A Novel Genetic Fuzzy System for Regression Problems

Abstract

Solving a regression problem is equivalent to finding a model that relates the behavior of an output or response variable to a given set of input or explanatory variables. An example of such a problem would be that of a company that wishes to evaluate how the demand for its product varies in accordance to its and other competitors’ prices. Another example could be the assessment of an increase in electricity consumption due to weather changes. In such problems, it is important to obtain not only accurate predictions but also interpretable models that can tell which features, and their relationship, are the most relevant. In order to meet both requirements—linguistic interpretability and reasonable accuracy—this work presents a novel Genetic Fuzzy System (GFS), called Genetic Programming Fuzzy Inference System for Regression problems (GPFIS-Regress). This GFS makes use of Multi-Gene Genetic Programming to build the premises of fuzzy rules, including in it t-norms, negation and linguistic hedge operators. In a subsequent stage, GPFIS-Regress defines a consequent term that is more compatible with a given premise and makes use of aggregation operators to weigh fuzzy rules in accordance with their influence on the problem. The system has been evaluated on a set of benchmarks and has also been compared to other GFSs, showing competitive results in terms of accuracy and interpretability issues.