On some advanced type inequalities for Sugeno integral and T-(S-)evaluators

Keywords: Nonadditive measure Sugeno integral Comonotone functions Chebyshev's inequality Minkowski's inequality Hölder's inequality a b s t r a c t In this paper strengthened versions of the Minkowski, Chebyshev, Jensen and Hölder inequalities for Sugeno integral and T-(S-)evaluators are given. As an application, some equivalent forms and some particular results have been established. The theory of nonadditive measures and integrals was a powerful tool in several fields [6,13]. Sugeno integral [29] is a useful tool in several theoretical and applied statistics. For instance, in decision theory, the Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility [7]. In most decision-making problems a global preference functional is used to help the decision-maker make the ''best'' decision. Of course, the choice of such a global preference functional is dictated by the behavior of the decision-maker but also by the nature of the available information, hence by the scale type on which it is represented. The use of the Sugeno integral can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making [8]. Su-geno integral is analogous to Lebesgue integral which has been studied by many authors, including Pap [11,23], Ralescu and Adams [24] and Wang and Klir [30], among others. Integral inequalities play important roles in classical probability and measure theory. These are useful tools in several theoretical and applied fields. For instance, integral inequalities play a role in the development of a time scales calculus [22]. In general, any integral inequality can be a very powerful tool for applications. In particular, when we think of an integral operator as a predictive tool then an integral inequality can be very important in measuring and dimensioning such process. The study of inequalities for Sugeno integral was initiated by Román-Flores et al. [9,25–28], and then followed by the