Fuzzy Interpolation Systems and Applications

Fuzzy inference systems provide a simple yet effective solution to complex non-linear problems, which have been applied to numerous real-world applications with great success. However, conventional fuzzy inference systems may suffer from either too sparse, too complex or imbalanced rule bases, given that the data may be unevenly distributed in the problem space regardless of its volume. Fuzzy interpolation addresses this. It enables fuzzy inferences with sparse rule bases when the sparse rule base does not cover a given input, and it simplifies very dense rule bases by approximating certain rules with their neighbouring ones. This chapter systematically reviews different types of fuzzy interpolation approaches and their variations, in terms of both the interpolation mechanism (inference engine) and sparse rule base generation. Representative applications of fuzzy interpolation in the field of control are also revisited in this chapter, which not only validate fuzzy interpolation approaches but also demonstrate its efficacy and potential for wider applications

Big Data Analysis Using Neuro-Fuzzy System

This project addresses big data classification using hybrid IntelligenceClassification System. Hybrid Intelligence classification system is a system thatcombines at least two intelligent technologies. Specifically, the focus of this project is toapply hybrid Neuro-Fuzzy system to the IBM Watson data and InnocentiveTrustworthiness challenge data for prediction and classification. Neural network are low-level computational structure which has ability to learn and performs well on the rawdata. On the other hand, fuzzy logic deals with reasoning on higher level using If-thenrules and linguistic variables. So combining these two methods can provide us with avery powerful classification system

DATA CLASSIFICATION SYSTEM WITH FUZZY NEURAL BASED APPROACH

Knowledge Discovery in Database and Data Mining use techniques derived from machine learning, visualization and statistics to investigate real world data. Their aim is to discover patterns within the data which are new, statistically valid, interesting and understandable. In recent years, there has been an explosion in computation and information technology. With it have come vast amounts of data. Lying hidden in all this data is potentially useful information that is rarely made explicit or taken advantage. New tools based both on clever applications of established algorithms and on new methodologies, empower us to do entirely new things. In this context, data mining has arisen as an important research area that helps to reveal the hidden interesting information from the rawdatacollected. The project demonstrates how data mining can address the need of business intelligence in the process of decision making. An analysis on the field of data mining is done to show how data mining can help in business such as marketing, credit card approval. The project's objective is identifying the available data mining algorithms in data classification and applying new data mining algorithm to perform classification tasks. The proposed algorithm is a hybrid system which applied fuzzy logic and artificial neural network, which applies fuzzy logic inference to generate a set of fuzzy weighted production rules and applies artificial neural network to train the weights of fuzzy weighted rules for better classification results. Theresult of this system using the iris dataset and credit card approval dataset to evaluate the proposed algorithm's accuracy, interpretability. The project has achieved the target objectives; it can gain high accuracy for data classification task, generate rules which can help to interpret the output results, reduce the training processing. But the proposed algorithm still require high computation, the processing time will be long if the dataset is huge. However the proposed algorithm offers a promising approach to building intelligent systems

Inducción de conocimiento con incertidumbre en bases de datos relacionales borrosas

Este trabajo presenta un sistema para aprendizaje de definiciones lógicas con incertidumbre, a partir de una base de datos relacional borrosa. El campo de interés se centra, por tanto, en la programación lógica inductiva, introduciendo algunas interesantes aportaciones, principalmente en lo que se refiere a la entrada de datos y a los resultados producidos: Los datos de entrada pertenecen a una base de datos relacional borrosa. Por tanto, vienen expresados en forma de tablas de tuplas (relaciones), en las que las tuplas pueden llevar asociado un grado de pertenencia a la relación correspondiente. Se trata, por tanto, de relaciones borrosas, directamente identificables con conceptos borrosos (tan comunes en la realidad vista desde un punto de vista humano), y no de relaciones ordinarias con atributos borrosos (tal y como se entiende la "borrosidad" en muchos sistemas existentes). Los datos de salida vienen expresados en forma de definiciones lógicas de una relación (ordinaria o borrosa), que consta de una cláusula de Horn o de la disyunción de varias. Estas cláusulas de Horn se construyen mediante literales, aplicados sobre variables (generalmente), y asociados a relaciones borrosas u ordinarias. Los literales borrosos pueden ser modificados, además, por el empleo de etiquetas lingüísticas. Por tanto, se combina, en estas definiciones, la lógica de predicados con la lógica borrosa, en lo que podemos denominar "lógica borrosa de predicados", lo que constituye una aportación dentro de la inducción automática de conocimiento. Además, las definiciones inducidas llevan asociado un factor de incertidumbre, como hacen otros sistemas ya existentes. El punto de partida del trabajo lo constituye un sistema de inducción de definiciones lógicas bien conocido: FOIL, creado por Quinlan en 1990, basado en la lógica de predicados. Sobre este sistema inicial se realizan, además de las extensiones para lógica borrosa ya mencionadas, otra serie de modificaciones y ampliaciones enfocadas a mejorar la inducción de conocimiento. Estas mejoras se realizan, principalmente, en su parte heurística, al definir una función de evaluación de literales, basada en medidas de interés, que permite corregir algunas deficiencias del sistema original y aumentar la calidad de las reglas inducidas. Otras modificaciones se orientan hacia la introducción de conocimiento de base, mediante relaciones definidas intensionalmente, de modo similar a otros sistemas como FOCL. Como resultado tangible de la tesis, se ha desarrollado y probado un sistema, FZFOIL, disponible públicamente bajo la licencia GNU

