Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria dels Conjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics es potencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funció densitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps que les distribucions de probabilitat quàntiques

Fuzzy Set Theory Approach as the Basis of Analysis of Financial Flows in the Economical Security System

The problems of formalization of the process of matching different management subjects’ functioning characteristics obtained on the financial flows analysis basis is considered. Formal generalizations for gaining economical security system knowledge bases elements are presented. One of feedback directions establishment between knowledge base of the system of economical security and financial flows database analysis is substantiated.

Epidemiological Models of Directly Transmitted Diseases: An Approach via Fuzzy Sets Theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new approach for power system black-start decision-making with vague set theory

Power system restoration after a large area outage involves many factors, and the procedure is usually very complicated. A decision-making support system could then be developed so as to find the optimal black-start strategy. In order to evaluate candidate black-start strategies, some indices, usually both qualitative and quantitative, are employed. However, it may not be possible to directly synthesize these indices, and different extents of interactions may exist among these indices. In the existing black-start decision-making methods, qualitative and quantitative indices cannot be well synthesized, and the interactions among different indices are not taken into account. The vague set, an extended version of the well-developed fuzzy set, could be employed to deal with decision-making problems with interacting attributes. Given this background, the vague set is first employed in this work to represent the indices for facilitating the comparisons among them. Then, a concept of the vague-valued fuzzy measure is presented, and on that basis a mathematical model for black-start decision-making developed. Compared with the existing methods, the proposed method could deal with the interactions among indices and more reasonably represent the fuzzy information. Finally, an actual power system is served for demonstrating the basic features of the developed model and method.

A dinâmica dos recursos comuns em Unidades de Conservação e Assentamentos Rurais no Amazonas: uma abordagem fuzzy set

A teoria de Garret Hardin intitulada “A tragédia dos comuns” apresenta a privatização e o controle governamental como saída para evitar o esgotamento dos recursos naturais. Entretanto, outros autores demonstraram que os usuários dos recursos podem apresentar eficientes formas de manejo, aliando o uso pelo homem à conservação da natureza. Esta tese analisa o uso de recursos comuns em Unidades de Conservação e Assentamentos Rurais de Uso Sustentável, localizadas no interflúvio Purus-Madeira, região Sul do Estado do Amazonas. A pergunta que norteou a hipótese da pesquisa foi: Diante das especificidades amazônicas e das regras impostas pelas políticas ambientais e agrárias na região, quais condições apresentam-se como necessárias e suficientes ao bom desempenho no uso de recursos comuns? A análise foi realizada por meio da combinação de três métodos: o método comparativo Qualitative Comparative Analysis (QCA), o método de análise institucional Institutional Analysis and Development (IAD) Framework e a lógica fuzzy. Operacionalmente, foram consideradas como variáveis independentes (X) os aspectos socioeconômicos, produtivos, ambientais e institucionais, partindo-se do pressuposto de que os programas governamentais destinados às Unidades devem apresentar melhorias nestes indicadores, refletindo por sua vez no bom desempenho no uso de recursos comuns (variável dependente Y) a partir deste desenho institucional. Os resultados confirmaram as hipóteses levantadas, afirmando-se que o bom desempenho no uso de recursos comuns, preconizado pelos critérios da sustentabilidade, somente pode ser alcançado mediante a combinação de um desempenho também satisfatório nas variáveis socioeconômicas, produtivas, institucionais e ambientais, apresentando-se estas variáveis como individualmente necessárias e conjuntamente suficientes para ocorrência deste fenômeno.

Developing a fuzzy multi-criteria decision-making model for selecting design-build operational variations

Many academic researchers have conducted studies on the selection of design-build (DB) delivery method; however, there are few studies on the selection of DB operational variations, which poses challenges to many clients. The selection of DB operational variation is a multi-criteria decision making process that requires clients to objectively evaluate the performance of each DB operational variation with reference to the selection criteria. This evaluation process is often characterized by subjectivity and uncertainty. In order to resolve this deficiency, the current investigation aimed to establish a fuzzy multicriteria decision-making (FMCDM) model for selecting the most suitable DB operational variation. A three-round Delphi questionnaire survey was conducted to identify the selection criteria and their relative importance. A fuzzy set theory approach, namely the modified horizontal approach with the bisector error method, was applied to establish the fuzzy membership functions, which enables clients to perform quantitative calculations on the performance of each DB operational variation. The FMCDM was developed using the weighted mean method to aggregate the overall performance of DB operational variations with regard to the selection criteria. The proposed FMCDM model enables clients to perform quantitative calculations in a fuzzy decision-making environment and provides a useful tool to cope with different project attributes.

Intuitionistic fuzzy Choquet integral operator-based approach for black-start decision-making

Determining the optimal of black-start strategies is very important for speeding the restoration speed of a power system after a global blackout. Most existing black-start decision-making methods are based on the assumption that all indexes are independent of each other, and little attention has been paid to the group decision-making method which is more reliable. Given this background, the intuitionistic fuzzy set and further intuitionistic fuzzy Choquet integral operator are presented, and a black-start decision-making method based on this integral operator is presented. Compared to existing methods, the proposed algorithm cannot only deal with the relevance among the indexes, but also overcome some shortcomings of the existing methods. Finally, an example is used to demonstrate the proposed method. © 2012 The Institution of Engineering and Technology.

