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Ruziyeva, Alina. "Fuzzy Bilevel Optimization." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2013. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-106378.
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In the dissertation the solution approaches for different fuzzy optimization problems are presented. The single-level optimization problem with fuzzy objective is solved by its reformulation into a biobjective optimization problem. A special attention is given to the computation of the membership function of the fuzzy solution of the fuzzy optimization problem in the linear case. Necessary and sufficient optimality conditions of the the convex nonlinear fuzzy optimization problem are derived in differentiable and nondifferentiable cases. A fuzzy optimization problem with both fuzzy objectives and constraints is also investigated in the thesis in the linear case. These solution approaches are applied to fuzzy bilevel optimization problems.
In the case of bilevel optimization problem with fuzzy objective functions, two algorithms are presented and compared using an illustrative example. For the case of fuzzy linear bilevel optimization problem with both fuzzy objectives and constraints k-th best algorithm is adopted.
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Tada, Minoru. "STUDIES ON FUZZY COMBINATORIAL OPTIMIZATION." Kyoto University, 1994. http://hdl.handle.net/2433/160752.
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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものであるKyoto University (京都大学)
0048
新制・論文博士
博士(工学)
乙第8724号
論工博第2927号
新制||工||976(附属図書館)
UT51-94-Z475
(主査)教授 茨木 俊秀, 教授 長谷川 利治, 教授 片山 徹
学位規則第4条第2項該当
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Dadone, Paolo. "Design Optimization of Fuzzy Logic Systems." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/27893.
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Fuzzy logic systems are widely used for control, system identification, and pattern recognition problems. In order to maximize their performance, it is often necessary to undertake a design optimization process in which the adjustable parameters defining a particular fuzzy system are tuned to maximize a given performance criterion. Some data to approximate are commonly available and yield what is called the supervised learning problem. In this problem we typically wish to minimize the sum of the squares of errors in approximating the data.
We first introduce fuzzy logic systems and the supervised learning problem that, in effect, is a nonlinear optimization problem that at times can be non-differentiable. We review the existing approaches and discuss their weaknesses and the issues involved. We then focus on one of these problems, i.e., non-differentiability of the objective function, and show how current approaches that do not account for non-differentiability can diverge. Moreover, we also show that non-differentiability may also have an adverse practical impact on algorithmic performances.
We reformulate both the supervised learning problem and piecewise linear membership functions in order to obtain a polynomial or factorable optimization problem. We propose the application of a global nonconvex optimization approach, namely, a reformulation and linearization technique. The expanded problem dimensionality does not make this approach feasible at this time, even though this reformulation along with the proposed technique still bears a theoretical interest. Moreover, some future research directions are identified.
We propose a novel approach to step-size selection in batch training. This approach uses a limited memory quadratic fit on past convergence data. Thus, it is similar to response surface methodologies, but it differs from them in the type of data that are used to fit the model, that is, already available data from the history of the algorithm are used instead of data obtained according to an experimental design. The step-size along the update direction (e.g., negative gradient or deflected negative gradient) is chosen according to a criterion of minimum distance from the vertex of the quadratic model. This approach rescales the complexity in the step-size selection from the order of the (large) number of training data, as in the case of exact line searches, to the order of the number of parameters (generally lower than the number of training data). The quadratic fit approach and a reduced variant are tested on some function approximation examples yielding distributions of the final mean square errors that are improved (i.e., skewed toward lower errors) with respect to the ones in the commonly used pattern-by-pattern approach. Moreover, the quadratic fit is also competitive and sometimes better than the batch training with optimal step-sizes, thus showing an improved performance of this approach. The quadratic fit approach is also tested in conjunction with gradient deflection strategies and memoryless variable metric methods, showing errors smaller by 1 to 7 orders of magnitude. Moreover, the convergence speed by using either the negative gradient direction or a deflected direction is higher than that of the pattern-by-pattern approach, although the computational cost of the algorithm per iteration is moderately higher than the one of the pattern-by-pattern method. Finally, some directions for future research are identified.Ph. D.
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Arnett, Timothy J. "Iteratively Increasing Complexity During Optimization for Formally Verifiable Fuzzy Systems." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin156387481300899.
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Hu, Cheng Lin. "Design optimization of fuzzy models in system identification." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2493501.
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Lehar, Matthew A. 1977. "A branching fuzzy-logic classifier for building optimization." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32512.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 109-110).
We present an input-output model that learns to emulate a complex building simulation of high dimensionality. Many multi-dimensional systems are dominated by the behavior of a small number of inputs over a limited range of input variation. Some also exhibit a tendency to respond relatively strongly to certain inputs over small ranges, and to other inputs over very large ranges of input variation. A branching linear discriminant can be used to isolate regions of local linearity in the input space, while also capturing the effects of scale. The quality of the classification may be improved by using a fuzzy preference relation to classify input configurations that are not well handled by the linear discriminant.
by Matthew A. Lehar.
Ph.D.
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Gasir, Fathi Sidig. "Optimization of fuzzy regression trees using artificial immune systems." Thesis, Manchester Metropolitan University, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.574508.
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This thesis presents the development of a novel fuzzy regression tree algorithm known as Elgasir, which is based on the CHAID regression tree algorithm and Takagi-Sugeno fuzzy inference. The Elgasir Algorithm is applied to crisp regression trees to produce fuzzy regression trees in order to soften sharp decision boundaries inherited in crisp trees. Elgasir generates a fuzzy rule base by applying fuzzy techniques to crisp regression trees using Trapezoidal membership functions. Then Takagi-Sugeno fuzzy inference is used to aggregate the final output from the fuzzy implications. A novel optimization method based on the Artificial Immune Network model (opt-aiNet) is also proposed to optimize the fuzzification of fuzzy regression trees generated by the Elgasir Algorithm. Finally, the Elgasir Algorithm is developed further by proposing a new approach to creating fuzzy regression tree forests based upon the induction of multiple fuzzy regression decision trees from one training sample, where each tree will represent a different view of the data domain. A significant number of experiments were carried out for each of the proposed approaches, using five real-world regression problems from the VCI repository and KEEL repository. The empirical results have shown the effectiveness of using the proposed methods by increasing the prediction accuracy and robustness of fuzzy regression trees.
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Bahri, Oumayma. "A fuzzy framework for multi-objective optimization under uncertainty." Thesis, Lille 1, 2017. http://www.theses.fr/2017LIL10030/document.
