Shape Of Fuzzy Membership Functions Research Articles

Bee Colony Optimization metaheuristic for fuzzy membership functions tuning

The successfulness of the application of fuzzy logic to real-life problems depends on a number of parameters, such as the number and shapes of fuzzy membership functions, which are usually defined upon intuition or the subjective knowledge of relevant experts. One way to improve the performance of the fuzzy reasoning model is to use heuristic or metaheuristic techniques in order to optimize the shapes of membership functions. In this paper, the Bee Colony Optimization (BCO) algorithm is applied as a tool suitable for the specified optimization problem. The BCO belongs to the group of nature-inspired metaheuristics. The purpose of this paper is to present and discuss a strategy for the adjustment of fuzzy logic membership functions using the variant of the BCO algorithm based on the improvement of complete solutions and show its real-life application to the problem of the estimation of freight train energy consumption. According to the obtained results, it can be concluded that the precision of the developed fuzzy reasoning model is significantly increased after tuning membership functions by the BCO.

A Chromosome Representation Encoding Intersection Points for Evolutionary Design of Fuzzy Classifiers

ABSTRACT—Unlike the conventional chromosome representation to search the shape of fuzzy membership functions, a novel encoding scheme to search the optimal intersection points between adjacent fuzzy membership functions is originally presented for evolutionary design of fuzzy classifiers. Since the proposed representation contains the intersection points directly related to the boundary of classification, it is intuitively expected that redundancy of the search space is reduced and the performance is better in comparison with the conventional encoding scheme. The experimental results show that the proposed encoding scheme gives superior or competitive performance in two real-world datasets and gives more interpretable fuzzy classifiers. This short paper has provided additional explanation to the previous works introduced in the latest conference. Key Words: Fuzzy classifiers, genetic algorithms, encoding scheme, intersection points of membership functions 1. INTRODUCTION In classical data-driven fuzzy modeling, design of optimal fuzzy classifier has been commonly dealt with as a search problem [1][2]. Optimal design of fuzzy classifiers (FCs) is one of the most complex search problems since there are various feasible solutions according to the combination of fuzzy rules and membership functions (MFs). In other words, the optimal design of FCs is described as a non-convex and multimodal search problem. Besides, the high-order and large scale problems caused by the large number of rules, MFs, and input attributes also exist in the optimal design of FCs. In order to overcome these difficulties, many researchers have applied meta-heuristic search methods to optimally design FCs. Among them, evolutionary algorithms (EAs) such as genetic algorithms (GAs) have been widely used in the much of the literature due to their search ability and reliability [1]-[3]. EAs are basically general-purpose population-based stochastic search algorithms which use multiple candidate solutions simultaneously and find the best solution [4]. Irrespective of the given problem, the first step in applying EAs is to encode solutions for the given problem into a set of parameters: a chromosome. Thus, to optimize fuzzy models in a framework of EAs, the first step is to represent a fuzzy model into a chromosome. For evolutionary design of FCs, an encoding scheme relevant to the given problem is also required because an encoding scheme plays an important role to decide the property of search space [1][4]. The conventional encoding methods for evolutionary design of FCs are mainly designed to find the shape of the fuzzy MFs as a center and width of a Gaussian MF and 3 or 4 edge points of a triangular or trapezoidal MF. However, recent related works [5], providing an intuitive insight for properties of fuzzy rules, argue that the boundary of classification is formed in the intersection points between two adjacent MFs. In other Downloaded by [Iowa State University] at 12:35 10 January 2014

Application of the fuzzy performance measures to the City of London water supply system

Most engineering systems are subject to a wide range of possible uncertain future conditions. The probabilistic reliability analysis usually fails to address the problems of human error, subjectivity, and lack of system performance history and records. This paper explores the utility of the following fuzzy performance measures for evaluating the performance of a complex water supply system: (i) combined reliability–vulnerability, (ii) robustness, and (iii) resiliency. The regional water supply system for the City of London, Ontario, Canada, is used as the case study. The computational requirements for the implementation of the fuzzy performance measures and their sensitivity to different shapes of fuzzy membership functions are investigated. The study illustrates the capability of the fuzzy performance measures to handle uncertainty and identify critical system components. This can be of value in identifying the optimal level of improvement that will increase the overall system performance.Key words: water supply, fuzzy sets, risk, performance indicators.