Deriving fuzzy discretization from interval discretization

We examine two methods for deriving fuzzy discretization from interval discretization for classification problems. One method uses linear membership functions with trapezoidal shape. The other extends them to piecewise linear functions. In both methods, we use a control parameter that specifies the overlap grade between adjacent membership functions. The overlap grade can be viewed as the fuzzification grade of interval discretization. Through computer simulations, we examine three interval discretization methods from which fuzzy discretization is derived: equal width intervals, equal frequency intervals, and minimum entropy intervals. We extract fuzzy rules for wine data and sonar data with many continuous attributes. Simulation results show that the classification ability of fuzzy rules is improved in some cases and degraded in other cases by the increase in the fuzzification grade.