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Cette thèse est consacrée à l'étude de l’optimisation combinatoire multi-objective sous incertitudes. Plus particulièrement, nous abordons les problèmes multi-objectifs contenant des données floues qui sont exprimées par des nombres triangulaires floues. Pour faire face à ce type de problèmes, notre idée principale est d’étendre les concepts multi-objectifs classiques au contexte flou. Nous proposons, dans un premier temps, une nouvelle approche Pareto entre des objectifs flous (i.e. vecteurs des nombres triangulaires flous). Ensuite, nous étendons des méta-heuristiques basées sur Pareto afin de converger vers des solutions optimales floues. L’approche proposée est illustrée sur un problème bi-objectif de routage de véhicules avec des demandes floues. Dans le deuxième volet de ce travail, nous abordons l’aspect de robustesse dans le contexte multi-objectif flou en proposant une nouvelle méthodologie d’évaluation de robustesse des solutions. Finalement, les résultats expérimentaux sur des benchmarks flous du problème de routage de véhicules prouvent l’efficacité et la fiabilité de notre approcheThis thesis is devoted to the study of multi-objective combinatorial optimization under uncertainty. In particular, we address multi-objective problems with fuzzy data, in which fuzziness is expressed by fuzzy triangular numbers. To handle such problems, our main idea is to extend the classical multi-objective concepts to fuzzy context. To handle such problems, we proposed a new Pareto approach between fuzzy-valued objectives (i.e. vectors of triangular fuzzy numbers). Then, an extension of Pareto-based metaheuristics is suggested as resolution methods. The proposed approach is thereafter illustrated on a bi-objective vehicle routing problem with fuzzy demands. At the second stage, we address robustness aspect in the multi-objective fuzzy context by proposing a new methodology of robustness evaluation of solutions. Finally, the experimental results on fuzzy benchmarks of vehicle routing problem prove the effectiveness and reliability of our approach
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Spence, William G. "An Optimization Approach To Employee Scheduling Using Fuzzy Logic." DigitalCommons@CalPoly, 2011. https://digitalcommons.calpoly.edu/theses/618.
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An Optimization Approach to Employee Scheduling Using Fuzzy Logic
William G. Spence
Selection of sales employees is critical because the sales employees represent the company’s image, competitive advantage, technology, and values. In many service systems the majority of consumer contact is with the sales department. Since there are different types of customers, scheduling quality salespersons who can adequately help consumers may affect revenue.
This thesis proposes a new methodology for the scheduling of employees in a service system. The methodology uses Fuzzy Logic to calculate possible sales and Linear Programming to create an optimal schedule. This approach enables the rating of sales employees with respect to three customer’s types (Lookie Lou, Price Shopper and Buyer). The salesperson rating, along with customer arrival distribution is then used to optimize sale person scheduling, with the objective of revenue maximization. The uniqueness of this thesis lies in the combination of Fuzzy Logic and Linear Programming. The combination of these two disciplines provides an adaptive tool that can be used to optimize employee scheduling based on personality traits.
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Chiu, Kuan-Shiu. "Adaptive optimization of intelligent flow control." Thesis, University of Sunderland, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.288014.
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Feng, Yi. "Dynamic Fuzzy Logic Control of GeneticAlgorithm Probabilities." Thesis, Högskolan Dalarna, Datateknik, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:du-3286.
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Genetic algorithms are commonly used to solve combinatorial optimizationproblems. The implementation evolves using genetic operators (crossover, mutation,selection, etc.). Anyway, genetic algorithms like some other methods have parameters(population size, probabilities of crossover and mutation) which need to be tune orchosen.In this paper, our project is based on an existing hybrid genetic algorithmworking on the multiprocessor scheduling problem. We propose a hybrid Fuzzy-Genetic Algorithm (FLGA) approach to solve the multiprocessor scheduling problem.The algorithm consists in adding a fuzzy logic controller to control and tunedynamically different parameters (probabilities of crossover and mutation), in anattempt to improve the algorithm performance. For this purpose, we will design afuzzy logic controller based on fuzzy rules to control the probabilities of crossoverand mutation. Compared with the Standard Genetic Algorithm (SGA), the resultsclearly demonstrate that the FLGA method performs significantly better.
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Guo, Lizhu. "Key optimization issues for the design of fuzzy-inference system." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ35169.pdf.
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Walker, Alex R. "Genetic Fuzzy Attitude State Trajectory Optimization for a 3U CubeSat." University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1593265983802031.
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Santos, Patrick John. "Facial Expression Cloning with Fuzzy Membership Functions." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/26260.
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This thesis describes the development and experimental results of a system to explore cloning of facial expressions between dissimilar face models, so new faces can be animated using the animations from existing faces. The system described in this thesis uses fuzzy membership functions and subtractive clustering to represent faces and expressions in an intermediate space. This intermediate space allows expressions for face models with different resolutions to be compared. The algorithm is trained for each pair of faces using particle swarm optimization, which selects appropriate weights and radii to construct the intermediate space. These techniques allow the described system to be more flexible than previous systems, since it does not require prior knowledge of the underlying implementation of the face models to function.
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Pavski, Johann Joachim. "Handover Optimization in GSM." Thesis, Linköpings universitet, Optimeringslära, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-123445.
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In telecommunications in general and in GSM in particular, the handover is a feature that guarantees a smooth transition of a call from one base station - that is for the purpose of this project an antenna - to another. In the recent ten years, the amount of data traffic through mobile telecommunications has doubled annually, putting an enormous strain on the network and forcing operators to upgrade with more and more base stations and new features. Although 3G and 4G are responsible for data traffic in most countries, GSM still provides more than 80% of the coverage for mobile devices around the world. Due to the increase in data traffic, 3G and 4G need to use more and more frequencies at the expense of GSM. An optimization of the GSM network is thus vital. In this project, we research two methods to automatically choose the parameters of interest (PoI) that govern the handover feature in each cell which is, roughly speaking, the area of coverage of one antenna. In one of these methods, the choice of cell- and cell-to-cell-specific parameters has its origins in control theory while the other method is based on mathematical optimization. In the mathematical sense, our goal is to optimize the quality of service over PoIs. Extensive simulations have been run using these PoIs in order to evaluate if and how the two different methods can effectively be used in reality. Several useful insights have been gained that will provide the basis for future work. The optimization approach in particular has proved to deliver good results within the limitations of the simulated environment used for testing.
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Guyot, Nicolas E. "Fuzzy logic and utility theory for multiobjective optimization of automotive joints." Thesis, This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-08292008-063415/.
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Sarma, Kamal C. "Fuzzy discrete multicriteria cost optimization of steel structures using genetic algorithm /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488205318509081.
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Kim, Sungshin. "A neuro-fuzzy approach to optimization and control of complex nonlinear processes." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/14820.
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Zheng, Xinmin, and 鄭新敏. "A fuzzy genetic algorithms (GAs) model for time-cost optimization in construction." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B27510839.
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Silva, Ricardo Coelho. "Programação multi-objetivo fuzzy." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260594.
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Orientadores: Akebo Yamakami, Jose Luis Verdegay GaldeanoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: O objetivo deste trabalho é buscar, estudar e estabelecer as condições de otimali-dade para resolver problemas de programação multi-objetivo irrestritos e restritos em um ambiente impreciso. Essas imprecisões estão presentes nos problemas da vida real e existem muitas formas de tratá-las, mas nesse trabalho será usado a teoria de conjuntos nebulosos. Utilizando como base a otimização nebulosa, foram desenvolvidas duas abordagens para resolver problemas multi-objetivo nebulosos. A primeira abordagem transforma um problema nebuloso em um problema clássico paramétrico com um número maior de funções objetivo, a qual é chamada de paramétrica. A segunda abordagem, chamada de possibilística, usa a teoria de possibilidade como um índice de comparação entre números nebulosos com a finalidade de garantir condições de otimalidade em um ambiente nebuloso. Alguns exemplos numéricos são resolvidos usando um algoritmo genético chamado NSGA-II elitista, com algumas modificações para a comparação de números nebulosos, e depois feita uma análise dos resultados encontrados por ambos os enfoques.
Abstract: The main goal of this work is to search, study and present the optimality conditions to solve the unconstraint and constraint multiobjetive programming problems in imprecise environment. These imprécisions can be found in the real-world optimization problems and there are utmost ways for dealing with them, but in this work will be used the theory of fuzzy sets. Using as a basis the fuzzy optimization, two approaches were developed to solve fuzzy multiobjective problems. The first approach transforms a fuzzy problem into a parametric classic multiobjective programming problem with many more objective functions, which is called parametric approach. The second one, called possibilistic, uses the possibility theory as a comparison index between two fuzzy numbers in order to ensure optimality conditions in a fuzzy environment. Some numerical examples are solved by using a genetic algorithm called elitist NSGA-II with some modifications to compare fuzzy numbers, and then the results obtained with both approaches are analysed.
Doutorado
Automação
Doutor em Engenharia Elétrica
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Lee, Shinhak. "Projections onto fuzzy convex sets and its application to radiation beam optimization in radiotherapy /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/6128.
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Bordin, Deyver [UNESP]. "Plataforma computacional fuzzy para avaliação nos estágios do tomateiro dos efeitos da irrigação e salinidade da água." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/138168.
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O tomate é uma importante cultura, não só em termos de produção, mas também em valor econômico, por ser uma hortaliça bastante industrializada e ainda conta com um aumento da produção per capita anual no Brasil, o que coloca o produto em destaque, além de estar diariamente na dieta alimentar de grande parte da população. Para o cultivo do tomate, duas preocupações devem ser levadas em conta: a quantidade de água, pois a baixa umidade do solo restringe seu crescimento reduzindo, sua produção e a qualidade da água que será utilizada na irrigação do tomateiro, pois, esta deve estar livre de contaminantes biológicos, teor de sais inferior a 1,5 g L-1 para evitar o murchamento foliar nos horários mais quentes do dia, queimadura do ápice e dos bordos da folha pela morte do tecido foliar e até mesmo da planta. Visando economia de recursos e aumento na produtividade no cultivo do tomate, o presente trabalho teve como objetivo desenvolver um sistema computacional para a avaliação da cultura do tomate híbrido (Licopersicum esculentum). Em que foi utilizado um sistema baseado em regras fuzzy por meio do software Matlab® utilizando dados biométricos da cultura do tomate submetido em diferentes níveis de irrigação e salinidade, sendo avaliado ao longo do ciclo. O experimento foi realizado em uma casa de vegetação da UNESP/FCA. Para tanto, foi utilizado a linguagem Delphi, os dados do experimento e a modelagem fuzzy. Este software possibilita ao produtor um indicativo da viabilidade de produção, além de fornecer subsídios para avaliar e manejar de forma eficiente e eficaz, assim sendo uma poderosa ferramenta de tomada de decisão, que visa obter maior produtividade e economia dos recursos hídrico e enérgicos.
The tomato is an important crop, not only in terms of production, but also in economic value, being a vegetable very industrialized and also includes an increase in annual per capita production in Brazil, which puts the product highlighted, and be daily in the diet of most of the population. For growing tomatoes, two concerns should be taken into account: the amount of water because of the low soil moisture restricts its growth reducing production and quality of water to be used in tomato irrigation, therefore it must be free of biological contaminants, salt content less than 1.5 g L-1 to prevent leaf wilting in the hottest times of the day, apex burn and leaf edges of the death of leaf tissue and even the plant. Aiming to save resources and increase productivity in growing tomatoes, this study aimed to develop a computer system for the evaluation of hybrid tomato crop (Licopersicum esculentum). It was used a system based on fuzzy rules using the Matlab software using biometric data of the tomato crop submitted at different levels of irrigation and salinity, and evaluated over the cycle. The experiment was conducted in a greenhouse at UNESP/FCA. Therefore, we used the Delphi language, experimental data and fuzzy modeling. This software enables the producer indicative of production feasibility, and provide subsidies to assess and manage efficiently and effectively, making it a powerful decision-making tool, which aims to achieve greater productivity and economy of water and energetic resources.
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Dosi, Shubham. "Optimization and Further Development of an Algorithm for Driver Intention Detection with Fuzzy Logic and Edit Distance." Master's thesis, Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-202567.
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Inspired by the idea of vision zero, there is a lot of work that needs to be done in the field of advance driver assistance systems to develop more safer systems. Driver intention detection with a prediction of upcoming behavior of the driver is one possible solution to reduce the fatalities in road traffic. Driver intention detection provides an early warning of the driver's behavior to an Advanced Driver Assistance Systems (ADAS) and at the same time reduces the risk of non-essential warnings. This will significantly reduce the problem of warning dilemma and the system will become more safer. A driving maneuver prediction can be regarded as an implementation of driver's behavior. So the aim of this thesis is to determine the driver's intention by early prediction of a driving maneuver using Controller Area Network (CAN) bus data.
The focus of this thesis is to optimize and further develop an algorithm for driver intention detection with fuzzy logic and edit distance method. At first the basics concerning driver's intention detection are described as there exists different ways to determine it. This work basically uses CAN bus data to determine a driver's intention. The algorithm overview with the design parameters are described next to have an idea about the functioning of the algorithm. Then different implementation tasks are explained for optimization and further development of the algorithm. The main aim to execute these implementation tasks is to improve the overall performance of the algorithm concerning True Positive Rate (TPR), False Positive Rate (FPR) and earliness values. At the end, the results are validated to check the algorithm performance with different possibilities and a test drive is performed to evaluate the real time capability of the algorithm.
Lastly the use of driver intention detection algorithm for an ADAS to make it more safer is described in details. The early warning information can be feed to an ADAS, for example, an automatic collision avoidance or a lane change assistance ADAS to further improve safety for these systems.
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Huber, Martin [Verfasser]. "Structural Design Optimization Including Quantitative Manufacturing Aspects Derived from Fuzzy Knowledge / Martin Huber." München : Verlag Dr. Hut, 2011. http://d-nb.info/1011441276/34.
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Ruziyeva, Alina. "Fuzzy Bilevel Optimization." Doctoral thesis, 2012. https://tubaf.qucosa.de/id/qucosa%3A22842.
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In the dissertation the solution approaches for different fuzzy optimization problems are presented. The single-level optimization problem with fuzzy objective is solved by its reformulation into a biobjective optimization problem. A special attention is given to the computation of the membership function of the fuzzy solution of the fuzzy optimization problem in the linear case. Necessary and sufficient optimality conditions of the the convex nonlinear fuzzy optimization problem are derived in differentiable and nondifferentiable cases. A fuzzy optimization problem with both fuzzy objectives and constraints is also investigated in the thesis in the linear case. These solution approaches are applied to fuzzy bilevel optimization problems.
In the case of bilevel optimization problem with fuzzy objective functions, two algorithms are presented and compared using an illustrative example. For the case of fuzzy linear bilevel optimization problem with both fuzzy objectives and constraints k-th best algorithm is adopted.:1 Introduction 1
1.1 Why optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Fuzziness as a concept . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2
1.3 Bilevel problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Preliminaries 11
2.1 Fuzzy sets and fuzzy numbers . . . . . . . . . . . . . . . . . . . . . 11
2.2 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Fuzzy order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Fuzzy functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
3 Optimization problem with fuzzy objective 19
3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Solution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Local optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Existence of an optimal solution . . . . . . . . . . . . . . . . . . . . 25
4 Linear optimization with fuzzy objective 27
4.1 Main approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 Optimality conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4 Membership function value . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.1 Special case of triangular fuzzy numbers . . . . . . . . . . . . 36
4.4.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
5 Optimality conditions 47
5.1 Differentiable fuzzy optimization problem . . . . . . . . . . .. . . . 48
5.1.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.2 Necessary optimality conditions . . . . . . . . . . . . . . . . . . .. 49
5.1.3 Suffcient optimality conditions . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Nondifferentiable fuzzy optimization problem . . . . . . . . . . . . 51
5.2.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.2 Necessary optimality conditions . . . . . . . . . . . . . . . . . . . 52
5.2.3 Suffcient optimality conditions . . . . . . . . . . . . . . . . . . . . . . 54
5.2.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6 Fuzzy linear optimization problem over fuzzy polytope 59
6.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.2 The fuzzy polytope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
6.3 Formulation and solution method . . . . . . . . . . . . . . . . . . .. . 65
6.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7 Bilevel optimization with fuzzy objectives 73
7.1 General formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.2 Solution approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
7.3 Yager index approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.4 Algorithm I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.5 Membership function approach . . . . . . . . . . . . . . . . . . . . . . .78
7.6 Algorithm II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80
7.7 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8 Linear fuzzy bilevel optimization (with fuzzy objectives and constraints) 87
8.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2 Solution approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
8.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
9 Conclusions 95
Bibliography 97
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Wang, Shinn-Wen, and 王信文. "Optimization of Fuzzy System by Fuzzy Clustering Analysis." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/91650923483074530257.
Full textAbstract:
碩士大葉工學院
電機工程研究所
84
Optimization of Fuzzy System by Fuzzy Clustering Analysis ABSTRACT Fuzzy rule base and fuzzy membership functions(MFs) are two major factors in deciding the performance of fuzzy inference system. Therefore, the design plays an important role for the performance stated above. Trial and error was usually the way to solution, which was not only costly and time-consuming but also promised no optimized result. In recent years, many papers were presented about this topic, but none of them has perfect answer. To attack the above problems, we propose the Modified Fuzzy C- Means Method(MFCM) for tuning the parameters of MFs. Then, we fine-tune the MFs with backpropagation learning method. MFCM will be examed for modeling with highly complicated nonlinear functions, such as sinc function and gaussian function, and pattern classification. Finally,there is a simulation test of anti-collision driving system, including first kind of trajectory, second kind of trajectory and evading trajectory of anti-collision driving system, to prove MFCM is suitable for the real world application. The results are quite impressive compared with other approaches such as equalized universe methods(EUM) and subtractive methods(SCM) and show the efficacy of MFCM. Via the MFCM, the bottleneck to be overcomed while designing MFs and the fuzzy system is optimized and has better performance. (Key words: Fuzzy System, Fuzzy Rule Base, FUzzy Membership Function, Fuzzy C-Means, Neural Networks, Backpropagation, Modeling.)
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Jung-Ping, Huang, and 黃榮彬. "Fuzzy optimization for uncertain systems." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/76100837603015279428.
