The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals. Those integrals admit a discrete bipolar formulation, useful in those situations where the underlying scale is bipolar. In this paper we propose the concept of discrete bipolar universal integral, in order to provide a common framework for bipolar discrete integrals, including as specia...

In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect a not necessarily additive set function. Based on their properties, quantitative estimate for nonlinear Korovkin approximation theorem associated Bernstein-Kantorovich-Choquet is proved. The paper also includes large generalization H\"{o}lder's inequality within framework mono...

The aim of this paper is to investigate the cone of non-negative, radial, positivedefinite functions in the set of continuous functions on R. Elements of this cone admit a Choquet integral representation in terms of the extremals. The main feature of this article is to characterize some large classes of such extremals. In particular, we show that there many other extremals than the gaussians, t...

A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical nonnegative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on ...

Establishing a good algorithm for predicting temperature of thermostable proteins is an important issue. In this study, a new thermostable proteins prediction method by using Hurst exponent and Choquet integral regression model with respect to maximized L-measure is proposed. The main idea of this method is to integrate the physicochemical properties, long term memory property and Choquet integ...

The assertion in question comes from the short final section in the Theory of Capacities of Choquet 1953/54, in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this formation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and the counterpart with superadditive. His treatmen...

In this paper the Portfolio Choice problem is studied under ambiguity, formalized by means of the Choquet Expected Utility. Agents are supposed to be Choquet Expected Utility maximizers and are split into two categories: optimists, who hold a concave capacity, and pessimists, who hold a convex one. Portfolio inertia is defined and analyzed. Necessary and sufficient conditions are established be...

Choquet integral with respect to fuzzy measure is a generalization of weighted arithmetic mean aggregation operator. It allows taking into account the phenomenon of dependence between criteria. Due to this it is possible to reflect the expert knowledge more accurately without making the model simplification which is the assumption of independence of the aggregation criteria. The problems of Cho...

The paper discusses about the Choquet Fuzzy Integral (CFI) based identification and control of a Real Time Dynamical System. The plant is modeled using Choquet fuzzy Integral based Neural Network with Gradient Descent as learning algorithm. This model is used for designing and simulating CFI based controller. Then this designed controller is implemented on real time system through MATLAB. Final...