Representation of Conic and Parabolic Fuzzy Numbers Using Bezier Curves

ABSTRACT

In our studies of quality of randomness for streams of fuzzy numbers (FNs), we identify two formulations for conic and parabolic FNs. Here we show how membership functions of these FN may be represented by Bezier curves. We show that 5-tuples are sufficient for computer representation, our motivation being to reduce the curse of dimensionality of higher order random numbers. In the process, we show the ease and efficiency with which they may be rendered in parametric form, and how they may be converted to implicit form. Our work begins advanced research in fuzzy Monte Carlo methods.

Key Words:

fuzzy numbers, conic, parabolic, Bezier generated, Sylvester Resultant.