A historical account of types of fuzzy sets and their relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

Modelo preditivo fuzzy da mobilização do solo no sistema de plantio direto.

As culturas do milho e da soja respondem pela maior parte da produção nacional de grãos, predominando o sistema de plantio direto. Para uma semeadura direta de qualidade, o bom aterramento do sulco é indispensável, pois garante um ambiente adequado às sementes. Neste sentido, é importante estimar a mobilização de solo promovida por uma haste sulcadora estreita durante esta operação. O modelo analítico existente visa representar a mobilização do solo no sistema de plantio convencional. Como consequência, há situações em que este não pode se aplicado, como no caso de hastes sulcadoras estreitas utilizadas em semeadoras de plantio direto. Nestas situações, o mecanismo de falha do solo pode se alterar, assumindo um comportamento não modelado na literatura. Essa pesquisa propõe um modelo fuzzy capaz de representar estas situações, aproveitando conhecimento da teoria de mecânica dos solos e da análise de resultados experimentais. No modelo proposto, parte das regras descrevem situações não abrangidas pelo modelo analítico, as quais foram formuladas a partir da estimativa das prováveis áreas de solo mobilizado. O modelo fuzzy foi testado com dados de experimentos conduzidos durante a pesquisa, em duas condições de granulometria de solo (arenoso e argiloso). O modelo proposto reproduziu as tendências observadas nos dados experimentais, mas superestimou os valores de área observados, sendo esse efeito bem mais intenso para os dados do experimento em solo arenoso. A superestimativa ocorreu devido à soma de diversos fatores. Um deles é a diferença entre as leituras experimentais, as quais consideram apenas o solo realmente movimentado, e a premissa do modelo analítico, que considera toda a área de solo incluindo aquela cisalhada, porém não mobilizada. Outro fator foi devido ao efeito do disco de corte da palha, que pré-cisalha o solo à frente da ferramenta. No ensaio em solo arenoso os valores observados de área de solo mobilizado foram menores que os esperados, intensificando o efeito de superestimativa do modelo fuzzy, sendo que este efeito não representa uma deficiência deste modelo.

An application of fuzzy logic for hardware/software partitioning in embedded systems

Hardware/Software partitioning (HSP) is a key task for embedded system co-design. The main goal of this task is to decide which components of an application are to be executed in a general purpose processor (software) and which ones, on a specific hardware, taking into account a set of restrictions expressed by metrics. In last years, several approaches have been proposed for solving the HSP problem, directed by metaheuristic algorithms. However, due to diversity of models and metrics used, the choice of the best suited algorithm is an open problem yet. This article presents the results of applying a fuzzy approach to the HSP problem. This approach is more flexible than many others due to the fact that it is possible to accept quite good solutions or to reject other ones which do not seem good. In this work we compare six metaheuristic algorithms: Random Search, Tabu Search, Simulated Annealing, Hill Climbing, Genetic Algorithm and Evolutionary Strategy. The presented model is aimed to simultaneously minimize the hardware area and the execution time. The obtained results show that Restart Hill Climbing is the best performing algorithm in most cases.

Truth Values in t-norm based Systems Many-valued FUZZY Logic

In t-norm based systems many-valued logic, valuations of propositions form a non-countable set: interval [0,1]. In addition, we are given a set E of truth values p, subject to certain conditions, the valuation v is v=V(p), V reciprocal application of E on [0,1]. The general propositional algebra of t-norm based many-valued logic is then constructed from seven axioms. It contains classical logic (not many-valued) as a special case. It is first applied to the case where E=[0,1] and V is the identity. The result is a t-norm based many-valued logic in which contradiction can have a nonzero degree of truth but cannot be true; for this reason, this logic is called quasi-paraconsistent.

Coverage and invariability in fuzzy systems

This paper presents a new complex system systemic. Here, we are working in a fuzzy environment, so we have to adapt all the previous concepts and results that were obtained in a non-fuzzy environment, for this fuzzy case. The direct and indirect influences between variables will provide the basis for obtaining fuzzy and/or non-fuzzy relationships, so that the concepts of coverage and invariability between sets of variables will appear naturally. These two concepts and their interconnections will be analyzed from the viewpoint of algebraic properties of inclusion, union and intersection (fuzzy and non-fuzzy), and also for the loop concept, which, as we shall see, will be of special importance.

Invariability, orbits and fuzzy attractors

In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality.

Profitability analysis of a femtosecond laser system for cataract surgery using a fuzzy logic approach

AIM: To define the financial and management conditions required to introduce a femtosecond laser system for cataract surgery in a clinic using a fuzzy logic approach. METHODS: In the simulation performed in the current study, the costs associated to the acquisition and use of a commercially available femtosecond laser platform for cataract surgery (VICTUS, TECHNOLAS Perfect Vision GmbH, Bausch & Lomb, Munich, Germany) during a period of 5y were considered. A sensitivity analysis was performed considering such costs and the countable amortization of the system during this 5y period. Furthermore, a fuzzy logic analysis was used to obtain an estimation of the money income associated to each femtosecond laser-assisted cataract surgery (G). RESULTS: According to the sensitivity analysis, the femtosecond laser system under evaluation can be profitable if 1400 cataract surgeries are performed per year and if each surgery can be invoiced more than $500. In contrast, the fuzzy logic analysis confirmed that the patient had to pay more per surgery, between $661.8 and $667.4 per surgery, without considering the cost of the intraocular lens (IOL). CONCLUSION: A profitability of femtosecond laser systems for cataract surgery can be obtained after a detailed financial analysis, especially in those centers with large volumes of patients. The cost of the surgery for patients should be adapted to the real flow of patients with the ability of paying a reasonable range of cost.

