Convexity and level sets for interval-valued fuzzy sets

Abstract Convexity is a deeply studied concept since it very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity required as well and some important applications can be found fuzzy optimization, particular sets. In this paper have extended notion for interval-valued sets order to able cover wider area imprecision. We show its interesting properties, study preservation under intersection cutworthy property. Finally, applied decision-making problems.