A New Point of View for Fuzzy Numbers and Their Defuzzification

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification. The calculations involved in the proposed method and the resultant representation use Moore's semiplane for intervals and therefore are far simpler than those involved in other approaches.

We start by representing triangular and trapezoidal fuzzy numbers in Moore's semiplane. Then we extend this work to any fuzzy number. Although this extension has to be undertaken in ${ℝ}^3$, it preserves all the properties we study for trapezoidal and triangular fuzzy numbers in Moore's semiplane.