43 zyxwvutsrqp Estimation of Fuzzy Memberships from Histograms B. BHARATI-II DEW and V. V. S. SARMA School of Automation, h&an institute of S&we, ~ang~~Q~e M&W_‘, India ABSTRACT Based on the conclusions drawn in the bijective tr~sfo~ation between possibility and probability, a method is proposed to estimate the fuzzy member&p function for pattern recognition purposes. A rational function approximation to the probability density function is obtained from the histogram of a finite (and sometimes very small) number of samples. This function is normalized such that the bighest ordinate is one. The parameters representing the rational function are used for classifying the pattern samples based on a maw-min decision rule. The method is ilhzstrated with examples. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM 1. INTRODUCTION A fuzzy set is characterized by grades of membership. These grades or values of membership are either obtained subjectively or as the values of a function for those particular events or patterns. This membership Function enables us to perform qu~titative c~cula~ons in fuzzy decision making. Its choice and justification are important for the success of applications. Once a functional form is chosen, the estimation of the parameters of this characteristic function using the training set of data is termed abs~~~c~~~~ fl]. Desirable characteristics of the form of a membership function are: (1) The form represents the subjective nature of the fuzzy behavior. This relative grading or the nature of the variation is important, and the chosen form should reflect the real fuzziness. (2) The number of parameters in the functional representation should be as small as possible, with a provision to vary this number to suit the application and the context [9]. (3) We should be able to infer the parameters from a few sample prototypes of the elements of the fuzzy set concerned (as only a limited set of training samples will be available in real life problems). *:Elsevier Science Pub~s~ng Co., Inc. 1985 52 Vanderbilt Ave., New York, NY 10017