Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers

Coevolutionary fuzzy modeling

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

Advances in Evolutionary Algorithms

With the recent trends towards massive data sets and significant computational power, combined with evolutionary algorithmic advances evolutionary computation is becoming much more relevant to practice. Aim of the book is to present recent improvements, innovative ideas and concepts in a part of a huge EA field

Exploiting a coevolutionary approach to concurrently select training instances and learn rule bases of Mamdani fuzzy systems

When applied to high d imensional datasets, multiobjective evolutionary learning (MOEL) of fuzzy rule-based systems suffers from high computational costs, mainly due to the fitness evaluation. To use a reduced training set (TS) in place of the overall TS could considerably lessen the required effort. How this reduction should be performed, especially in the context of regression, is still an open issue. In this paper, we propose to adopt a co-evolutionary approach. In the execution of the MOEL, periodically, a single-objective genetic algorithm (SOGA) evolves a population of reduced TSs. The SOGA aims to maximize a purposely-defined index which measures how much a reduced TS is representative of the overall TS in the context of the MOEL. We tested our approach on a real world high dimensional dataset. We show that the Pareto fronts generated by applying the MOEL with the overall and the reduced TSs are comparable, although the use of the reduced TS allows saving on average the 75% of the execution time

A Serendipitous Software Framework for Facilitating Collaboration in Computational Intelligence

A major flaw in the academic system, particularly pertaining to computer science, is that it rewards specialisation. The highly competitive quest for new scientific developments, or rather the quest for a better reputation and more funding, forces researchers to specialise in their own fields, leaving them little time to properly explore what others are doing, sometimes even within their own field of interest. Even the peer review process, which should provide the necessary balance, fails to achieve much diversity, since reviews are typically performed by persons who are again specialists in the particular field of the work. Further, software implementations are rarely reviewed, having as a consequence the publishing of untenable results. Unfortunately, these factors contribute to an environment which is not conducive to collaboration, a cornerstone of academia | building on the work of others. This work takes a step back and examines the general landscape of computational intelligence from a broad perspective, drawing on multiple disciplines to formulate a collaborative software platform, which is flexible enough to support the needs of this diverse research community. Interestingly, this project did not set out with these goals in mind, rather it evolved, over time, from something more specialised into the general framework described in this dissertation. Design patterns are studied as a means to manage the complexity of the computational intelligence paradigm in a flexible software implementation. Further, this dissertation demonstrates that releasing research software under an open source license eliminates some of the deficiencies of the academic process, while preserving, and even improving, the ability to build a reputation and pursue funding. Two software packages have been produced as products of this research: i) CILib, an open source library of computational intelligence algorithms; and ii) CiClops, which is a virtual laboratory for performing experiments that scale over multiple workstations. Together, these software packages are intended to improve the quality of research output and facilitate collaboration by sharing a repository of simulation data, statistical analysis tools and a single software implementation.Dissertation (MSc)--University of Pretoria, 2006.Computer ScienceUnrestricte

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms