4615-5645-9_9
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发表时间：
1999-04
期刊：
影响因子：
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通讯作者：
A. Esogbue;J. Kacprzyk
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文献类型：
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作者：
A. Esogbue;J. Kacprzyk
过程的性能是在某个计划范围内测量的，并通过部分分数的总和表示，部分分数表示特定阶段决策的性能。这种总和可以采取各种形式，例如，从悲观的，“安全第一”的最小值到乐观的最大值，通过（加权）平均值举例说明的所有中间情况。然后，在假设的规划范围（政策）的连续阶段中寻求决策或控制的最优序列。动态规划是处理大范围多阶段决策问题的一种强大的形式化工具。自20世纪50年代中期（参见Bellman， 1957）成立以来，动态规划已成为许多领域的标准工具，包括运筹学，系统分析，工程，数据分析，控制，计算机科学等。在现实世界的问题中，我们面临着不完全信息（数据）。我们必须处理现有的不确定的、不精确的、模糊的等资料。在建模和分析这类问题时，以前的作品倾向于将不完全信息的所有方面与不确定性（随机字符）等同起来。因此，提出了大量的概率模型。动态规划的使用也是如此。然而，直到20世纪60年代中期Zadeh（1965）提出模糊集合理论之前，还没有一种简单而适当的正式仪器来处理不精确的数据——这些数据可能源于人类对自然语言的使用。事实上，动态规划是模糊集理论最早应用的通用技术之一（Chang, 1969; Bellman And Zadeh, 1970; Esogbue And Ramesh, 1970）。这些开创性的工作之后，又有许多基础性和应用性的贡献。他们已经在许多调查中进行了回顾，例如，Esogbue和Bellman (1984), Esogbue， Fedrizzi和Kacprzyk (1988), Kacprzyk (1994)， Kacprzyk和Esogbue（1996）以及Kacprzyk （1983b, 1997）。最近，人们可能会注意到对模糊动态规划越来越感兴趣，这当然是越来越多的应用所隐含的（d. Kacprzyk, 1997），其中一些也将在本章中提到。本章的目的是提供一个简短的、可读的、最新的模糊动态规划概览，其中包括对主要问题类别、基础、发展和更多相关应用的回顾。由于篇幅有限，我们将假设读者熟悉传统的（非模糊的）动态规划，尽管只需要基本的知识。对于那些还没有接触过动态规划的读者，我们可以推荐任何关于运筹学、控制、决策分析等方面的书籍。这样的书几乎可以从所有主要出版商那里买到。我们的讨论基本上将在决策分析和运筹学的广泛背景下进行，尽管我们必须意识到（模糊）动态规划是一种更普遍的问题解决技术，远远超出了这两个领域。例如，在工程和医学、数据分析、计算机科学、经济学等各个方面的应用中，它对控制至关重要。
The performance of the process is measured over some planning horizon, and is expressed by an aggregate of partial scores which expresses the performance of the particular stage decision. This aggregate may take on various forms as, eg, from a pessimistic," safety-first" minimum to an optimistic maximum, through all intermediate cases exemplified by an (weighted) average. An optimal sequence ofdecisions or controls at the consecutive stages over the planning horizon (policy) assumed is then sought. Dynamic programming is a powerful formal apparatus for dealing with a large spectrum of multistage DM problems. Since its inception in the mid-1950's (cf. Bellman, 1957), dynamic programming has become a standard tool in many fields including operations research, systems analysis, engineering, data analysis, control, computer science, etc.In real world problems, we are faced however with imperfect information (data). We have to deal with, eg, uncertain, imprecise, vague, etc. data available. In modeling and analyzing problems of this genre, previous works tended to equate all aspects of imperfect information with uncertainty (of a random character). Thus, a multitude of probabilistic models were proposed. This was also the case with the use of dynamic programming. However, no simple and adequate formal apparatus for handling imprecise data-which may stem, eg, from the use of natural language by humans-was available until the mid-1960's when Zadeh (1965) proposed fuzzy sets theory. And, indeed, dynamic programming has been one of the earliest general techniques to which fuzzy sets theory has been applied (Chang, 1969; Bellman and Zadeh, 1970; Esogbue and Ramesh, 1970). These pioneering works have been followed by numerous contributions of both a foundational and applied character. They have been reviewed in many surveys as, eg, by Esogbue and Bellman (1984), Esogbue, Fedrizzi and Kacprzyk (1988), Kacprzyk (1994), Kacprzyk and Esogbue (1996) as well as in Kacprzyk (1983b, 1997). Recently, one may notice an increased interest in fuzzy dynamic programming which is certainly implied by more and more applications (d. Kacprzyk, 1997) some of which will be mentioned in this chapter too. The purpose of this chapter is to provide a short, readable, and up-to-date survey of fuzzy dynamic programming which would include a review of main problem classes, foundations, developments, and more relevant applications. Due to lack ofspace, we will assume that the reader is familiar with conventional (nonfuzzy) dynamic programming, though only a basic knowledge is required. To those readers who have not yet been exposed to dynamic programming, we can recommend any book on operations research, control, decision analysis, etc. Such books are available from virtually all major publishers. Our discussion will basically proceed in a broadly perceived context of decision analysis and operations research, though we have to be aware of the fact that (fuzzy) dynamic programming is a more general problem solving technique which goes well beyond these two fields. For instance, it is crucial for control with applications in all aspects of engineering and medicine, data analysis, computer science, economics, etc.