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Optimal stabilization of linear stochastic systems
Having introduced and motivated our concepts of stochastic control systems in the previous chapter we now turn to optimal and suboptimal...
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Linear map**s on ordered vector spaces
Before we can start to analyze the generalized Riccati operators derived in the previous chapter, we have to deal with generalized Lyapunov operators...
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Modeling of Fuzzy Data
Fuzzy data are imprecise data obtained from measurements, perception or by interviewing people. Typically, those data are expressed in linguistic...
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Set-valued Data
Since fuzzy sets are generalizations of ordinary sets, we present in this Chapter the essentials of random set theory for statistics. This material...
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Tests of Hypothesis: Means
In many expositions of fuzzy methods, fuzzy techniques are described as an alternative to a more traditional statistical approach. In this chapter,...
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Fuzzy Time Series Analysis and Forecasting
The problem of system modeling and identification has attracted considerable attention during the past decades mostly because of a large number of...
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Fuzzy Statistical Analysis and Estimation
In social science research, many decisions, evaluations, or purposes of evaluations are done by surveys or questionnaires to seek for people’s...
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Aspects of stochastic control theory
In the present chapter, we introduce linear stochastic control systems and the corresponding notions of stability, stabilizability and detectability....
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Aspects of Statistical Inference
With the background in previous chapters, problems of statistical inference with fuzzy data should be somewhat straightforward in principle! By that...
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Convergence of Random Fuzzy Sets
As in Chapter 5, we view random fuzzy sets as generalizations of random closed sets on R d , or more generally on...
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Random Fuzzy Sets
Statistical models for observations which are numbers or vectors are random variables and random vectors, respectively. Similarly, if the...
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Introduction
First like fuzzy logics are logics with fuzzy concepts, by fuzzy statistics we mean statistics with fuzzy data. Data are fuzzy when they are...
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Hermitian matrices and Schur complements
Throughout the text, $\mathbb{K}$ denotes either the field of real or the...
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Newton’s method
This chapter contains some of our main results. It largely follows the presentation in [49]. Our object is to tackle rational matrix equations of the...
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Solution of the Riccati equation
In Chapter 2 we have discussed various optimal and worst-case stabilization problems for linear stochastic control systems and reformulated them in...
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Toward Scalable Empirical Dynamic Modeling
Empirical Dynamic Modeling (EDM) is an emerging non-linear time series analysis framework that allows prediction and analysis of non-linear dynamical...
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Correlations, Shapes, and Fragmentations of Ultracold Matter
This 2022 report summarizes our activities at the HLRS facilities (Hawk) in the framework of the multiconfigurational time-dependent Hartree for...
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Bulk Features of the Quark Gluon Plasma at Finite Density
Pressure, energy density, entropy density and baryon number are the basic bulk features of quark gluon plasma (QGP), the deconfined phase of Quantum...
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Favorable-Pressure-Gradient Influence on Supersonic Film Cooling with Turbulent Main Flow
Cooling of a hot supersonic turbulent boundary-layer flow by wall-parallel blowing of a high-heat-capacity gas through a backward-facing step is an...
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Polaron Formation Dynamics in Lithium Niobate from Massively Parallel ab-initio Simulations
Polarons influence decisively the performance of lithium niobate for optical applications. In this project, the formation of (defect) bound polarons...