臺灣博碩士論文加值系統

當分析一個具有多重輸入訊息的系統時，系統某一特定輸出之特性與哪些輸入訊息間具有依賴性，這樣的關連結構必須予以慎重考慮，本質上這類系統便屬於資訊融合系統。傳統上最常使用的處理方式乃是以加權平均與線性回歸方式作為輸入信息之融合工具。這些線性融合的方法之所以能妥善運行，都是基於系統之輸入訊息間彼此皆是獨立且無交互作用的假設下。然而，絕大多數的實務問題上，系統之輸出都是輸入訊息間彼此交互作用所產生的合成效應。例如，行為導向的智慧型機器人系統、天氣預報系統…等。這些都是必須考慮輸入訊息間交互作用的系統，而且本質上此一交互作用並非單純地加總行為所能描述。因此，當處理此類系統時，就必須引用具有非可加特性之非線性積分，方能適切地將問題予以模型化。同時，如欲精確地估算出模型的參數，適當的系統觀測數據也是不可缺。將可用之觀測數據引入模型用以估算模型之參數，此實屬於非線性規劃之問題。因此，適當地選用高效率的智慧型計算技巧也是相當重要的研究課題。
在本論文中，引用以 Choquet 積分為核心的非線性多變數回歸模型來處理此類非可加系統，並針對不同型態的輸入訊息，以不同形式之模型予以妥善描述。有鑒於觀測數據引入模型後將執行龐大的計算，本論文採用具量子行為之粒子群優化演算法（QPSO），並予以修改而命名為 MQPSO 演算法作為基礎模型參數的估算工具。此一修改乃將基因演算法的精英交配的概念融入 QPSO 演算法中，以加速演算法收斂至最佳解。但對一般化的非線性多變數回歸模型而言，需要更多的參數才能將系統妥善地描述。因此再將 MQPSO 演算法予以改良，此一改進乃針對原為線性遞減的步長係數 ，調整為非線性衰變，此一衰變模式相似於模擬退火演算法，故將改良後的演算法命名為 MQPSO-NLB 演算法。得到初步成效後，更進一步地將模型擴展成可以處理離異點隨機發生之結構，這樣的模型方能與實務上之非可加系統相符合。也因為考慮到離異點發生時，勢必將造成所估計的模型參數偏離實際值，因此，引入具有高容許誤差的最小截斷平方（LTS）運算子，用以消除離異點所產生的偏離效應。由第一階段的模擬結果中可看出，MQPSO 演算法相較於基因演算法確實更有效率。此外，為因應非可加系統模型受到離異點干擾後所引發之效應，本論文再將 MQPSO 演算法進一步改良，即融入 LTS 運算子，形成名為 LTS-MQPSO-NLB 演算法。同樣地透過模擬分析與實際問題測試，均可得到相當準確之結果。

To analyze a system with many attributes, we always need to recognize how a specified objective attribute depend on other attributes. It is essential a frequent problems in information fusion. Traditionally, the most common aggregation tools are the weighted average method and the linear regression. These methods are all linear and must make a basic assumption that there are no interactions among predictive attributes. However, in many real-world problems such as a behavior-based intelligent mobile robot, the weather forecast, etc., the inherent interaction among predictive attributes must be considered circumspectly; meanwhile, these kinds of problems are essential non-additive systems. Hence, a nonlinear integral model with respective to a non-additive set function is suitable for dealing with these kinds of problems. In general, these kinds of models constitute over-determined systems with nonlinear integrals and then, it is extremely difficult to acquire the analytic solution. Therefore, an efficiently intelligent computing technique is necessary for these models to perform precise estimations of model’s parameter.
In this dissertation, different nonlinear multi-regression models based on the Choquet integral (NMRCI) are considered for modeling non-additive systems with different type of predictive attributes, respectively. Meanwhile, the parameters estimation for the simplest model is also performed via a modified particle swarm optimization with quantum-behavior (MQPSO) algorithm, in which the mechanism of multi-elitist crossover is included and then, concepts of elitist reproductions and adaptive decay are introduced to improve the MQPSO algorithm such that the generalized NMRCI model can be estimated well. That is, the genetic algorithm (GA) and the simulated annealing (SA) algorithm are embedded in the improved algorithm which is named MQPSO with nonlinear creative coefficient (MQPSO-NLB) algorithm. Furthermore, the effects which are caused from outliers are also considered for extending these proposed NMRCI models such that the extended model can model a real-world non-additive system well. Meanwhile, to efficiently estimate the extended model parameters, the robustness of the proposed MQPSO-NLB algorithm must be gained. Therefore, the high breakdown regression estimator, least trimmed squares (LTS) is then introduced to eliminate the deviations caused by the observations contaminated with outliers. That is, the LTS estimator is instead of the LS estimator in the MQPSO-NLB algorithm and then, the proposed intelligent computing algorithm which combines the mechanisms of the GA, the SA algorithm and the LTS estimator into the QPSO algorithm named LTS-MQPSO-NLB algorithm can deal with the generalized NMRCI model with contaminated observations for a non-additive system with outliers. From the numerical simulations, satisfied results can be achieved.

Chinese Abstract i
English Abstract iii
Acknowledgments v
Contents vi
List of Tables viii
List of Figures x

Chapter 1 Introduction 1
1.1 Literature Survey 1
1.2 Motivation and Contributions 4
1.3 Organization of the Dissertation 5

Chapter 2 Preliminary Background and Problem Definition 6
2.1 The non-additive set functions 7
2.1.1 The fuzzy measure 7
2.1.2 The -fuzzy measure 8
2.1.3 The possibility measure 9
2.1.4 The -order additive measure 10
2.1.5 The measure 12
2.1.6 The general measure 14
2.2 The nonlinear integrals 16
2.2.1 The Choquet integral 16
2.2.2 The Sugeno integral 19
2.2.3 The upper integral 21
2.3 The Least Trimmed Squares Estimator 26
2.3.1 The initial -subset 28
2.3.2 The initial C-step 30
2.2.3 The nested extensions 33
2.4 The proposed NMRCI models for the non-additive systems 36
Chapter 3 The Modified Particle Swarm Optimization algorithm with Quantum Behavior 42
3.1 The traditional PSO algorithm 42
3.2 The PSO algorithm with time-varying inertia weight 43
3.3 The PSO algorithm with time-varying cognitive and social parameters 44
3.4 The PSO algorithm with quantum behavior 47
3.5 A modified QPSO algorithm with nonlinear creative coefficient 50

Chapter 4 Parameter estimations for the non-additive systems under the NMRCI models with modified QPSO algorithms 58
4.1 Parameter estimations for the non-additive systems under the original NMRCI models 58
4.2 Parameter estimations for the non-additive systems under the weighted and generalized NMRCI models 62
4.3 Simulation results 63

Chapter 5 Modeling of the non-additive systems with outliers under the NMRCI models with the robust intelligent computing algorithm 78
5.1 Two stage structure for the non-additive systems with outliers under the NMRCI models 78
5.2 The robust intelligent computing algorithm for the non-additive systems with outliers under the NMRCI models 81
5.3 Simulation results 84

Chapter 6 Conclusions and Discussions 96

Summary 99
References 100
Autobiography 107
Publications 108

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