Multi-objective evolutionary generation of mamdani fuzzy rule-based systems based on rule and condition selection International Workshop On Genetic And Evolutionary Fuzzy Systems, p.p , April 2011

Outline Abstract Introduction Mamdani fuzzy systems The proposed approach Experimental results Conclusions References

Abstract In the framework of multi-objective evolutionary fuzzy systems applied to regression problems, we propose to concurrently exploit a two-level rule selection (2LRS) and an appropriate learning of the membership function (MF) parameters to generate a set of Mamdani fuzzy rule-Based systems with different trade-offs between accuracy and RB complexity. The 2LRS aims to select a reduced number of rules from a previously generated rule base and a reduced number of conditions for each selected rule.

Introduction During the last years, the research trend on genetic fuzzy systems has mainly focused on multi-objective evolutionary fuzzy systems (MOEFSs) [1][2]. MOEFSs exploit multiobjective evolutionary algorithms (MOEAs) to generate sets of fuzzy rule-based systems (FRBSs), especially of the Mamdani type (MFRBSs), characterized by different trade-offs between accuracy and interpretability. Although several researchers have proposed different definitions of FRBS interpretability [3][4] by considering different perspectives and factors, interpretability in MOEFS has been usually measured in terms of rule base (RB) complexity [5]-[13] and data base (DB) integrity [15]-[17]

Mamdani fuzzy systems

The proposed approach In the proposed approach, rules Rm are selected from a set of candidate rules generated by applying some rule generation approach to the training data. To this aim, several heuristic approaches have been proposed. In this work, we exploit one of the most famous techniques, namely the WM algorithm [19].

The proposed approach

Experimental results

Conclusions In this paper, we have proposed a multi-objective evolutionary approach to generate MFRBSs with different trade-offs between accuracy and rule base complexity. The novelty of the approach relies on exploiting a two-level rule selection together with an appropriate learning of the membership function parameters. The proposed approach has been experimented on two real world regression problems and the results have been compared with those obtained by applying the same multi-objective evolutionary approach for learning concurrently rules and membership function parameters.

References