Coevolutionary Fuzzy Modeling

Ph.D. thesis by Carlos Andrés Peña-Reyes


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

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.