Full textAbstract:
碩士國立臺灣大學
化學工程學研究所
89
In this thesis,we mainly discuss how to solve the single objective and multi-objective fuzzy optimization problems and ,moreover,introduce the methodology in detail. In single objective optimization problem,by means of fuzzy logic,we transfer uncertain parameters and constraints into fuzzy sets with membership functions.Therefore,objective function is considered as a fuzzy one.Through the analysis of mathematical programming, we know that original objective value locates between the condition of pessimistic view and the condition of optimistic view.According to above two objective values, the fuzzy description of objective function could be constructed.After fuzzification ,one can reformulate the original single objective optimization into a new mathematical model by principle of fuzzy decision and solve it.We again apply the concept of fuzzy decision in multi-objective optimization problem. Base on the optimum of each objective we can establish a payoff table . And using the value of unacceptable level and optimal value of each objective fuzzification can be achieved by means of mathematical programming.Similarly,the problem of muti-objective optimization problem can be reformulated and solved.Finally,we apply methodology and procedures for single objective and multi-objective fuzzy optimization on batch process design.
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Hung, Kuo-Chen, and 洪國禎. "alpha Cut Fuzzy Arithmetic Simplifying Rules, Fuzzy Weighted Average and Fuzzy Function Optimization." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/36542834489043779403.
Full textAbstract:
博士東海大學
工業工程與經營資訊學系
94
The fuzzy theory has been used to solve various problems in management science and engineering. Hence, it becomes important to use fuzzy arithmetic operations. The main purpose of this dissertation is to investigate the procedures of fuzzy arithmetic operation. Furthermore, it provides simplifying rules of fuzzy arithmetic to save required time of arithmetic operation efficiently. We divided this article into three parts to investigate: simplifying rules, fuzzy weighted average (FWA) and fuzzy function optimization. First, the problems of Alpha-cut fuzzy arithmetic have been shown, like in interval arithmetic, that distinct states of fuzzy parameters (or fuzzy variable values) may be chosen and produce an overestimated fuzziness. Meanwhile, local extrema of a function may exist inside the support of fuzzy parameters and cause an underestimation of fuzziness and an illegal fuzzy number’s result. Previously approaches to overcoming these problems have appeared in the literature. Yet, the computational burden of these approaches got even heavier. Thus, this article is based on the vertex method in the literature and extensively proposes newly devised rules observed greatly useful for simplifying the vertex method. These rules are devised through a function partitioned into sub-functions, distinguishing the types of fuzzy parameter/variable occurrences, and types of sub-functions or functions with the various observations. The improved efficiency has been found able to significantly reduce the combination (vertex) test of the vertex method for the fuzzy parameters’ Alpha cut endpoints possibly to only a few fuzzy parameters’ endpoint combinations. Moreover, fuzzy weighted average as function of fuzzy numbers, is suitable for the problem of multiple occurrences of fuzzy parameters. We have reviewed and compared discrete algorithms for the FWAs in both theoretical comparison and numerical comparisons. An alternative efficient algorithm is also proposed. The algorithm introduces an all-candidate (criteria ratings) weights-replaced benchmark adjusting procedure other than a binary (dichotomy) search in the existing methods. In the number of element comparisons, Lee and Park’s algorithm is shown numerically generally slightly better than the alternative algorithm due to the simple binary search scheme used. However, from criterion of average CPU time and average number of evaluations, the alternative algorithm is efficiently, the results outperform than other FWA methods. It has been demonstrated efficient by the proposed alterative algorithm. Finally, a procedure for the fuzzy optimization of fuzzy functions with a fuzzy blurred argument (a single decision variable) is examined base on the -cut arithmetic and the vertex method. When a variable appeared a local solution problem, it becomes important to adjust between function and variable. In this article, a proper and useful preliminary algorithm is proposed. Numerical examples with results are also provided.
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Li, Pingke. "Fuzzy relational equations resolution and optimization /." 2009. http://www.lib.ncsu.edu/theses/available/etd-03202009-173601/unrestricted/etd.pdf.
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Yu, K. G., and 余國駿. "Multiobjective Fuzzy Optimization With Interactive Membership." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/11652998229491168026.
Full textAbstract:
碩士淡江大學
機械工程研究所
81
The thesis develops a method to deal with the important de- gree of multiobjective functions in fuzzy design domain. Specially ,if the fuzzy condition of pairwise comparison fully or partially exist in the objective functions, we can judge the contradiction and fuzzy degree according to Cardinal scale rating method to co- rrect the unreasonable weighting coefficient among the criteria. The fuzzy optimization method then can combined with the in- teractive program of membership functions in the optimization process. The method and program show the satisfying results with illustrative mechanical and structural design problems.
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Jen-Hung, Hsiao, and 蕭仁宏. "Robust Design with Fuzzy parameters and Engineering Optimization with Fuzzy Variables." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/09348960804353597494.
Full textAbstract:
碩士淡江大學
機械工程學系
89
In the real-world problems, fuzzy information exists in the design constraints, objective functions and design variables. These fuzzy information mostly is expressed as fuzzy parameters and fuzzy constraints. This paper presents the method of how to deal with fuzzy parameters or variables existing in the optimization problems. The basic idea is that a fuzzy problem can be transformed into a crisp problem and solved by general nonlinear programming. Due to the fuzzy characteristics, feasible robustness and performance robustness are considered is the paper. As a result, the final design is much reasonable than the design without the consideration of fuzzy information. The robust design concept can further help to improve the quality of the optimal design.
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Hsiao, Chi-Che, and 蕭祺哲. "Fuzzy Multiple Criteria Optimization for Redundancy Allocation." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/49707362836044825442.
Full textAbstract:
碩士國立交通大學
工業工程研究所
83
It is well known that redundancy is one of the effective methods to increase the reliability of system. However, cost, weight and volumn of system are also the important criteria for the redundancy allocation problem. In this study,we provide a fuzzy multiple criteria mathematical model for the redundancy allocation problem. The reliability and cost are represent as fuzzy numbers. This redundancy allocation mathematical model is nonlinear and integer programming. We also provide an interactive approach to solve the model. Finally,a numerical example is given to illustrate the approach.
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Chen, Chun-Fu, and 陳俊富. "Structure Design Optimization using Fuzzy-Genetic Algorithm." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/w923q7.
