The Sugeno fuzzy integral of concave functions

Abstract

<span class="fontstyle0">The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membership<br />value of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is present<br />has been well established. Most of the integral inequalities studied in the fuzzy integration context normally consider<br />conditions such as monotonicity or comonotonicity. In this paper, we are trying to extend the fuzzy integrals to the<br />concept of concavity. It is shown that the Hermite-Hadamard integral inequality for concave functions is not satisfied in<br />the case of fuzzy integrals. We propose upper and lower bounds on the fuzzy integral of concave functions. We present<br />a geometric interpretation and some examples in the framework of the Lebesgue measure to illustrate the results.</span> <br /><br />