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For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given.

In this article, we elaborate on the use of the Sugeno integral in the context of machine learning. More specifically, we propose a method for binary classification, in which the Sugeno integral is used as an aggregation function that combines several local evaluations of an instance, pertaining to different features, or measurements, into a single global evaluation. Due to the specific nature of the Sugeno integral, this approach is especially suitable for learning from ordinal data, i.e., when measurements are taken from ordinal scales. This is a topic that has not received much attention in machine learning so far. The core of the learning problem itself consists of identifying the capacity underlying the Sugeno integral. To tackle this problem, we develop an algorithm based on linear programming. The algorithm also includes a suitable technique for transforming the original feature values into local evaluations (local utility scores), as well as a method for tuning a threshold on the global evaluation. To control the flexibility of the classifier and mitigate the problem of overfitting the training data, we generalize our approach toward $k$ -maxitive capacities, where $k$ plays the role of a hyperparameter of the learner. We present experimental studies, in which we compare our method with competing approaches on several benchmark datasets. [ABSTRACT FROM AUTHOR]

The theory of non-additive measures and relevant nonlinear integrals has recently been developed as a new branch of mathematics with various applications in other sciences. In this area, pseudo-additive measures and pseudo-integrals play important roles as new extensions of measures and integrals. The aim of this paper is to prove Hölder type integral inequalities with different pseudo-operations. Several examples are given to show the inequalities in more tangible forms. [ABSTRACT FROM AUTHOR]

In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form. [ABSTRACT FROM AUTHOR]

Estimation of sediment mass carried by rivers is an important issue in Hydrological Sciences. The main purpose of this research was to find an appropriate method to compute sediment discharge. Some machine-learning approaches have been used to forecast river-suspended sediments, correctly. One of the most effective and traditional approaches for forecasting events is to use artificial neural networks (ANNs). So, we are going to improve the performance of ANNs in estimation of suspended sediments, upon a data of Baba Aman basin in Iran. We first apply a typical neural network and obtain the root-mean-square-error ofand the correlation coefficient of. Then, to improve the prediction ability of ANNs, we hybridize this method with cuckoo optimization algorithm (COA). Combination of ANNs with COA causes reduction in root-mean-square-error to, increasing in correlation coefficient toand also proposing a better model. [ABSTRACT FROM AUTHOR]