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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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UCB Strategies in a Gaussian Two-Armed Bandit Problem
We consider the two-armed bandit problem in the application to batch data processing if there are two alternative processing methods with different a...
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Accelerated Stochastic Gradient Method with Applications to Consensus Problem in Markov-Varying Networks
Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse domains ranging from operations...
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How to Use Barriers and Symmetric Regularization of Lagrange Function in Analysis of Improper Nonlinear Programming Problems
In the note, we present a new approach to numerical analysis of improper mathematical programming problems based on ideas of symmetrically...
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Filtering Correction for Robotic Arms Multipurpose Regulators
The paper is devoted to the problem of compensating the external disturbances while stabilizing the robotic arm in the specified position by...
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Decision Analysis of Military Supply Chain Based on Stackelberg Game Model
The military supply chain assumes a paramount role in national security and defense infrastructure development, entailing substantial economic...