Another extension of Nonlinear Integral, Upper and Lower Nonlinear Integrals, which is a pair of extreme nonlinear integrals to contain all types of Nonlinear Integrals in the same scheme, is also proposed. It can give a set of upper and lower bounds which include all types of Nonlinear Integrals. We tried to find a solution with the smallest distance between the upper and lower bounds and the smallest error which is a NP hard problem. So we use the multi-objective optimization method to find a set of results for the regression model based on the Upper and Lower Nonlinear Integrals. We can just select one or more optimal solution(s) for a specific problem from the set of results. A weather predictor based on this model has been constructed to predict the next days temperature changing trend and range. / Finally, a NI based data mining framework has been established for identifying the chance of developing liver cancer based on the Hepatitis B Virus DNA sequence data. We have shown that the framework obtains the best diagnosing performance amongst many existing classifiers. / Nonlinear Integral (NI) is a useful integration tool. It has been applied to many areas including classification and regression. The classical method relies on a large number of training data, which lead to large time and space complexity. Moreover, the classical Nonlinear Integral has many limitations. For dealing with different situation, we propose Double Nonlinear Integrals and Nonlinear Integrals with Polynomial Kernel to deal with the problems transversely and longitudinally. / The classical Nonlinear Integrals implement projection along a line with respect to the features. But in many cases the linear projection cannot achieve good performance for classification or regression due to the limitation of the integrand. The linear function used for the integrand is just a special type of polynomial functions with respect to the features. We propose Nonlinear Integral with Polynomial Kernel (NIPK) in which a polynomial function is used as the integrand of Nonlinear Integral. It enables the projection to be along different types of curves on the virtual space, so that the virtual values gotten by the Nonlinear Integrals with Polynomial Kernel can be better regularized and easier to deal with. Experiments show that there is evident improvement of performance for NIPK compared to classical NI. / When the data to be classified have special distribution in the data space, the projection may overlap and the classification accuracy will be lowered. For example, when one group of the data is surrounded by the data of another group, or the number of classes for the data is large. To handle this kind of problems; we propose a new classification model based on the Double Nonlinear Integrals. Double Nonlinear Integral means projecting to a 2-Dimensional space by using the Nonlinear Integral twice in succession and classifying the virtual values in the 2-D space corresponding to the original data. Double Nonlinear Integrals can lessen loss of information due to the intersection of different classes on real axis. Accuracy will also be increased accordingly. / Wang, Jinfeng. / Advisers: Kwong Sak Leung; Kin Hong Lee. / Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 139-151). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Thesis (M.S.)--University of Texas at El Paso, 2008. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

The fuzzy inference system has been tuned and revamped many times over and applied to numerous domains. New and improved techniques have been presented for fuzzification, implication, rule composition and defuzzification, leaving rule aggregation relatively underrepresented. Current FIS aggregation operators are relatively simple and have remained more-or-less unchanged over the years. For many problems, these simple aggregation operators produce intuitive, useful and meaningful results. However, there exists a wide class of problems for which quality aggregation requires nonditivity and exploitation of interactions between rules. Herein, the fuzzy integral, a parametric non-linear aggregation operator, is used to fill this gap. Specifically, recent advancements in extensions of the fuzzy integral to “unrestricted” fuzzy sets, i.e., subnormal and non-convex, makes this now possible. The roles of two extensions, gFI and the NDFI, are explored and demonstrate when and where to apply these aggregations, and present efficient algorithms to approximate their solutions.

