Answers to some questions about Zadeh's extension on metric spaces

Abstract

This paper shows that there exists a contraction whose Zadeh's extension is not a contraction under the Skorokhod metric, answering negatively Problems 5.8 and 5.12 posted in [Jardón, Sánchez, and Sanchis, Some questions about Zadeh's extension on metric spaces, Fuzzy Sets and Systems, 2018].