The input of the **system** is the OO metrics extracted from java application. The Fuzzifier calculates the matching degree of the metrics that matches the condition of the **fuzzy** rules. The Inference Engine calculates the rule’s conclusion based on its matching degree by using the clipping method, and combines the conclusion inferred by all **fuzzy** rules in a final conclusion. Finally, the Defuzzifier process coverts the **fuzzy** conclusion into a crisp value by using the mean of max method. There are two types of results given by the **system**: A fine-grained **classification** for each of the classes and a general **classification** for the java application being evaluated [11]. For this reason two sets of rules are defined: one set of rules to classify single classes and another one to evaluate the application. Moreover a decomposition tree is generated for all the classes reported during the fined-grain **classification**. This tree will help the developer to analyze and address classes with similar values. Unfortunately due to performance constraints only systems that report less than 200 classes will generate this similarity tree.

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Abstract — A hybrid **Fuzzy** Neural Network (FNN) **system** is presented in this paper. The proposed FNN can handle numeric and **fuzzy** inputs simulta- neously. The numeric inputs are fuzzified by input nodes upon presentation to the network while the **fuzzy** inputs do not require this translation. The connections between input to hidden nodes repre- sent **rule** antecedents and hidden to output nodes represent **rule** consequents. All the connections are represented by Gaussian **fuzzy** sets. The mutual subsethood measure for **fuzzy** sets that indicates the degree to which the two **fuzzy** sets are equal and is used as a method of activation spread in the network. A volume based defuzzification method is used to compute the numeric output of the network. The training of the network is done using gradient descent learning procedure. The model has been tested on three benchmark problems i.e. sine−cosine and Narazaki Ralescu’s function for approximation and Iris flower data for **classification**. Results are also compared with existing schemes and the proposed model shows its natural capability as a function approximator, and classifier.

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Implementing a **fuzzy** **system** requires that the different categories of the different inputs be represented by **fuzzy** sets which, in turn, is represented by membership functions. The domain of membership function is fixed, usually the set of real numbers, and whose range is the span of positive numbers in the closed interval [0, 1]. There are total 11 membership functions available in Mat Lab. We considered Triangular Membership Functions (TMF) for our problem, because of its simplicity and heavy use by researchers for prediction models [18]. It is a three-point function, defined by minimum α, maximum β and modal value m i.e. TMF (α, m, β), where (α ≤ m ≤ β). This process is known as fuzzification. These membership functions are then processed in **fuzzy** domain by inference engine based on knowledge **base** (**rule** **base** and data **base**) supplied by domain experts and finally the process of converting back **fuzzy** numbers into single numerical values is called defuzzification [17].

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an input values in each **fuzzy** set defining the given attribute. This way, a confidence degree is calculated for each **rule**. This confidence degree is used by the **classification** process and gives credibility to the final classi- fication. Notice that, for a well defined **fuzzy** data **base**, each input value presents membership degrees greater than zero in at most two **fuzzy** sets, i.e., the two corresponding branches of the test node are fired simulta- neously. On the other hand, if the decision tree is large, the inference process might require considerable computational effort when compared to the classic C4.5, since more branches are fired. This issue can be soft- ened by defining a minimum threshold of membership degree in order to continue testing the rules or not.

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The methodology used for genetic adjustment of the **fuzzy** **system** was proposed by, Pires (2004), Valdez et al. (2011), Starczewski et al. (2014), Georgieva (2016) and Tan et al. (2016). In this methodology, there is a knowledge **base** to which a genetic tuning process is applied to improve **system** performance without changing the basis of existing rules. This is done in order to adjust the **fuzzy** **system** parameters to improve their performance by adjusting the relevance functions and output variables. The method consists of two steps. The first is the generation of rules by a method driven by data for the rapid construction of the **rule** **base**, focusing on simplicity and transparency of the rules. The second relates to the genetic optimization of **system** performance by tuning the membership functions.

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An appropriate decision of traffic splitting is performed among the computed number of LSPs required by Traffic Splitting Algorithm (TSA). The computed **fuzzy** based LSPs for forwarding packets are obtained to avoid the situation of underutilization and over utilization of paths. None of the paths remains idle for longer time and proper utilization of resources takes place. Hence, it is better for congestion to be prevented rather than corrected. Implementation of FL using Mamdani **Fuzzy** Inference **System** [31] evaluates final decisions as LsS_value and TSS_value. The available number of rules in the **Rule** **Base** matrix LsS and TSS represents intermediate situations and provides the control mechanism with a highly dynamic action.

