Interpretable fuzzy modeling using multi-objective immune-inspired optimization algorithms

In this paper, an immune inspired multi-objective fuzzy modeling (IMOFM) mechanism is proposed specifically for high-dimensional regression problems. For such problems, high predictive accuracy is often the paramount requirement. With such a requirement in mind, however, one should also put considerable efforts in making the elicited model as interpretable as possible, which leads to a difficult optimization problem. The proposed modeling approach adopts a multistage modeling procedure and a variable length coding scheme to account for the enlarged search space due to the simultaneous optimization of the rule-base structure and its associated parameters. IMOFM can account for both Singleton and Mamdani Fuzzy Rule-Based Systems (FRBS) due to the carefully chosen output membership functions, the inference and the defuzzification methods. The proposed algorithm has been compared with other representatives using a simple benchmark problem, and has also been applied to a high-dimensional problem which models mechanical properties of hot rolled steels. Results confirm that IMOFM can elicit accurate and yet transparent FRBSs from quantitative data.