%0 Journal Article
%T Convexity Invariance of Fuzzy Sets under the Extension Principles
%A Dong Qiu
%A Weiquan Zhang
%J Journal of Function Spaces and Applications
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/849104
%X We discuss the convexity invariance of fuzzy sets under the extension principles. Particularly, we give a necessary and sufficient condition for a mapping to be an inverse *-convex transformation, and also obtain some sufficient conditions for a mapping to be an *-convex transformation. Two applications are given to illustrate the obtained results. Finally, we give some applications of the main results to the hyperstructure convexity invariance of type 2 fuzzy sets under hyperalgebra operations, and to the convexity invariance of fuzzy numbers under basic arithmetic operations.
%U http://www.hindawi.com/journals/jfsa/2012/849104/