滿意度函數(shù)的動態(tài)建立及靈敏度分析

包括外文翻譯

摘  要

隨著科學技術的不斷發(fā)展以及人們對自然科學和對自身處理問題過程本質的認識的不斷加深，人們發(fā)現(xiàn)傳統(tǒng)的優(yōu)化理論和優(yōu)化技術在求解許多問題上困難重重，于是人們開始把當今其他科技領域的研究成果引入到優(yōu)化理論和優(yōu)化算法中，自從H.A.Simon提出用滿意方案代替最優(yōu)方案的思想，提出了令人滿意準則后，人們紛紛追求滿意，而不是最優(yōu)，從而開辟了一個嶄新的知識體系。雖然滿意問題無處不在，但由于缺乏堅實的數(shù)學理論基礎，其形式化和分析工作都非常困難。滿意方法更加趨向于啟發(fā)式方法，而不是傳統(tǒng)的數(shù)學推導。

本文的目的在于系統(tǒng)的研究滿意問題中滿意度函數(shù)的建立，以求找到一個普遍適用的滿意度函數(shù)。文章從幾種滿意度的定義開始，提出了滿意度函數(shù)的四種建立方法。在此基礎上引出滿意度函數(shù)的動態(tài)建立方法。同時，靈敏度分析的概念也涉及在文章的最后，為滿意度函數(shù)的建立提供了定性分析。

滿意度原理具有普遍性、模糊性、智能性以及相對性等特點，更能反映人類的人性化本質。滿意度原理不僅包容了最優(yōu)化原理，而且也適用于推理機、知識獲取、人工智能、模式識別、管理工程及可靠性等領域。而滿意度函數(shù)的設計在滿意優(yōu)化中更是占有重要地位。本文針對問題的不同情況,提出幾種滿意度函數(shù)的建立方法。對于滿意優(yōu)化在現(xiàn)實問題中的應用以及滿意度原理的進一步推廣具有一定的推動作用。

 關鍵詞：滿意度，滿意度函數(shù)，靈敏度分析

Abstract

With the development of the science ，we understand the natural science and the problems of essence that we deal with., we found that there were a lot of problems in optimization theory and technology in traditional ways. Naturally, people introduced many useful achievements to this field. Since H.A.Simon, who proposed to replace optimization plan with satisfactory one., After Simon’s theory, people turned to satisfactory degree, which made another brand-new knowledge system. Though satisfactory problems are common to see, formalization and analysis of it are difficult because of lack of mathematical foundation. Satisfactory method is close to inspiring method rather than traditional mathematical reasoning.

The purpose of this paper is to build up satisfactory functions in satisfactory problems systematically in order to find a proper satisfactory function which will be effective at any time.From the beginning of several ways to define satisfactory degree,the paper bring up the forms of satisfactory functions and ways to build up them. On the basis of this,it leads to dynamic conditions.Moreover, sensitivity analysis is including in the final article which for provides a qualitative analys for the establishment of satisfaction function.

Satisfactory theory is famous for its universality, fuzziness ,intelligence and relativity, which reflect humanity. The satisfactory theory includes theory of optimizaiton, inference engine , intellectual captune,artificial intelligence, pattern recognition， management Engineering and security. The design of satisfactory functions plays an important part in satisfactory optimization. This paper proposed several ways to define satisfactory functions under different occasions. It has done some work in popularizaiton of satisfactory optimization in our real life and  satisfactory degree theory.

Keywords: Satisfactory degree, The design of the satis-factory-degree, Sensitivity analysis

目  錄

第一章  緒論 1

1.1 令人滿意準則的提出 1

1.2 滿意度原理的發(fā)展階段[9] 1

1.3 滿意度原理研究的發(fā)展趨勢 3

1.4 本文研究的主要內(nèi)容和意義 3

第二章  基本概念 5

2.1　最優(yōu)化問題 5

2.2  滿意標準 5

2.3　滿意度 5

2.3.1 基于模糊數(shù)學的定義 6

2.3.2 基于線性取值的滿意度的定義 6

2.3.3 基于模糊神經(jīng)計算的定義 7

2.3.4 基于遺傳算法的滿意度的定義 7

2.3.5 滿意度的性質 8

2.3.6 滿意度函數(shù)的表示 8

2.4  靈敏度分析 8

2.4.1 靈敏度分析的概念 8

2.4.2 靈敏度分析的應用價值 9

第三章  滿意度函數(shù)的建立及動態(tài)建立 10

3.1  滿意度函數(shù)的表示[9] 10

3.1.1 單調減函數(shù)(戒上型) 10

3.1.2 單調增函數(shù)(戒下型) 12

3.2  建立滿意度函數(shù)的基本準則 13

3.3  滿意度函數(shù)的建立方法[9] 14

3.3.1 基于目標函數(shù)的直接法 14

3.3.2 利用模糊邏輯構造滿意度函數(shù) 14

3.3.3 利用神經(jīng)網(wǎng)絡確定滿意度函數(shù) 15

3.3.4 按照解的搜索代價建立滿意度函數(shù) 17

3.4  滿意度函數(shù)的動態(tài)建立 18

第四章  靈敏度分析 20

4.1  靈敏度分析一般研究的問題[2] 20

4.1.1 改變系數(shù)向量 20

4.1.2 改變右端向量 21

4.1.3 改變約束矩陣 22

4.1  關于動態(tài)滿意度函數(shù)的靈敏度分析 22

總  結 23

參考文獻 24

致  謝 26

附錄一：外文翻譯原文 27

附錄二：譯文 39