Convexity Invariance of Fuzzy Sets under the Extension Principles

Abstract EN

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.