Improving Transparency in Approximate Fuzzy Modeling Using Multi-objective Immune-Inspired Optimisation

Abstract

In this paper, an immune inspired multi-objective fuzzy modeling (IMOFM) mechanism is proposed specifically for high-dimensional regression problems. For such problems, prediction accuracy is often the paramount requirement. With such a requirement in mind, however, one should also put considerable efforts in eliciting models which are as transparent as possible, a ‘tricky’ exercise in itself. The proposed mechanism adopts a multi-stage modeling procedure and a variable length coding scheme to account for the enlarged search space due to simultaneous optimisation of the rule-base structure and its associated parameters. We claim here that IMOFM can account for both Singleton and Mamdani Fuzzy Rule-Based Systems (FRBS) due to the carefully chosen output membership functions, the inference scheme and the defuzzification method. The proposed modeling approach has been compared to other representatives using a benchmark problem, and was further applied to a high-dimensional problem, taken from the steel industry, which concerns the prediction of mechanical properties of hot rolled steels. Results confirm that IMOFM is capable of eliciting not only accurate but also transparent FRBSs from quantitative data.

Keywords:

• Interpretability
• Immune-inspired multi-objective optimisation
• Variable length coding scheme