Representation of maxitive measures: an overview

Idempotent integration is an analogue of Lebesgue integration where $\sigma$-maxitive measures replace $\sigma$-additive measures. In addition to reviewing and unifying several Radon--Nikodym like theorems proven in the literature for the idempotent integral, we also prove new results of the same kind.Comment: 40 page

Commutative POVMs and Fuzzy Observables

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.Comment: Contribution to the Pekka Lahti Festschrif

The structure of classical extensions of quantum probability theory

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed

Generalized I of strongly Lacunary of x2 over p-metric spaces defined by Musielak Orlicz function

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of x2 sequence spaces over p-metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform Δ2 condition, and we also discuss some topological properties of the resulting spaces of x2 with respect to ideal structures which is solid and monotone. Hence, given an example of the space x2 this is not solid and not monotone. This theory is very useful for statistical convergence and also is applicable to rough convergence

A stochastic-variational model for soft Mumford-Shah segmentation

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte-Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. We show that soft segmentation leads to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis, and computational implementation of the new model are explored in detail, and numerical examples of synthetic and natural images are presented.Comment: 22 page

RISE-Based Integrated Motion Control of Autonomous Ground Vehicles With Asymptotic Prescribed Performance

This article investigates the integrated lane-keeping and roll control for autonomous ground vehicles (AGVs) considering the transient performance and system disturbances. The robust integral of the sign of error (RISE) control strategy is proposed to achieve the lane-keeping control purpose with rollover prevention, by guaranteeing the asymptotic stability of the closed-loop system, attenuating systematic disturbances, and maintaining the controlled states within the prescribed performance boundaries. Three contributions have been made in this article: 1) a new prescribed performance function (PPF) that does not require accurate initial errors is proposed to guarantee the tracking errors restricted within the predefined asymptotic boundaries; 2) a modified neural network (NN) estimator which requires fewer adaptively updated parameters is proposed to approximate the unknown vertical dynamics; and 3) the improved RISE control based on PPF is proposed to achieve the integrated control objective, which analytically guarantees both the controller continuity and closed-loop system asymptotic stability by integrating the signum error function. The overall system stability is proved with the Lyapunov function. The controller effectiveness and robustness are finally verified by comparative simulations using two representative driving maneuvers, based on the high-fidelity CarSim-Simulink simulation

Vector valued information measures and integration with respect to fuzzy vector capacities

[EN] Integration with respect to vector-valued fuzzy measures is used to define and study information measuring tools. Motivated by some current developments in Information Science, we apply the integration of scalar functions with respect to vector-valued fuzzy measures, also called vector capacities. Bartle-Dunford-Schwartz integration (for the additive case) and Choquet type integration (for the non-additive case) are considered, showing that these formalisms can be used to define and develop vector-valued impact measures. Examples related to existing bibliometric tools as well as to new measuring indices are given.The authors would like to thank both Prof. Dr. Olvido Delgado and the referee for their valuable comments and suggestions which helped to prepare the manuscript. The first author gratefully acknowledges the support of the Ministerio de Economia, Industria y Competitividad (Spain) under project MTM2016-77054-C2-1-P.Sánchez Pérez, EA.; Szwedek, R. (2019). Vector valued information measures and integration with respect to fuzzy vector capacities. Fuzzy Sets and Systems. 355:1-25. https://doi.org/10.1016/j.fss.2018.05.004S12535