Fuzzy logic to evaluate driving maneuvers: An integrated approach to improve training

Driver training is one of the interventions aimed at mitigating the number of crashes that involve novice drivers. Our failure to understand what is really important for learners, in terms of risky driving, is one of the many drawbacks restraining us to build better training programs. Currently, there is a need to develop and evaluate Advanced Driving Assistance Systems that could comprehensively assess driving competencies. The aim of this paper is to present a novel Intelligent Driver Training System (IDTS) that analyses crash risks for a given driving situation, providing avenues for improvement and personalisation of driver training programs. The analysis takes into account numerous variables acquired synchronously from the Driver, the Vehicle and the Environment (DVE). The system then segments out the manoeuvres within a drive. This paper further presents the usage of fuzzy set theory to develop the safety inference rules for each manoeuvre executed during the drive. This paper presents a framework and its associated prototype that can be used to comprehensively view and assess complex driving manoeuvres and then provide a comprehensive analysis of the drive used to give feedback to novice drivers.

Fuzzy-expert approach for voltage-reactive power dispatch

The voltage stability control problem has become an important concern for utilities transmitting power over long distances. This paper presents an approach using fuzzy set theory for reactive power control with the purpose of improving the voltage stability of a power system. To minimize the voltage deviations from pre-desired values of all the load buses, using the sensitivities with respect to reactive power control variables form the basis of the proposed fuzzy logic control (FLC). Control variables considered are switchable VAR compensators, On Load Tap Changing (OLTC) transformers and generator excitations. Voltage deviations and controlling variables are translated into fuzzy set notations to formulate the relation between voltage deviations and controlling ability of controlling devices. The developed fuzzy system is tested on a few simulated practical Indian power systems and some IEEE standard test systems. The performance of the fuzzy system is compared with conventional optimization technique and results obtained are encouraging. Results obtained for a 24 - node equivalent EHV system of part of Indian southern grid and IEEE New England 39-bus system are presented for illustration purposes. The proposed Fuzzy-Expert technique is found suitable for on-line applications in energy control centre as the solution is obtained fast with significant speedups.

A Refined Methodology for Durability-Based Service Life Estimation of Reinforced Concrete Structural Elements Considering Fuzzy and Random Uncertainties

A reliable method for service life estimation of the structural element is a prerequisite for service life design. A new methodology for durability-based service life estimation of reinforced concrete flexural elements with respect to chloride-induced corrosion of reinforcement is proposed. The methodology takes into consideration the fuzzy and random uncertainties associated with the variables involved in service life estimation by using a hybrid method combining the vertex method of fuzzy set theory with Monte Carlo simulation technique. It is also shown how to determine the bounds for characteristic value of failure probability from the resulting fuzzy set for failure probability with minimal computational effort. Using the methodology, the bounds for the characteristic value of failure probability for a reinforced concrete T-beam bridge girder has been determined. The service life of the structural element is determined by comparing the upper bound of characteristic value of failure probability with the target failure probability. The methodology will be useful for durability-based service life design and also for making decisions regarding in-service inspections.

Fuzzy Expert Approach with Curtailed Controllers for Improved Reactive Power Dispatch

This paper addresses the problem of curtailing the number of control actions using fuzzy expert approach for voltage/reactive power dispatch. It presents an approach using fuzzy set theory for reactive power control with the purpose of improving the voltage profile of a power system. To minimize the voltage deviations from pre-desired values of all the load buses, using the sensitivities with respect to reactive power control variables form the basis of the proposed Fuzzy Logic Control (FLC). Control variables considered are switchable VAR compensators, On Load Tap Changing (OLTC) transformers and generator excitations. Voltage deviations and controlling variables are translated into fuzzy set notations to formulate the relation between voltage deviations and controlling ability of controlling devices. The developed fuzzy system is tested on a few simulated practical Indian power systems and modified IEEE-30 bus system. The performance of the fuzzy system is compared with conventional optimization technique and results obtained are encouraging. Results obtained for a modified IEEE-30 bus test system and a 205-node equivalent EHV system a part of Indian southern grid are presented for illustration purposes. The proposed fuzzy-expert technique is found suitable for on-line applications in energy control centre as the solution is obtained fast with significant speedups with few number of controllers.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Free algebras in Von Neumann-Bernays-Gӧdel set theory and positive elementary inductions in reasonable structures

This thesis consists of two independent chapters. The first chapter deals with universal algebra. It is shown, in von Neumann-Bernays-Gӧdel set theory, that free images of partial algebras exist in arbitrary varieties. It follows from this, as set-complete Boolean algebras form a variety, that there exist free set-complete Boolean algebras on any class of generators. This appears to contradict a well-known result of A. Hales and H. Gaifman, stating that there is no complete Boolean algebra on any infinite set of generators. However, it does not, as the algebras constructed in this chapter are allowed to be proper classes. The second chapter deals with positive elementary inductions. It is shown that, in any reasonable structure ᶆ, the inductive closure ordinal of ᶆ is admissible, by showing it is equal to an ordinal measuring the saturation of ᶆ. This is also used to show that non-recursively saturated models of the theories ACF, RCF, and DCF have inductive closure ordinals greater than _ω.