Full textAbstract:
碩士國立臺北科技大學
車輛工程系所
99
Nowadays, vehicle designs heavy rely on computer simulation. And optimization analysis becomes one of the key processes. The study investigates the feasibility of applying fuzzy and genetic algorithm to the structure optimization. A method combing with newly developed fuzzy rule set and genetic algorithm was proposed and called Fuzzy-Genetic algorithm. In the study, a fuzzy logical set was defined based on the decent function and constraints. In the study, traditional gradient optimization, optimization combined with fuzzy, genetic optimization, genetic combined with fuzzy optimization were studied and compared. Fuzzification was defined and coded using Matlab. Optimization analysis was performed using the commercial code HyperStudy. For Fuzzy-Genetic optimization, genetic optimization was performed, and then fuzzy logic was applied. The proposed method intended to expedite optimization convergence. Optimization results were compared. Results showed the proposed Fuzzy-genetic algorithm could help in reach optimization quick from the studied examples. It is improve the efficiency of iteration around 21%.
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Hsu, Chih-Chiang, and 許志強. "Fuzzy Particle Swarm Optimization for Data Clustering." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/25242692505059030762.
Full textAbstract:
碩士大同大學
資訊經營學系(所)
96
This paper proposes a new data clustering algorithm which is based on fuzzy techniques and particle swarm optimization (PSO). As pointed out by some researchers: the standard PSO always converges very quickly towards the optimal positions but may slow its convergence speed when it is reaching a minimum [9]. This paper is trying to solve this problem by integrating a Fuzzy technique with PSO to allow each particle to update its new velocity and next position according to the current position of other better particles, in addition to gbest, pbest and itself. Not all of other particles are considered by a particle; only those particles which have higher degree of fuzzy membership with the current global best particle are taken into account. This provides more information to direct the particle to fly toward a better direction. Finally, the proposed algorithm was evaluated by testing a couple of hard and soft clustering problems, also compared to some famous clustering methods. The experimental results show that the proposed approach has better convergence ability than its original PSO algorithm.
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Wang, Chien-Seng, and 王建生. "Reliabilty-Based Fuzzy Optimization for Engineering Design." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/37601428491290601111.
Full textAbstract:
碩士淡江大學
機械工程學系
85
In an engineering design, there are many uncertainties. For a mechanical system ,the uncertainties include fatigue, strain ,bulking, etc. Reliability concept is the most effective approach to handle these problems. This paper uses Hasofer-Lins'' s reliability method, which uses recursive numerical method to compute the optimal solution.In addition to the representation of system reliability, this paper takes account the system reliability into one of the objective functions in the optimization process. A reasonable Reliability-Based multiobjective optimization structural design thus is established.Traditionally the constrained functions are crisp. Here, not only deterministic, but fuzzy and fuzzy probability constraints including random variables and random parameters are considered.A general probability optimum problem can be transformed to a deterministic optimization problem by chance constrained programming.In the multiobjective optimum problem, there is usually a trade-off among objective functions. Fuzzy theory is used to deal with the conflict among each individual objective function. Fuzzy theory also can be applied to relax the constraint function that a maximum satisfactory optimum solution can be obtained. An objective weighting technique is used in the multiobjective fuzzy optimization that can generate a design representing the relative important degree of individual objective function and reliability.
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Tzu-Chi, Liu. "Developing a Fuzzy Proportional-Derivative Controller Optimization Engine for Engineering Optimization Problems." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0009-2507200619025100.
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Liu, Tzu-Chi, and 劉子吉. "Developing a Fuzzy Proportional-Derivative Controller Optimization Engine for Engineering Optimization Problems." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/37952044191114862239.
Full textAbstract:
博士元智大學
機械工程學系
94
This paper proposes a fuzzy proportional-derivative (PD) controller optimization engine for engineering optimization problems. Engineering design problems have two characteristics: the design variables are often monotonic in the objective function and constraints. Moreover, the objective function and constraints are often implicit functions which cannot be expressed explicitly in terms of design variables. Traditional numerical optimization algorithms treat engineering optimization problems as pure mathematical problems. Engineering heuristics are totally ignored. The idea of using the fuzzy PD controller in engineering optimization is that, instead of using purely numerical information to obtain the new design point in the next iteration, engineering knowledge, such as monotonicity of the design variables and activities of the constraints, are be modeled in the optimization algorithm using fuzzy rules. The fuzzy PD controller optimization engine is developed through three stages. In the first two stages, the optimization engine is applied to solve engineering optimization problems with optimality criteria methods. In the third stage, the fuzzy PD controller optimization engine is extended to apply on more general engineering optimization problems with monotonicity. Several engineering design optimization problems commonly seen in research literature are used to demonstrate the practicality of the fuzzy PD controller optimization engine. Numerical optimal solutions are successfully obtained in all problems. The fuzzy PD controller seems to be robust to various initial design points and move limits.
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Chen, Wen-Hsiang, and 陳文祥. "Applying Response Surface Approximation for Engineering Optimization with Fuzzy Parameters and Fuzzy Variables." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/66916544357726532692.
Full textAbstract:
碩士淡江大學
機械與機電工程學系碩士班
95
A design optimization problem contains fuzzy information such as fuzzy parameters and variable is often confronted in engineering applications. Particularly in the modern engineering problems, finite element method is popular used for the analysis in various engineering optimization problems with fuzzy information. This thesis presents the study of finite-element based engineering design optimization containing fuzzy parameters and fuzzy design variables; and the crisp design variables contain a mix of real continuous variables and discrete variables. For dealing with such kind of problem, the optimization with approximation technique of applying the response surface method is developed and presented in this thesis. The simple first-order response surface approximation with suitable sequential searching technique including confidence move limit technique has been used for locating the optimum. There are three critical sides considerably influence the result. The first one is how to deal with the fuzzy optimization problem containing fuzzy information existing in design variables and parameters so that a crisp optimization can be solved. Because of the fuzzy region of each fuzzy variable is vary, it is required to consider a way of design control so that the performance robustness can be achieved. The second one is how to deal with the discrete variables in the approximation environment constructed by response surface function. The third one is how to perform the optimization searching process to obtain the optimum result. For applying the proposed design methodology to the two-objective problem, the important point is how to define and select the ideal solution corresponding to individual objective during the whole optimization searching process. All above three considerations are presented in the thesis. One ten-bar truss with finite element analysis optimization problem is adopted in the thesis as a model for proposed development and demonstrating the presented concept, process and application.
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Hu, Fang-Bin, and 胡芳斌. "Application of Fuzzy Theory for Structural Topology Optimization." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/16736911515539457525.
