An e?cient and ?exible mechanism for constructing membership functions

Andr e es L. Medaglia, Shu-Cherng Fang *, Henry L.W. Nuttle, James R. Wilson

Department of Industrial Engineering & Graduate Program in Operations Research,

College of Engineering, Operations Research and Industrial Engineering,

North Carolina State University, Raleigh, NC 27695-7906, USA

Received 13 September 2000; accepted 27 March 2001

FS 05

Abstract

This paper introduces a B e ezier curve-based mechanism for constructing membership functions of convex normal fuzzy sets. The mechanism can ?t any given data set with a minimum level of discrepancy. In the absence of data, the mechanism can be intuitively manipulated by the user to construct membership functions with the desired shape. Some numerical experiments are included to compare the performance of the proposed mechanism with conventional methods.  2002 Elsevier Science B.V. All rights reserved.

Keywords:

Fuzzy sets; Membership functions; B e ezier curves; Measures of information; Fuzzy numbers