On Fuzzy Simplex and Fuzzy Convex Hull

In many scientific and engineering applications, the fuzzy set concept plays an important role. The fuzziness appears when we need to perform, on manifold, calculations with imprecision variables. The fuzzy set theory was introduced initially by Zadeh [1] in 1965. In the theory and applications of fuzzy sets, convexity is a most useful concept. In fact, in the basic and classical paper [1], Zadeh paid special attention to the investigation of the convex fuzzy sets which covers nearly the second half of the space of the paper. Following the seminal work of Zadeh on the definition of a convex fuzzy set, Ammar and Metz defined another type of convex fuzzy sets in [2]. A lot of scholars have discussed various aspects of the theory and applications of fuzzy convex analysis. In [3], by use of the relations between fuzzy points and fuzzy sets, Yuan and Lee gave some generalizations of convex fuzzy set. In [4], Wu and Cheng introduced and studied the concept of semi-strictly convex fuzzy sets, and presented the important connections between these convex fuzzy sets. In order to solve the open problem in fuzzy analysis that we proposed in [5], we introduced some new and more general definitions in the area of fuzzy starshapedness, and developed several theorems on the shadows of starshaped fuzzy sets [6], which generalize the important results obtained by Liu [7]. The