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First, we perform two-category **classification** problems as in Fig.2 to investigate the basic feature of the proposed method and to compare it with the SIRMs model. In the **classification** problems, points on [0, 1] × [0, 1] × [0, 1] are classified into two classes: class 0 and class 1. The class boundaries are given as spheres centered at (0.5, 0.5, 0.5). For Sphere, the inside of sphere is associated with class 1 and the outside with class 0. For Double-Sphere, the area between Spheres 1 and 2 is associated with class 1 and the other area with class 0. For triple-Sphere, the inside of Sphere1 and the area between Sphere2 and Sphere3 is associated with class 1 and the other area with class 0. The desired output y r

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The identification of **fuzzy** model consists of two major phases: structure identification and parameter optimization. The first phase is the determination of number of **fuzzy** if-then rules and membership functions of the premise **fuzzy** sets while the second phase is the tuning of the parameter values of the **fuzzy** model [11]. However, there will be two problems if we directly use the traditional Takagi Sugeno model for the speech recognition **system**. The first one is the network reasoning will fail if the input dimension is too large. The second problem is that with the increase of input dimension, **rule** numbers will have an exponential growth and cause “**rule** disaster”. Thus, determination of an appropriate structure becomes an important issue, then clustering techniques are applied to solve this problem. [12] [13] [14].

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RESUMO: Este trabalho apresenta um sistema baseado em regras **fuzzy** que resultou em um índice que indica o nível de incerteza relacionada com as transações comerciais entre produtores de mandioca e de seus compradores, com **base** na abordagem da Economia dos Custos de Transação. O sistema **fuzzy** foi desenvolvido utilizando como variáveis de entrada "Previsão de Demanda/compra", "Previsão de Produção" e "Compartilhamento de informações acerca de inovações de produção". A variável de saída consiste no nível de incerteza da transação entre vendedor e agente comprador, que pode servir como um sistema para a detecção de ineficiências. Entrevistas realizadas com 27 produtores de mandioca registrados nos Escritórios de Desenvolvimento Regionais de Tupã e Assis, São Paulo, Brasil, e 48 de seus compradores sustentaram o desenvolvimento do sistema. O modelo matemático aplicado na avaliação destes produtores indicou que 55% dos produtores têm relações comerciais com nível de incerteza Muito Alta, 25% Média ou Alta; e os demais, classificados entre Baixa ou Média. A partir dos resultados encontrados, simulações de ações poderiam ser implementadas para reduzir o grau de incerteza e os custos de transação envolvidos.

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Defects are commonly defined as deviations from or expectations that might lead to failures in operation for the **software** quality [9]. **Software** defect is a deficiency in a **software** product that causes it to perform unexpectedly. From a **software** user’s perspective, a defect is anything that causes the **software** not to meet their expectations. In this context, a **software** user can be either a person or another piece of **software** [1]. A defect is any blemish, imperfection, or undesired behavior that occurs either in the deliverable or in the product. Anything related to defect is a continual process and not a state [3].**Software** defects are expensive. Moreover, the cost of finding and correcting defects represents one of the most expensive **software** activities. It is well known that **software** production organizations spend a sizeable amount of their project budget to rectify the defects introduced in to the **software** systems during development process.

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In this work we present a research carried out in the classroom with the objective of treating subjective questions through the **Fuzzy** Logic with students of the third year of high school. We begin with the study of the basic concepts of **Fuzzy** Set Theory and systems based on **fuzzy** rules. Then, aiming at an application, we developed a **fuzzy** **system** to evaluate the risk of an individual developing type 2diabetes, from risk factors. Finally, we propose a didactic sequence to the students, through a questionnaire and a lecture given by the author. The results of the research are presented and, if on the one hand they indicate the diﬃculty of the students with the **fuzzy** reasoning, on the other hand, demonstrated the interest and the role of Logica **Fuzzy**, and therefore, of Mathematics in solving problems of our daily life.