Due to increase global competitive pressure, shortened product life cycles and ease of imitation, firms must continue to innovate to maintain their competitiveness. Technological innovation has become the primary basis of productivity improvements, sales volume growth, and competitiveness of firms, especially for the high-tech companies. Thus, identification and evaluation of technologies from a variety of perspectives now play important roles in the effective technological sources management. Traditionally, technological innovation studies stressed single model or variable having effects on firm productivity and performance. However, the challenge for business environment is continually changing; single model or variable is not good enough to explain the overall impact of technological innovation. The most difficult aspect of technological innovation performance measurement is the identification of appropriate metrics and approaches that provide information concerning these facets. In this study, the researcher tried to develop a technological innovation performance measurement model and determine tangible and intangible factors from the systematical perspective. That is, technological innovation in its nature is multi-dimensional and multi-criteria. Furthermore, technology innovation performance measurement can be conceptualized as multi-criteria a complex problem which involves the simultaneous consideration of multiple quantitative and qualitative requirements. In this empirical study, the researcher firstly utilizes the Delphi technique to build a hierarchical network structure model for evaluating the technological innovation performance measurement of high tech firms. Secondly, analytic network process (ANP) was applied to determine the importance weights of each dimension and criterion while exists interdependencies among criteria within the same dimension. Thirdly, Non-additive fuzzy integral method was then applied for information fusion and calculates the synthetic performance on a hierarchical network model structure for which criteria are interdependent and interactive. This study applied fuzzy measure and non-additive fuzzy integral method to derive the synthetic performance values of each dimension and firm. Through the technological innovation performance evaluation model can provide firms with an overview of their strengths and weaknesses with regards to technological innovation management. Furthermore, R&D managers and senior managers can apply this model to evaluate and determine the technological innovation capabilities of a firm to improve its technological innovation performance. Finally, this model may provide the useful information for managers and to reduce the overall technological innovation uncertainty.

Data/information fusion is an integral component of many existing and emerging applications; e.g., remote sensing, smart cars, Internet of Things (IoT), and Big Data, to name a few. While fusion aims to achieve better results than what any one individual input can provide, often the challenge is to determine the underlying mathematics for aggregation suitable for an application. In this dissertation, I focus on the following three aspects of aggregation: (i) efficient data-driven learning and optimization, (ii) extensions and new aggregation methods, and (iii) feature and decision level fusion for machine learning with applications to signal and image processing. The Choquet integral (ChI), a powerful nonlinear aggregation operator, is a parametric way (with respect to the fuzzy measure (FM)) to generate a wealth of aggregation operators. The FM has 2N variables and N(2N − 1) constraints for N inputs. As a result, learning the ChI parameters from data quickly becomes impractical for most applications. Herein, I propose a scalable learning procedure (which is linear with respect to training sample size) for the ChI that identifies and optimizes only data-supported variables. As such, the computational complexity of the learning algorithm is proportional to the complexity of the solver used. This method also includes an imputation framework to obtain scalar values for data-unsupported (aka missing) variables and a compression