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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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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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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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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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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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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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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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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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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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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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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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Lattice-Based Polynomial Commitments: Towards Asymptotic and Concrete Efficiency
Polynomial commitments schemes are a powerful tool that enables one party to commit to a polynomial p of degree d , and prove that the committed...
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Assessment of loss of life caused by dam failure based on fuzzy theory and hybrid random forest model
Dam failure may lead to significant casualties among downstream residents. Therefore, it is crucial to study a reliable method to quantitatively...
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Empirical likelihood change point detection in quantile regression models
Quantile regression is an extension of linear regression which estimates a conditional quantile of interest. In this paper, we propose an empirical...
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The Price of Active Security in Cryptographic Protocols
We construct the first actively-secure Multi-Party Computation (MPC) protocols with an arbitrary number of parties in the dishonest majority setting,...