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Abstract This paper considers a GIS methodological framework based on **fuzzy** sets theory for land use management. Some principles of development of the GIS methodological framework are formu- lated. Applications of the GIS methodological framework are designed. In particular GIS knowledge management **fuzzy** models for analysis of soil commutative contamination by heavy metals, for the study of soil acidity, and for evaluation of soil conservation actions are obtained.

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An Integrated System of Classification of Flowering Plamts.. Boletim do IMPA[r]

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The relation between mutual fund performance and fund characteristics is of much interest to financial market practitioners and investors. However, there is a lack of conclusive knowledge on this issue. This study introduces a method which examines the relation between fund returns and fund asset size, loads, expense ratios and turnover. The study focuses developing Techno-Portfolio Advisor which provides investment options and optimal funds for achieving their objectives. The **system** is developed based on the **fuzzy** inference **rule**. The **system** fulfills the investor’s objectives and preferences in terms rate of return, risk and asset allocation and diversification in order to reach an optimum solution. Therefore, Techno-Portfolio Advisor provides a solid support for decision making in mutual fund investment. The study also creates awareness among the investor community in choosing the best mutual fund scheme.

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One field of applied mathematics that has many applications in various areas of science is solving a **system** of linear equations. Systems of simultaneous linear equations play a major role in various areas such as operational research, physics, statistics, engineering and social sciences. When the estimation of the **system** coefficients is imprecise and only some vague knowledge about the actual values of the parameters is available, it may be convenient to represent some or all of them with **fuzzy** numbers [22]. **Fuzzy** number arithmetic is widely applied and useful in computation of linear **system** whose parameters are all or partially represented by **fuzzy** numbers.

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(3)The rules in LEM2 have bigger mean coverage, but longer mean length and lower mean accuracy than RGD. The bigger mean coverage because LEM2 select the attribute values with biggest coverage to construct a **rule**. The longer mean length and lower mean accuracy is due to that LEM2 use the formula (1) as the stop schema when forming a **rule**, and as a result for an inconsistent example the rule's length is as long as the example itself, and the final **classification** performance is worsened.

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In this paper, by combining the Backstepping method and the T-S **fuzzy** model method, the **fuzzy** backstepping sliding mode control was presented for a class of mismatched uncertain **system**. In this new method, nonlinear **system** is described based on T-S **fuzzy** dynamical model, and the nonlinear **system** is translated into local linear model by **fuzzy** method, not only make the **system** is stable, and avoid the chattering phenomenon of sliding mode control, Then the global stability of the control law was also achieved by a Lyapunov function. Simulation results indicate that the proposed controller is valid and effective, and it has strong robustness to external disturbance and the performance of **system**.

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(7) With the classification results from the previous procedure, the forecast outflow discharge was found by fuzzy inference. The model was named Gauss. Fuzzy inference w[r]

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Abstract —With the advancement of computer technology, computer simulation in the field of education are more realistic and more effective. The definition of simulation is to create a virtual environment that accurately and real experiences to improve the individual. So Simulation Based Training is the ability to improve, replace, create or manage a real experience and training in a virtual mode. Simulation Based Training also provides large amounts of information to learn, so use data mining techniques to process information in the case of education can be very useful. So here we used data mining to examine the impact of simulation-based training. The database created in cooperation with relevant institutions, including 17 features. To study the effect of selected features, LDA method and Pearson's correlation coefficient was used along with genetic algorithm. Then we use **fuzzy** clustering to produce **fuzzy** **system** and improved it using Neural Networks. The results showed that the proposed method with reduced dimensions have 3% better than other methods.

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O modelo de ´arvore decis´oria para o tipo de demˆencia foi refinado com uma **base** de dados de 49 casos. Para essa avalia¸c˜ao foi criada uma tabela que cont´em informa¸c˜oes como tipo de in´ıcio (Mem´oria ou inicio insidioso), achados na neuroimagem (imagem caracter´ıstica da doen¸ca), velocidade da evolu¸c˜ao (evolu¸c˜ao r´apida ou lenta) entre outros crit´erios. O especialista avaliou o caso e escolheu marcando um X na op¸c˜ao que ele acredita ser a hip´otese diagn´ostica daquele caso. A figura 3.16 apresenta um exemplo do formul´ario modelo utilizado para testes dos caminhos do diagrama de decis˜ao.

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