algorithm (lossy or losselss) of the learned variables. I also propose a genetic algorithm (GA) to optimize the ChI for non-convex, multi-modal, and/or analytical objective functions. This algorithm introduces two operators that automatically preserve the constraints; therefore there is no need to explicitly enforce the constraints as is required by traditional GA algorithms. In addition, this algorithm provides an efficient representation of the search space with the minimal set of vertices. Furthermore, I study different strategies for extending the fuzzy integral for missing data and I propose a GOAL programming framework to aggregate inputs from heterogeneous sources for the ChI learning. Last, my work in remote sensing involves visual clustering based band group selection and Lp-norm multiple kernel learning based feature level fusion in hyperspectral image processing to enhance pixel level classification.

在電子商務的環境中，透過資訊科技的使用與通訊網路的連結，將會有愈來愈多的產品或服務需求者透過新興的電子化媒體 (如網際網路) 來尋找可行的交易互動夥伴，進而完成交易。因此，交易結構□每一份子間的互動關係，將面臨新的衝擊與挑戰。而納入電子商務觀念的供應鏈管理，將是以資訊科技與通訊技術為基礎的新領域，在此一領域中，供應鏈可以簡單地概念化成三部份：即產品/服務的供給者 (賣方)、產品/服務的需求者或是消費者 (買方)、及提供兩者溝通服務的資訊服務提供者。而在三者間，除了存在著生產與配送過程中既有的物料流/產品流、服務流及完成交易所必須的金流之外，更重要的是還有提供控制機能的資訊流。如何有效地管理與利用資訊流便成為供應鏈管理成功與否的關鍵性因素，而企業也因此產生了對於資訊服務的需求。 因此，本論文的目的在於發展出一個完整的研究體系，以針對傳統供應鏈中之供需雙方與資訊服務業之間的關係，發展出一個供需互動模式，以使電子商務環境中資訊服務的供需雙方能夠據此制定重要的決策與策略。此一體系包含了以下三個子體系：概念體系、評估體系、以及規劃體系。在概念體系的部份，本研究將透過文獻探討，針對供應鏈中的供需者 (可被視為資訊服務的需求者) 與資訊服務提供者，發展出一個整合的概念性互動模式，此一模式將解釋各個體之目標與其行為屬性，而這些目標與屬性也將成為後續評估及規劃體系發展的基礎。而後續兩個體系的發展，將以資訊服務的供需互動為研究主體。就評估體系而言，本研究將分別使用加法型 (層級分析法) 與非加法型 (模糊積分法) 方法來發展評選資訊服務提供者的多準則決策模式。而根據上述的結果，決策者便可針對其手邊現有的可選擇方案，來進行評選。一旦評選結果確定之後，決策者便可與其進行後續的供需互動。至於規劃體系的部份，則是要分析供需雙方如何根據自身的目標與資源限制，經由資訊的分享與交換，與所選取的夥伴進行互動。根據供需關係的型態及供需互動的主導者這兩個分類的標準，本研究將供需互動分成四種不同的狀況來探討。而透過模糊二階多目標規劃模式與多階段解題流程圖的應用，我們可以分析供需單位間如何透過資訊的交換以進行互動，並解釋互動所可能出現的結果，亦即失敗或成功。最後，本研究也將使用一個簡例來說明模式的可用性。 第一章 緒論…………………………………………… 1 第一節 研究動機與背景………………………… 1 第二節 研究目的………………………………… 3 第三節 研究方法與發展流程…………………… 5 第四節 論文結構與內容………………………… 6 第二章 文獻探討……………………………………… 7 第一節 電子商務………………………………… 7 壹、電子商務之定義……………………………. 7 貳、電子市場……………………………………. 12 第二節 供應鏈管理……………………………… 15 壹、供應鏈管理之定義………………………… 15 貳、關係的管理與分析………………………...… 17 參、買賣雙方之供需關係………………………... 21 肆、資訊服務提供者之中介……………………... 24 第三節 個體之目標與行為……………………… 29 壹、供應鏈管理之整體目標……………………... 29 貳、供給者 (賣方) 之立場……………………… 32 參、需求者 (買方) 之立場……………………… 35 肆、資訊服務提供者之立場…………………… 39 第三章 研究模式與方法……………………………… 49 第一節 研究模式………………………………. 49 壹、研究定位與個體定義………………………. 49 貳、供需互動模式………………………………. 51 參、研究範圍與分類架構………………………. 52 第二節 研究類型與步驟………………………… 54 第三節 評估方法論……………………………… 58 壹、因子分析……………………………………... 58 貳、加法型多準則評估…………………………. 59 參、非加法型多準則評估………………………. 61 肆、方案績效值的取得………………………… 63 第四節 規劃方法論……………………………… 70 壹、多目標規劃法…………………………… 70 貳、二階規劃法…………………………………. 73 第四章 評估面之研究 – 資訊服務提供者之評選…… 78 第一節 樣本特徵與資訊服務之使用現況……… 78 第二節 評選資訊服務提供者之準則分析……… 81 壹、評選準則之敘述統計分析………………… 81 貳、評選準則之因子分析……………………… 82 參、後續之效度驗證程序……………………… 90 第三節 多準則評估與決策體系之建立………… 93 壹、加法型多準則評估 – 層級分析法………… 93 貳、非加法型多準則評估 – 模糊積分法……… 97 參、實例說明與比較……………………………. 99 第五章 規劃面之研究 – 供需互動模式之發展…...….. 103 第一節 各種供需互動之說明…………………. 103 第二節 供需互動模式之發展………………… 106 壹、問題特性與解題流程……………………… 106 貳、互動規劃模式之建立……………………… 107 參、不同關係型態對互動過程的影響………… 113 第三節 簡例說明……………………………… 117 壹、背景說明…………………………………… 117 貳、問題求解過程說明………………………… 118 參、討論………………………………………… 125 第六章 結論與建議…………………………………… 127 第一節 結論……………………………………… 127 第二節 研究限制與困難………………………… 129 第三節 未來發展方向…………………………… 130 參考文獻………………………………………………… 131 附錄一………………………………………………………… 141 附錄二………………………………………………………… 145 附錄三………………………………………………………… 150 附錄四………………………………………………………… 153 附錄五………………………………………………………… 155 附錄六………………………………………………………… 163 附錄七………………………………………………………… 165 博士候選人簡歷……………………………………………… 172 / In the environment of Electronic Commerce (EC), there are more and more demanders of products or services looking for available interactive partners of transaction through the burgeoned electronic media (such as the Internet), who then complete transactions with the use of information technology and the connection of communication networks. Therefore, the interactive relationship between each member in the transaction structure will face new poundings and challenges. And the supply chain (SC) management, which fits into the notion of EC, will be a new field based on information technology and communication infrastructure. Within