Full textAbstract:
碩士淡江大學
航空太空工程學系碩士班
96
A methodology of topology optimization design by fuzzy theory was used in this study. The concept of fuzzy theory used in this study is to find the applicable membership function and the Pareto solution of multi-objective optimization problem. The finite element analysis software ANSYS was used for structural analysis. The optimum shape design was obtained by the concept of material distribution borrowed from density method with sequential linear programming. Three stages topology design were employed in this study. In addition to using the element growth-removal combined method (EGRCM) to decrease the absurd situation, the concept of B-spline curve was used to smooth the design shape. After three stages design strategy , the primitive optimum design can be improved to more practical design. Different multi-objective optimization problems were discussed in the numerical examples. The results of final design were more considerable than that only to consider single-objective optimization problem in the traditional topology design. We hope the results of this study can provide the convenience of manufacturing to the industry of structural design.
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Chia-HungLin and 林嘉宏. "Fuzzy Image Filter Design Using Ant Colony Optimization." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/73334362904253576694.
Full textAbstract:
碩士國立成功大學
電機工程學系專班
100
The digital images are easily affected by the noises; hence the image filters are often regarded as pre-processing of image processing system. If the image has serious damage or high-noise, the traditional image filters are usually unable to handle well. Therefore, this thesis utilizes the advantages of the fuzzy system to improve the traditional median filter, and then use ant colony optimization (ACO) algorithm to adjust the parameters of fuzzy image filter and make the filter to achieve better performance. ACO algorithm is an optimal method that developed from pheromones concentration level on the path. With the time past, the concentration of pheromones on the long path is lower, the concentration of pheromones of the short path is higher, then the shortest path will be selected. ACO algorithm includes the calculation of the pheromone concentration, the evaporation coefficient set, and the state transition probability calculation. In addition, ACO algorithm possesses the global and local search capability. Therefore, the ACO algorithm has the characteristics of muti-point search and fast convergence. This thesis combines the advantages of the fuzzy filter and ACO algorithm to improve the overall image quality. The final image filtering results demonstrate the effectiveness and feasibility of the proposed method.
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Shih, Chia-Sheng, and 施嘉勝. "Structural Optimization Using Genetic Algorithms with Fuzzy Rules." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/14259379352933239695.
Full textAbstract:
博士國立臺灣大學
機械工程學研究所
94
This thesis presents two fuzzy rules employed to adapt both parameters of genetic operators and penalty factor in genetic algorithms for optimum design of structures. Namely, one system adjusts the crossover rate as well as the mutation rate dynamically according to the information of current population, and the other adjusts penalty factor according to the amount and level of constraint violations by individuals. Two studies are conducted for the research. In the first one (as for the core study), an improved dynamic penalty method is applied to transform the constrained structural optimization problem into an unconstrained problem for the optimization procedure using genetic algorithms. With the developed program, several constrained structural optimization problems are thus investigated. The results demonstrate that the developed algorithm can be applied successfully to solve general structural optimization problems. In the second study, a further attempt is made to seek solutions to the multi-objective optimization problems. Hence a simple aggregating function method is raised to assign the fitness of individuals with fuzzy rules according to the original values of each objective function. To maintain the diversity of the population and reduce the computational complexity, the mutation rate was tested and chosen before the optimization process. Elitism was also adopted by using an external population to keep the elite individuals of the population. Through the use of the method, several nonconvex, disconnected Pareto-optimal solutions to multi-objective optimization problems are tested. Numerical experimental results demonstrate that the proposed method is simple and efficient in achieving optimum solutions to multi-objective problems.
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Wang, Shiang-Yu, and 王庠予. "Fuzzy Rule Optimization for Elevator Group Control System." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/4c2j5g.
Full textAbstract:
碩士國立虎尾科技大學
資訊管理研究所
99
Nowadays, elevator system has been an important role in mansions. Elevator system is an essential transportation in high buildings. How to design an Intelligent Elevator Control System has become a research focus in recent years. This study aims to reduce average waiting time of elevator process efficiently at peak hours and to save power at off-peak hours. Elevator Group Control System (EGCS) is used to layout the schedule of elevators.. Besides, there are many factors will influence EGCS, such as the number of elevators, traffic flow, direction, passenger preferences (for instance, department stores, hospitals, hotels, office buildings), congestion and VIP priority floor and so on. This study uses fuzzy rule of Genetic Algorithms (GA) to substitute traditional elevator dispatching mode. The fuzzy rule helps EGCS to make the best decision of elevator dispatching based on different traffic flows and to let EGCS become more efficient and save more power. The result shows that the performance of the experiment which uses the optimized fuzzy rule of GA is much better than the performance of the experiment which didn’t use the fuzzy rule of GA.
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Shan-Fu, Yuan, and 袁山富. "Application of Genetic Algorithm on Fuzzy Dynamic Optimization." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/20924385215430028791.
Full textAbstract:
碩士國立臺灣大學
化學工程學研究所
89
The main concerns in this thesis are to use genetic algorithms(GAs) as a solution tool and to solve fuzzy dynamic optimization problems. Fisrt, we introduce the basic operational procedures and definitions of genetic algorithms. Then, we test different kinds of optimization problems and conclude the results. We find that genetic algorithms has the abilty to find the global solution of static optimization problems. When applying genetic algorithms to solve optimization problems with constraints, we propose a simple procedure to handle these problems. Finally, we apply genetic algorithms for solving nonlinear dynamic optimization problems subjected to flexible path constraints. Becase using traditional optimization methods to solve such kinds of problems, the produres will become inextricable and hard to solve, especially optimzation problems with highly nonlinear character. Thus, we transform flexible path constraints into fuzzy contraints. Solving fuzzy dynamic optimization, we discrete the continuous control inputs. Therefore, this problem changes into a multistage fuzzy decision optimization problem. At last, we apply genetic algorithms to solve such optimization and understand the effect on solutions of different approximate control inputs.
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王正苡. "Multiobjective optimization using genetic algorithm and fuzzy theory." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/27561126267315445765.
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Zhang, Guo Feng, and 張國峰. "FUZZY OPTIMIZATION IN DESIGN OF REINFORCED CONCRETE MEMBERS." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/08442419391420123837.
