A high-order fuzzy classifier learned through clustering and gradient descent algorithm for classification problems

Fuzzy classifiers (FCs) are based on fuzzy if-then classification rules. Traditional FCs use either zero- or first-order Takagi-Sugeno (TS)-type fuzzy rules, where the consequent of a fuzzy rule is a linear decision function and may restrict the rule discrimination capability. This paper uses a high-order FC (HOFC) that expands the entire rule-mapped consequent space of a first-order TS-type fuzzy classifier via trigonometric function transformations. The expanded space can be regarded as the inclusion of high-order function terms for discrimination capability improvement. The HOFC is constructed via clustering and parameter learning. In parameter learning, consequent parameters in the rule-mapped consequent space are optimized using the gradient descent algorithm. Performance of the HOFC with gradient descent learning is verified through comparisons with different FCs.