Elliptical Fuzzy Number and the Method of Circular Fuzzy Structured Element

For the need of studying the fuzzy plane or space geometry, under the background of plane or space fuzzy points, this paper presents the definition of the fuzzy number in R² based on the definition of fuzzy point which is introduced by Buckley, and define two-dimensional fuzzy number. In order to realize the expression of two-dimensional fuzzy number´s membership function, the paper defines elliptical fuzzy number that is a special fuzzy set in R² . What´s more, we provide the circular structured element representation theorem of elliptical fuzzy number and study some of its fundamental properties. The operations of fuzzy sets is easier with the new represented theorem than that based on the extension principle. The method of circular fuzzy structured element not only provides a tool for the fuzzy calculations, but also paves a new wa.y for studying the fuzzy number in R² .