Full textAbstract:
碩士國立臺灣科技大學
營建工程技術學系
83
The main purpose of this research is trying to find a reasonable and effective way to design a reinforced concrete member within a tolerable cost. The general method is based on traditional structural optimization with crisp concepts. But it is inevitable for traditional method to encounter some unavoidable faults dismatching with real engineering condition a fuzzy optimization is herein introduced in this research in order to solve the problem as mentional previously.A concept of fuzzy interval for inuolving variable may required during the analysis and coomputation.In addition, the oeder-paired comparison technique is also used for determining the interval of fuzzy constraints in this research to establish the combined effects among weighting factors. There-after the generalized reduced gradient method is employed to find out the answer of fuzzy optimization in relation to the design of reinforced concrete members (e.g. columns in this research).
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Chiang, Lo. "Fuzzy Controller Design by Ant Colony Optimization with Fuzzy Clustering and Its FPGA Implementation." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0005-1607200623014500.
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Lo, Chiang, and 羅強. "Fuzzy Controller Design by Ant Colony Optimization with Fuzzy Clustering and Its FPGA Implementation." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/35058560902407924766.
Full textAbstract:
碩士國立中興大學
電機工程學系所
94
This thesis proposes a novel design method of Fuzzy Controller by Ant Colony Optimization (ACO) algorithm with Fuzzy Clustering (FC-ACOFC). The objective of FC-ACOFC is to improve both the design efficiency of fuzzy controller and control performance. Structure of FC-ACOFC, including the number of rules and fuzzy sets in each input variable, is created on-line by a newly proposed fuzzy clustering method. In contrast to conventional grid-type partition, the antecedent part of FC-ACOFC is flexibly partitioned, and the phenomenon of highly overlapped fuzzy sets is avoided. Once a new rule is generated, the consequence is selected from a list of candidate control actions by ACO. In ACO, the tour of an ant is regarded as a combination of consequent actions selected from every rule. A pheromone matrix among all candidate consequent actions is constructed and an on-line learning algorithm for heuristic value update is proposed. Searching for the best one among all consequence combinations involves using the pheromone matrix and heuristic values. To verify the performance of FC-ACOFC, simulations on nonlinear system control, water bath temperature control and chaotic system control are performed. Simulations on these problems and comparisons with other algorithms have demonstrated the performance of FC-ACOFC. The ACO used here is hardware implemented on Field Programmable Gate Array (FPGA) chip. The use of Programmable Logic Device (PLD) is more and more general in recent years, and the procedure of circuit deign is fast and elastic. Application of the ACO chip to fuzzy control a simulated water bath temperature control problem has verified the effectiveness of the designed chip.
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Jing, Chang Huei, and 井長慧. "The Problem of Fuzzy Optimization for Ethanol Fermentation Processes." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/02073005591580916837.
Full textAbstract:
碩士國立中正大學
化學工程研究所
85
In describing engineering problems, many of them don''t need to fix in a rigid and definite range. In solving the optimization problems, rigid restrictions may produce the long time in solving problems or no convergentanswer. The major purpose of this paper is to use the method of fuzzy optimization to solve problems. We use fuzzy method to convert unexplicitrestriction problems into explicit problem. Problems with constraints couldbe solved by genetic algorithm with penalty functions. Fuzzy problems could be first converted into explicit problem by definingmembership functions and then optimized by fuzzy decision method. Decisionmaker could provide fuzzy range to convert the objective function orrestrictive function into suitable membership function. Two ethanolfermentation processes, the fermentation process using the recombinantSaccharomyces 1400(pLNH33) and beer fermentation are simulated toinvestigate the effect of using the fuzzy method.
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Kung, Shu-Ming, and 龔淑銘. "CNC Milling process Optimization Using Taguchi-Fuzzy-ANN Approach." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/28406133141969657740.
Full textAbstract:
碩士國立高雄第一科技大學
機械與自動化工程所
92
The milling machining is very popular in the industry all of the word. However we will face many different kinds of quality features to find the optimization problems. Take the CNC milling for example, the precision of parts; the roughness and the tool wear are very important index for the quality feature. The optimum process parameters will be different with the features of quality, so there are contradictions between parameters design. The fuzzy logical and Taguchi’s analysis method are employed in this study. An L18 orthogonal array allocating with three factors such as dimensional accuracy, tool wear, surface roughness, are applied in the experiment. We got Multiple Performance Characteristics Index (MPCI) by means of three S/N ratios, which are the input variables of fuzzy logical unit and calculated from experiment’s data. Also, we can find the key factor and the optimum parameters by means of the analysis of factor’s effect and variances. The results show that we can get the requirements of the optimum process parameters by Taguchi-Fuzzy analysis method. There are several parameters for the machining center such as cutting speed, federate, tool material and workpiece material. It’s very difficult for us to setup parameters. Therefore, we will combine the Neural-Fuzzy to establish parameters according to the index of the machining quality, and adjust the optimum process parameters automatically. The studying is based on the experiment of a Taguchi’s orthogonal array to collect the data that we can establish process parameters and the predicting model of the quality feature S/N ratio for precision. The results show that we can calculate the ability for predicting model milling by means of network training example according to few data made by Taguchi’s array experiment. Finally, we can really predict the optimum process parameters. On the other hand, we can combine the predicting model and fuzzy logical unit to calculate the relative for optimum process parameters according to the quality index.
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Wu, Shiue-Guang, and 吳學光. "Fuzzy Optimization with Hybrid Numbers for Intelligent Production Management." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/74936631627043613020.
Full textAbstract:
碩士國立海洋大學
機械與輪機工程學系
87
Traditional mathematical programming algorithms usually rely on known information to establish their models correctly. However, in real world, these information does not only exist in crisp numbers, but also in random variables and fuzzy numbers. This research focuses on handling data that are of different types and traits and developing a set of rules is based the Fuzzy Theory. Hence, many problems with complex information can be solved by modified mathematical programming algorithm. We apply this methodology to the production management which is the main focus of our research. This methodology is based on the Fuzzy linear Programming algorithm develop by Julien (1992) and hybrid number defined by Kaufmann (1984). The theories of fuzzy number and probability are integrated into the algorithm of linear programming. We adapt Monte Carlo simulation method to get the closet results, and the results we found with our algorithm show very small errors compared to traditional methods. Moreover, this method could not only be used on production management, but also be applied to Network and Transportation Flow problems.