Order Relations, Convexities, and Jensen's Integral Inequalities in Interval and Fuzzy Spaces

Abstract

This study presents new interval and fuzzy versions of the Jensen's integral inequality, which extend the classical Jensen's integral inequality for real-valued functions, using Aumann and Kaleva integrals. The inequalities for interval-valued functions are interpreted through the preference order relations given by Ishibuchi and Tanaka, which are useful for dealing with interval optimization problems. The order relations adopted in the space of fuzzy intervals are extensions of those considered the interval spaces.