this field, the SC can be simply conceptualized into three parts: (1) Those act as the suppliers of products and services (the sellers), (2) The demanders or consumers of products and services (the buyers) and (3) the information service provider (ISP) which provides the information service for both parties. Among these three parties, in addition to the material/product flow and service flow existed in the production and distribution processes together with the financial flow required of accomplishing transactions, what is more important is the information flow that provides control function. Thus, how to effectively manage and use information flow becomes a key factor for successful SC management. As a result, the needs from enterprises for information service arise. This dissertation aims to establish a complete research system which helps develop an interactive supply-demand model for SC in EC, especially focusing on the relationship between the demanders and suppliers of information service. The research system includes three sub-systems: system of conceptualization, system of evaluation and system of planning. The system of conceptualization develops an integrated conceptual model to depict the interactive supply-demand relationship within SC. This model explains the objectives and the behavioral attributes of every individual, which then become the foundation of follow-up development of the systems of evaluation and planning. As for system of evaluation, this paper uses both additive (Analytic Hierarchy Process) and non-additive methods (Fuzzy Integral) to develop the multiple criteria decision making model for evaluating and selecting ISPs. In accordance with the results above, decision-makers are able to evaluate and select from alternatives on hand. Once the evaluation result is confirmed, decision-makers can proceed with the follow-up supply-demand interaction. As for the planning system, analysis of how supplier and demander of information service interact with each other according to their objectives and resource constraints is carried out. This dissertation also divides the supply-demand interaction into four different situations according to the type of relationship and the dominance. Through the application of fuzzy bi-level multiple objective programming (fuzzy BLMOP) technique and the multi-stage problem solving flow chart, we can analyze how the supply and demand units interact with each other by exchanging information and the possible outcomes of interactions can be explained. Finally, this dissertation illustrates the applicability of the fuzzy BLMOP model with a simple example.

Η παρούσα διατριβή εκπονήθηκε με σκοπό να γενικεύσει το πρόβλημα του ελέγχου υποθέσεων που εμπεριέχουν στοχαστική διάταξη στα πλαίσια της Μη Παραμετρικής Στατιστικής. Για τον σκοπό αυτό μελετήθηκε η σχετική βιβλιογραφία, εξετάσθηκε η ορολογία, οι ήδη υπάρχοντες ορισμοί και οι σχετικές προταθείσες μέθοδοι και ακολούθως έγινε προσπάθεια γενίκευσης του προαναφερθέντος προβλήματος. Η έρευνα αυτή απέδωσε δύο ομάδες αποτελεσμάτων. Στην πρώτη, ορίσθηκε μια νέα ολική διάταξη (XFO) σε κάθε σύνολο ασαφών αριθμών που έχουν διαφορετικές κορυφές οι οποίες σχηματίζουν συμπαγές υποσύνολο του ℝ. Η ασαφής αυτή διάταξη αποδίδει την σύγκριση των ασαφών αριθμών με ένα ασαφές μέτρο αναγκαιότητας και με το δυϊκό του μέτρο δυνατότητας. Η σύγκριση αυτής της μεθόδου με την πλέον αναγνωρισμένη αντίστοιχη μέθοδο διάταξης ασαφών αριθμών απέδειξε ότι η εισαχθείσα μέθοδος XFO είναι πιο κοντά στην αρχική μας εκτίμηση για την διάταξη και ανταποκρίνεται πιο αισιόδοξα. Στην δεύτερη ομάδα αποτελεσμάτων εισάγεται η έννοια της στοχαστικής διάταξης ασαφών τυχαίων μεταβλητών, με σύντηξη των ακολούθων εννοιών: α) της στοχαστικής διάταξης, β) της ανωτέρω ασαφούς διάταξης και γ) της εισαγόμενης έννοιας της ασαφούς συνάρτησης κατανομής. Ο ορισμός της στοχαστικής διάταξης δίδεται σε αρμονία με την μέθοδο XFO, αφού και οι δύο έχουν τις ρίζες τους στην ίδια διάταξη κλειστών διαστημάτων που εισάγεται αρχικά στην εργασία, μπορεί δε να θεωρηθεί η ασαφής στοχαστική διάταξη ως επέκταση της XFO. Η δεύτερη αυτή ομάδα περιλαμβάνει ένα εισαγόμενο για πρώτη φορά τρόπο ορισμού Ασαφών Υποθέσεων που περιέχουν στοχαστική