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Concept# Fuzzy logic

Summary

Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1.
The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Iranian Azerbaijani mathematician Lotfi Zadeh. Fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.
Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certaint

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This thesis presents Fuzzy CoCo, a novel approach for system design, conducive to explaining human decisions. Based on fuzzy logic and coevolutionary computation, Fuzzy CoCo is a methodology for constructing systems able to accurately predict the outcome of a human decision-making process, while providing an understandable explanation of the underlying reasoning. Fuzzy logic provides a formal framework for constructing systems exhibiting both good numeric performance (precision) and linguistic representation (interpretability). From a numeric point of view, fuzzy systems exhibit nonlinear behavior and can handle imprecise and incomplete information. Linguistically, they represent knowledge in the form of rules, a natural way for explaining decision processes. Fuzzy modeling —meaning the construction of fuzzy systems— is an arduous task, demanding the identification of many parameters. This thesis analyses the fuzzy-modeling problem and different approaches to coping with it, focusing on evolutionary fuzzy modeling —the design of fuzzy inference systems using evolutionary algorithms— which constitutes the methodological base of my approach. In order to promote this analysis the parameters of a fuzzy system are classified into four categories: logic, structural, connective, and operational. The central contribution of this work is the use of an advanced evolutionary technique —cooperative coevolution— for dealing with the simultaneous design of connective and operational parameters. Cooperative coevolutionary fuzzy modeling succeeds in overcoming several limitations exhibited by other standard evolutionary approaches: stagnation, convergence to local optima, and computational costliness. Designing interpretable systems is a prime goal of my approach, which I study thoroughly herein. Based on a set of semantic and syntactic criteria, regarding the definition of linguistic concepts and their causal connections, I propose a number of strategies for producing more interpretable fuzzy systems. These strategies are implemented in Fuzzy CoCo, resulting in a modeling methodology providing high numeric precision, while incurring as little a loss of interpretability as possible. After testing Fuzzy CoCo on a benchmark problem —Fisher's Iris data— I successfully apply the algorithm to model the decision processes involved in two breast-cancer diagnostic problems: the WBCD problem and the Catalonia mammography interpretation problem. For the WBCD problem, Fuzzy CoCo produces systems both of high performance and high interpretability, comparable (if not better) than the best systems demonstrated to date. For the Catalonia problem, an evolved high-performance system was embedded within a web-based tool —called COBRA— for aiding radiologists in mammography interpretation. Several aspects of Fuzzy CoCo are thoroughly analyzed to provide a deeper understanding of the method. These analyses show the consistency of the results. They also help derive a stepwise guide to applying Fuzzy CoCo, and a set of qualitative relationships between some of its parameters that facilitate setting up the algorithm. Finally, this work proposes and explores preliminarily two extensions to the method: Island Fuzzy CoCo and Incremental Fuzzy CoCo, which together with the original CoCo constitute a family of coevolutionary fuzzy modeling techniques. The aim of these extensions is to guide the choice of an adequate number of rules for a given problem. While Island Fuzzy CoCo performs an extended search over different problem sizes, Incremental Fuzzy CoCo bases its search power on a mechanism of incremental evolution.

The novelty this article brings is the use of neural networks and neuro-fuzzy modeling to take the engine knock detection based on pressure and vibration samples taken from an internal combustion engine to the next step from previous achievements, the ultimate goal being higher detection rates and also faster response times than the classical non neuro-fuzzy methods. Work started from the theoretical works available in the domain, algorithms were adapted for the case in hand, then the study was led on how they would be affected by the variety of situations that occur in internal-combustion engines with the scope of real-time applications. Following the experiments, results were finally compared showing significantly greater knock detection rate-time improvements than other methods employed so far.

2012The objective of the work presented here is to develop a low cost active above knee prosthetic device exploiting bipedal robotics technology which will work utilizing the available biological motor control circuit properly integrated with a Central Pattern Generator (CPG) based control scheme. The approach is completely different from the existing Active Prosthetic devices, designed primarily as standalone systems utilizing multiple sensors and embedded rigid control schemes. In this research, first we designed a fuzzy logic based methodology for offering suitable gait pattern for an amputee, followed by formulating a suitable algorithm for designing a CPG, based on Rayleigh's oscillator. An indigenous probe, Humanoid Gait Oscillator Detector (HGOD) has been designed for capturing gait patterns from various individuals of different height, weight and age. These data are used to design a Fuzzy inference system which generates most suitable gait pattern for an amputee. The output of the Fuzzy inference system is used for designing a CPG best suitable for the amputee. We then developed a CPG based control scheme for calculating the damping profile in real time for maneuvering a prosthetic device called AMAL (Adaptive Modular Active Leg).

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