In the thesis, there are two kinds of fuzzy linear programming problems, one of them is a linear programming problem with fuzzy technological coefficients and the second is linear programming problem in which both the right-hand side and the technological coefficients are fuzzy numbers. I solve the fuzzy linear programming problems with fuzzy decisive set method.

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We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Thesis (MEng)--University of South Australia, 1997

Thesis (M.S.)--Rochester Institute of Technology, 1991. / Typescript. Includes bibliographical references (leaves 87-89).

Orientadores: Laécio Carvalho de Barros, Barnabas Bede / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-24T00:25:40Z (GMT). No. of bitstreams: 1 Gomes_LucianaTakata_D.pdf: 2706174 bytes, checksum: bb5833b7b2c8f5e094b30eefd64e7426 (MD5) Previous issue date: 2014 / Resumo: A partir da proposta das definições de derivada e integral fuzzy via extensão de Zadeh dos respectivos operadores para funções clássicas, obtemos uma versão do teorema fundamental do cálculo e desenvolvemos uma nova teoria de equações diferenciais fuzzy (EDFs). Diferentemente dos conceitos anteriores de derivadas (Hukuhara e generalizadas) e integrais para funções fuzzy, em que as funções assumem valores em conjuntos fuzzy, a abordagem aqui proposta lida com tubos fuzzy de funções (subconjuntos fuzzy de espaços de funções). Sob condições razoáveis, as novas operações equivalem a diferenciar (ou integrar) as funções clássicas dos níveis. Apresentamos as abordagens anteriores de EDFs mais conhecidas e, para realizar comparações com a nova teoria, calculamos os conjuntos atingíveis fuzzy das soluções. Provamos que algumas soluções da teoria proposta equivalem às via derivada fortemente generalizada. Também demonstramos a equivalência, sob determinadas condições, com as soluções via inclusões diferenciais fuzzy e extensão de Zadeh da solução clássica. Apesar destas duas abordagens não tratarem de EDFs, elas são largamente difundidas por utilizarem derivadas de funções clássicas (de modo similar ao aqui proposto) e de preservarem características das soluções de sistemas dinâmicos clássicos. Esses são fatos vantajosos, pois mostram que a teoria proposta, além de tratar de EDFs, possui propriedades desejáveis das outras duas mencionadas, permitindo a ocorrência de estabilidade e periodicidade de soluções, por exemplo. A teoria é ilustrada através de sua aplicação em modelos biológicos e análise dos resultados / Abstract: From the definition of fuzzy derivative and integral via Zadeh's extension of the derivative and integral for classical functions we obtain a fundamental theorem of calculus and develop a new theory for fuzzy differential equations (FDEs). Different from the previous concepts of fuzzy derivatives (Hukuhara and generalized derivatives) and integrals, defined for fuzzy-set-valued functions, the approach we propose deals with fuzzy bunches of functions (fuzzy subsets of spaces of functions). Under reasonable conditions, the new operations are equivalent to differentiating (or integrating) the classical functions of the levels. We present the most known previous approaches of FDEs. Comparisons with the new theory we propose are carried out calculating fuzzy attainable sets of the solutions. Under certain conditions, the solutions via strongly generalized derivative coincide with solutions using our approach. The same happens with solutions to fuzzy differential inclusions and Zadeh's extension of the crisp solution. Although these two methods do not treat FDEs, they are widespread for making use of classical functions (similarly to what is proposed in this thesis) and for preserving properties of classical dynamical systems. These are advantageous features since it shows that the new theory presents desirable properties of the other two mentioned theories (allowing for instance periodicity and stability of solutions), besides treating FDEs. The theory is illustrated by applying it on biological models and commenting the results / Doutorado / Matematica Aplicada / Doutora em Matemática Aplicada

Orientador: Stelamaris Rolla Bertoli / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil / Made available in DSpace on 2018-08-03T17:24:12Z (GMT). No. of bitstreams: 1 Alvarenga_BeneditoSergioTavaresde_M.pdf: 1200162 bytes, checksum: ac4e26b89e05718a132f263527a0ea0c (MD5) Previous issue date: 2003 / Mestrado

We start by discussing fuzzy sets and the algebra of fuzzy sets. We consider some properties of fuzzy modeling tools. This is followed by considering the Mamdani and Sugeno models for designing fuzzy controllers. Various methods for using sets of data for desining controllers are discussed. This is followed by a chapter illustrating the use of genetic algorithms in designing and optimizing fuzzy controllers.Finally we look at some previous applications of fuzzy control in telecommunication networks, and illustrate a simple application that was developed as part of the present work.

Identification of fuzzy rules is an important issue in designing of a fuzzy neural network (FNN). However, there is no systematic design procedure at present. In this paper we present a genetic algorithm (GA) based learning algorithm to make use of the known membership function to identify the fuzzy rules form a large set of all possible rules. The proposed learning algorithm initially considers all possible rules then uses the training data and the fitness function to perform ruleselection. The proposed GA based learning algorithm has been tested with two different sets of training data. The results obtained from the experiments are promising and demonstrate that the proposed GA based learning algorithm can provide a reliable mechanism for fuzzy rule selection.

This research work focuses on the optimal algorithms of decision making and forecasting respectively, in order to achieve a better prediction. Decision making techniques and forecasting methods are investigated due to the poor accuracy of forecasting in comparison with real world data. The uncertainty of real world data leads to the use of type-1 fuzzy sets, type-2 fuzzy sets, fuzzy decision tree and fuzzy time-series for fuzzy data-mining - to which they are applied for the look-ahead based interval-valued fuzzy decision tree with optimal perimeter of the neighbourhood (LAIVFDT-OPN) model, and high-order type-2 fuzzy time series (HO-T2FTS) model. In the experiment with a real world business, a ‘computerised maintenance integration management system’ (CMIMS) is constructed as a simulation model for a case study. The CMIMS model consists of the LAIVFDT-OPN and HO-T2FTS models. It is also applied to a set of real world data from a factory in Thailand. Due to the significant uncertainty involved in machine maintenance, most tasks in machine diagnosis are still carried out manually by technicians. In this research, a prototype of CMIMS employing fuzzy data mining to diagnose machine maintenance is constructed. Considering the special features of machine maintenance data, fuzzy decision trees and fuzzy time series are adopted in the proposal method. To represent the uncertain fuzzy memberships, interval-valued fuzzy decision trees are proposed and an optimal neighbourhood perimeter is defined for look-ahead fuzzy decision trees. Based on the existing first-order type-2 time-series and high-order type-1 fuzzy time series, an improved high-order type-2 fuzzy time series method is put forward. In this case study, the CMIMS model can be used to analyse and evaluate uncertain data. It also can be employed to facilitate decision making in machine equipment status, and forecast machine maintenance plan in the future in stead of technicians. Our results demonstrated that the proposal method is effective in fuzzy decision support for machine maintenance.