# Multiobjective Genetic Fuzzy Systems in Data Classification and Regression

##### Pulkkinen, Pietari (2011)

Pulkkinen, Pietari

Tampere University of Technology

2011

This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.

**Julkaisun pysyvä osoite on**

http://urn.fi/URN:NBN:fi:tty-201102161036

##### Tiivistelmä

This thesis presents data-driven methods to learn interpretable and accurate fuzzy models (FMs) for classification and regression problems. When FMs are identified based on data, the main advantage of FMs, namely interpretability can easily be deteriorated unless appropriate learning method is used.

Multiobjective evolutionary algorithms (MOEAs) are selected in this thesis to learn FMs because they are very flexible learning methods and have proved to be robust in many learning tasks. This approach to use MOEAs to learn FMs is often referred to as multiobjective genetic fuzzy systems (MGFSs). In this thesis MGFSs are applied to learn the rules, select input variables, determine the granularity of each input and output variable and to tune the membership function (MF) parameters. The goal is to maximize the accuracy and interpretability, which are conflicting objectives. MGFSs can find a set of Pareto optimal FMs presenting different trade-offs between accuracy and interpretability. After the user has seen the available choices, he/she selects one or more of them based on the preferences.

MGFSs face challenges especially in high-dimensional problems (i.e. the number of input variables is high). That is because the search space is large, which makes it difficult to find good FMs. This thesis proposes initialization methods to remove irrelevant input variables, which reduces the search space and eases the further optimization by MOEA. Another challenge is related to MFs tuning which usually improves accuracy but deteriorates transparency of fuzzy partitions unless adequate tuning strategy is used. Two solutions for that problem are proposed. First, an interpretability index is used to measure the transparency of fuzzy partitions and the purpose is to optimize its value. The second proposal uses dynamic constraints to guarantee that the user specified transparency conditions are met by each FM at any given phase of optimization. This proposal reduces the number of objective functions by one which improves the search efficiency of MOEAs.

Altogether five MGFSs are proposed in this thesis. Three of them are designed for classification problems and two of them for regression problems. They are evaluated on seven classification and 12 regression problems. Results comparisons show that they outperform several MGFSs in the literature. Finally, through an industrial application, it is shown that MGFSs are suitable for learning FMs to be used as a reasoning mechanism in a bioaerosol detector.

Multiobjective evolutionary algorithms (MOEAs) are selected in this thesis to learn FMs because they are very flexible learning methods and have proved to be robust in many learning tasks. This approach to use MOEAs to learn FMs is often referred to as multiobjective genetic fuzzy systems (MGFSs). In this thesis MGFSs are applied to learn the rules, select input variables, determine the granularity of each input and output variable and to tune the membership function (MF) parameters. The goal is to maximize the accuracy and interpretability, which are conflicting objectives. MGFSs can find a set of Pareto optimal FMs presenting different trade-offs between accuracy and interpretability. After the user has seen the available choices, he/she selects one or more of them based on the preferences.

MGFSs face challenges especially in high-dimensional problems (i.e. the number of input variables is high). That is because the search space is large, which makes it difficult to find good FMs. This thesis proposes initialization methods to remove irrelevant input variables, which reduces the search space and eases the further optimization by MOEA. Another challenge is related to MFs tuning which usually improves accuracy but deteriorates transparency of fuzzy partitions unless adequate tuning strategy is used. Two solutions for that problem are proposed. First, an interpretability index is used to measure the transparency of fuzzy partitions and the purpose is to optimize its value. The second proposal uses dynamic constraints to guarantee that the user specified transparency conditions are met by each FM at any given phase of optimization. This proposal reduces the number of objective functions by one which improves the search efficiency of MOEAs.

Altogether five MGFSs are proposed in this thesis. Three of them are designed for classification problems and two of them for regression problems. They are evaluated on seven classification and 12 regression problems. Results comparisons show that they outperform several MGFSs in the literature. Finally, through an industrial application, it is shown that MGFSs are suitable for learning FMs to be used as a reasoning mechanism in a bioaerosol detector.

##### Kokoelmat

- Väitöskirjat [3961]