διάταξη ασαφών τυχαίων μεταβλητών. Αυτό έχει αποτέλεσμα να βαθμολογείται θετικά μόνο η μία εκ των δύο ασαφών υποθέσεων, ασαφούς μηδενικής και ασαφούς εναλλακτικής, διευκολύνοντας έτσι την λήψη αποφάσεων. Προτείνεται διαδικασία ασαφούς ελέγχου που πιστοποιεί οποιαδήποτε ενυπάρχουσα στοχαστική διάταξη δύο ασαφών τυχαίων δειγμάτων, συμβατή με τον ορισμό, η οποία αντιστοιχεί θετικές τιμές αλήθειας μόνον στην αποδεκτή υπόθεση και μηδέν στην απορριπτόμενη. Τα αποτελέσματα του ελέγχου εκφράζονται με την βοήθεια δύο μέτρων αναγκαιότητας. Η μείζων συνεισφορά της προτεινόμενης ασαφούς διαδικασίας ελέγχου ασαφών υποθέσεων, που αναφέρονται σε στοχαστική διάταξη ασαφών τυχαίων μεταβλητών, είναι ότι παρέχει εργαλείο μετασχηματισμού του προβλήματος σε ένα περιορισμένο αριθμό ελέγχων κλασσικών υποθέσεων της μη Παραμετρικής Στατιστικής. Με τον τρόπο αυτό μπορούμε να συμβάλουμε στην επίλυση τέτοιων προβλημάτων ασαφών ελέγχων τόσο θεωρητικών ζητημάτων στοχαστικής διάταξης ασαφών τυχαίων μεταβλητών όσο και ενός αριθμού πρακτικών προβλημάτων, όπως της ασαφούς αξιολόγησης εξεταζομένων. / This dissertation has been carried out in order to extend the problem of testing hypotheses on stochastic orderings, with methods based on ranks. This study provides two sets of related results. In the first set of results we introduce a novel linear order, the “extended fuzzy order” (XFO), on every subset of F(ℝ), the members of which must have their modal values all different and form a compact subset of ℝ. A distinct new feature is that our linear determined procedure employs the corresponding order of a class interval associated with a confidence measure which assigns a necessity measure value on every comparison . This new XFO method measures the ordering of any two fuzzy numbers with a possibility and a necessity measure, a feature that makes the method relevant for processing of fuzzy statistical data. These fuzzy measures are compared with the widely accepted PD and NSD indices of D. Dubois and H. Prade. The comparison proves that our possibility and necessity measures are more optimistic and comply better with our intuition. In the second set of results it is investigated the fuzzy extension of hypotheses testing using non parametric methods based on ranks. To achieve this, the notion of fuzzy distribution function is introduced in a practical manner, which is proved to be equivalent to the known notion of Kruse and Mayer. The stochastic ordering of two fuzzy random samples is defined in a fusion of the notion of stochastic ordering, fuzzy distribution function and XFO method. A novel definition of fuzzy hypotheses related to a potential fuzzy stochastic order between two fuzzy random samples is given in a new manner so that the null and its alternative hypotheses do not overlap. Consequently, the method assigns positive possibility grades either to the null fuzzy hypothesis or to the its fuzzy alternative. This simplifies the fuzzy decision making, and moreover there is no need to defuzzify the results if a clear cut decision is required. A fuzzy statistical inference procedure of fuzzy hypotheses is proposed and it is carried out at a fuzzy significance level. The definition of a fuzzy critical value is required, which is carried out in a practical manner. The proposed method certifies any underlying stochastic fuzzy order between two fuzzy random samples giving grades of confidence to that. Two necessity measures are assigned to the rejection of the fuzzy null hypothesis in favor of its alternative. The first measures the necessity of the existence of any fuzzy stochastic ordering between the fuzzy random samples under examination. The second necessity measure expresses the confidence of the fuzzy null hypothesis rejection uniformly for all relevant α-cut levels. The main contribution of this thesis, as far as the second set of results is concerned, is that a problem of testing fuzzy hypotheses on stochastic orderings of fuzzy random variables at a fuzzy significance level, is transferred to a limited number of tests of classic hypotheses. These tests are carried out at a fuzzy significance level, and are processed with the application of the linear fuzzy ordering procedure XFO.