Fuzzy control of a water pump for an agricultural plant growth system

At the present time there is a high pressure toward the improvement of all the production processes. Those improvements can be sensed in several directions in particular those that involve energy efficiency. The definition of tight energy efficiency improvement policies is transversal to several operational areas ranging from industry to public services. As can be expected, agricultural processes are not immune to this tendency. This statement takes more severe contours when dealing with indoor productions where it is required to artificially control the climate inside the building or a partial growing zone. Regarding the latter, this paper presents an innovative system that improves energy efficiency of a trees growing platform. This new system requires the control of both a water pump and a gas heating system based on information provided by an array of sensors. In order to do this, a multi-input, multi-output regulator was implemented by means of a Fuzzy logic control strategy. Presented results show that it is possible to simultaneously keep track of the desired growing temperature set-point while maintaining actuators stress within an acceptable range.

Controlo fuzzy semi-activo para aparelhos de amortecimento variável na protecção sísmica

Trabalho apresentado no 10º Congresso Nacional de Sismologia e Engenharia Sísmica, 20-22 abril de 2016, Ponta Delgada, Açores, Portugal

Anwendungen von Fuzzy Logic im Controlling

Die wesentliche Aufgabe des Controllings besteht darin, dem Management aufbereitete Informationen zur Verfügung zu stellen. Die zu verarbeitenden Informationen liegen allerdings nicht immer in der gewünschten Genauigkeit vor. Trotz dieser Unschärfe muss eine Beschreibung stattfinden, um eine Entscheidungsfindung zu realsieren. Eine Möglichkeit ist der hier vorgestellte wissensbasierte Ansatz der Fuzzy Logic. Anhand von drei Controllinginstrumenten wird in der vorliegenden Arbeit das Anwendungspotential der Fuzzy Logic im Controlling bewertet.

Fuzzy logic in web data mining for website assessment

This paper proposes a novel application of fuzzy logic to web data mining for two basic problems of a website: popularity and satisfaction. Popularity means that people will visit the website while satisfaction refers to the usefulness of the site. We will illustrate that the popularity of a website is a fuzzy logic problem. It is an important characteristic of a website in order to survive in Internet commerce. The satisfaction of a website is also a fuzzy logic problem that represents the degree of success in the application of information technology to the business. We propose a framework of fuzzy logic for the representation of these two problems based on web data mining techniques to fuzzify the attributes of a website.

The fuzzy frontier

THE STORY OF HOW FEATHERS EVOLVED IS FAR FROM OVER. IN 1868, THOMAS HUXLEY declared that dinosaurs gave rise to birds. He based his claim on Compsognathus, a 150-million-year-old dinosaur fossil from Solnhofen, Germany, whose delicate hind legs were remarkably similar to those of table fowl. The discovery seven years earlier of Archaeopteryx, a fossil bird with a long bony tail, toothed jaws and clawed fingers, had convinced many people that birds were somehow related to reptiles. But Compsognathus was the fossil that placed dinosaurs firmly in the middle of this complex evolutionary equation. Wings, claimed Huxley, must have grown out of rudimentary forelimbs. And feathers? Whether Compsognathus had them, Huxley could only guess. Nevertheless, his theory clearly required that scales had somehow transformed into feathers. The question was not just how, but why?

Data-driven fuzzy analysis in quantitative mineral resource assessment

The integration of geo-information from multiple sources and of diverse nature in developing mineral favourability indexes (MFIs) is a well-known problem in mineral exploration and mineral resource assessment. Fuzzy set theory provides a convenient framework to combine and analyse qualitative and quantitative data independently of their source or characteristics. A novel, data-driven formulation for calculating MFIs based on fuzzy analysis is developed in this paper. Different geo-variables are considered fuzzy sets and their appropriate membership functions are defined and modelled. A new weighted average-type aggregation operator is then introduced to generate a new fuzzy set representing mineral favourability. The membership grades of the new fuzzy set are considered as the MFI. The weights for the aggregation operation combine the individual membership functions of the geo-variables, and are derived using information from training areas and L, regression. The technique is demonstrated in a case study of skarn tin deposits and is used to integrate geological, geochemical and magnetic data. The study area covers a total of 22.5 km(2) and is divided into 349 cells, which include nine control cells. Nine geo-variables are considered in this study. Depending on the nature of the various geo-variables, four different types of membership functions are used to model the fuzzy membership of the geo-variables involved. (C) 2002 Elsevier Science Ltd. All rights reserved.