Why Cauchy Membership Functions: Reliability

Abstract

An important step in designing a fuzzy system is the elicitation of the membership functions for the fuzzy sets used. Often the membership functions are obtained from data in a traininglike manner. They are expected to match or be at least compatible with those obtained from experts knowledgeable of the domain and the problem being addressed. In cases when neither are possible, e.g., insufficient data or unavailability of experts, we are faced with the question of hypothesizing the membership function. We have previously argued in favor of Cauchy membership functions (thus named because their expression is similar to that of the Cauchy distributions) and supported this choice from the point of view of efficiency of training. This paper looks at the same family of membership functions from the point of view of reliability