Convexity of n-dimensional fuzzy number-valued functions and its applications

The aim of this study is to generalize convexity from vector-valued maps to n-dimensional fuzzy number-valued functions and to investigate some relations among the convexity and generalized convexity of n-dimensional fuzzy number-valued functions, which are based on a new ordering of n-dimensional fuzzy numbers proposed in this study. Furthermore, some criteria are obtained for the convexity and generalized convexity under the conditions of lower and upper semicontinuity, respectively. Finally, we study the local–global minimum properties of the convex fuzzy number-valued functions.