Learning from Imprecise Granular Data Using Trapezoidal Fuzzy Set Representations

Abstract

We discuss the role and benefits of using trapezoidal fuzzy representa-tions of granular information. We focus on the use of level sets as a tool for implementing many operations involving trapezoidal fuzzy sets. Attention is particularly brought to the simplification that the linearity of the trapezoid brings in that it often allows us to perform operations on only two level sets. We investigate the classic learning algorithm in the case when our observations are granule objects represented as trapezoidal fuzzy sets. An important issue that arises is the adverse effect that very uncertain observations have on the quality of our estimates. We suggest an approach to addressing this problem using the specificity of the observations to control its effect. Throughout this work particular emphasis is placed on the simplicity of working with trapezoids while still retaining a rich representational capability.