Fuzzy set covering as a new paradigm for the induction of fuzzy classification rules

In 1965 Lofti A. Zadeh proposed fuzzy sets as a generalization of crisp (or classic) sets to address the incapability of crisp sets to model uncertainty and vagueness inherent in the real world. Initially, fuzzy sets did not receive a very warm welcome as many academics stood skeptical towards a theory of imprecise'' mathematics. In the middle to late 1980's the success of fuzzy controllers brought fuzzy sets into the limelight, and many applications using fuzzy sets started appearing. In the early 1970's the first machine learning algorithms started appearing. The AQ family of algorithms pioneered by Ryszard S. Michalski is a good example of the family of set covering algorithms. This class of learning algorithm induces concept descriptions by a greedy construction of rules that describe (or cover) positive training examples but not negative training examples. The learning process is iterative, and in each iteration one rule is induced and the positive examples covered by the rule removed from the set of positive training examples. Because positive instances are separated from negative instances, the term separate-and-conquer has been used to contrast the learning strategy against decision tree induction that use a divide-and-conquer learning strategy. This dissertation proposes fuzzy set covering as a powerful rule induction strategy. We survey existing fuzzy learning algorithms, and conclude that very few fuzzy learning algorithms follow a greedy rule construction strategy and no publications to date made the link between fuzzy sets and set covering explicit. We first develop the theoretical aspects of fuzzy set covering, and then apply these in proposing the first fuzzy learning algorithm that apply set covering and make explicit use of a partial order for fuzzy classification rule induction. We also investigate several strategies to improve upon the basic algorithm, such as better search heuristics and different rule evaluation metrics. We then continue by proposing a general unifying framework for fuzzy set covering algorithms. We demonstrate the benefits of the framework and propose several further fuzzy set covering algorithms that fit within the framework. We compare fuzzy and crisp rule induction, and provide arguments in favour of fuzzy set covering as a rule induction strategy. We also show that our learning algorithms outperform other fuzzy rule learners on real world data. We further explore the idea of simultaneous concept learning in the fuzzy case, and continue to propose the first fuzzy decision list induction algorithm. Finally, we propose a first strategy for encoding the rule sets generated by our fuzzy set covering algorithms inside an equivalent neural network

Fuzzy set covering as a new paradigm for the induction of fuzzy classification rules

In 1965 Lofti A. Zadeh proposed fuzzy sets as a generalization of crisp (or classic) sets to address the incapability of crisp sets to model uncertainty and vagueness inherent in the real world. Initially, fuzzy sets did not receive a very warm welcome as many academics stood skeptical towards a theory of imprecise'' mathematics. In the middle to late 1980's the success of fuzzy controllers brought fuzzy sets into the limelight, and many applications using fuzzy sets started appearing. In the early 1970's the first machine learning algorithms started appearing. The AQ family of algorithms pioneered by Ryszard S. Michalski is a good example of the family of set covering algorithms. This class of learning algorithm induces concept descriptions by a greedy construction of rules that describe (or cover) positive training examples but not negative training examples. The learning process is iterative, and in each iteration one rule is induced and the positive examples covered by the rule removed from the set of positive training examples. Because positive instances are separated from negative instances, the term separate-and-conquer has been used to contrast the learning strategy against decision tree induction that use a divide-and-conquer learning strategy. This dissertation proposes fuzzy set covering as a powerful rule induction strategy. We survey existing fuzzy learning algorithms, and conclude that very few fuzzy learning algorithms follow a greedy rule construction strategy and no publications to date made the link between fuzzy sets and set covering explicit. We first develop the theoretical aspects of fuzzy set covering, and then apply these in proposing the first fuzzy learning algorithm that apply set covering and make explicit use of a partial order for fuzzy classification rule induction. We also investigate several strategies to improve upon the basic algorithm, such as better search heuristics and different rule evaluation metrics. We then continue by proposing a general unifying framework for fuzzy set covering algorithms. We demonstrate the benefits of the framework and propose several further fuzzy set covering algorithms that fit within the framework. We compare fuzzy and crisp rule induction, and provide arguments in favour of fuzzy set covering as a rule induction strategy. We also show that our learning algorithms outperform other fuzzy rule learners on real world data. We further explore the idea of simultaneous concept learning in the fuzzy case, and continue to propose the first fuzzy decision list induction algorithm. Finally, we propose a first strategy for encoding the rule sets generated by our fuzzy set covering algorithms inside an equivalent neural network

An Inductive Learning Algorithm in Fuzzy Systems

The aim of this paper is to present a method for identifying the structure of a rule in a fuzzy model. For this purpose, an ATMS shall be used. An algorithm obtaining the identification of the structure will be suggested. The minimal structure of the rule (with respect to the number of variables that must appear in the rule) will be found by this algorithm. Furthermore, the identification parameters shall be obtained simultaneously. The proposed method shall be applied for classification to an example. The Iris Plant Database shall be learnt for all three kinds of plants. Keywords: Fuzzy logic, automatic learning, environment, Truth Maintenance System. 1 Introduction If we want to describe a system, it is necessary to know which are the inputs and the outputs of the system, and, more importantly, the relationship between them. This function, in most cases, is not easy to achieve, and in many others, it contains highly complicated mathematical relationships. So, it would be interesti..