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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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On the Prebiotic Synthesis of Nucleobases, Nucleotides, Oligonucleotides, Pre-RNA and Pre-DNA Molecules
All the strategies for the prebiotic syntheses of RNA and DNA assume the adequate availability of the presumptive precursors such as purine and...
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Biologically Produced Sulfur
Sulfur compound oxidizing bacteria Sulfur compound oxidizing bacteria produce sulfur as an intermediate in the...
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Application of Evolutionary Algorithms to Global Cluster Geometry Optimization
This contribution focuses upon the application of evolutionary algorithms to the nondeterministic polynomial hard problem of global cluster geometry...
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Liquid Sulfur
The molecular composition as well as the physical properties (including spectra) of liquid sulfur Liquid Sulfur...
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Speciation and Thermodynamics of Sulfur Vapor
Sulfur vapor Sulfur vapor at temperatures of between 200 and 1000 °C consists of all molecules with 2–10 atoms, some...
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Prediction of Crystal Structures Using Evolutionary Algorithms and Related Techniques
Methods, evolutionary and systematic search approaches, and applications of crystal structure prediction of closest-packed and framework materials...
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From the Prebiotic Synthesis of α-Amino Acids Towards a Primitive Translation Apparatus for the Synthesis of Peptides
The demonstration that ribosomal peptide synthesis is a ribozyme-catalyzed reaction does not establish that amino acids and peptides have been...
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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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Solid Sulfur Allotropes
Sulfur is the element with the largest number of solid allotropes. Most of these consist of unbranched cyclic molecules with ring sizes ranging from...
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Aqueous Sulfur Sols
Sulfur Sulfur sols are colloidal colloidal solutions of elemental sulfur or of...