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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... -
Modeling of Fuzzy Data
Fuzzy data are imprecise data obtained from measurements, perception or by interviewing people. Typically, those data are expressed in linguistic... -
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... -
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,... -
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... -
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... -
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... -
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... -
Biologically Produced Sulfur
Sulfur compound oxidizing bacteria Sulfur compound oxidizing bacteria produce sulfur as an intermediate in the... -
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... -
Liquid Sulfur
The molecular composition as well as the physical properties (including spectra) of liquid sulfur Liquid Sulfur... -
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... -
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... -
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... -
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... -
Random Fuzzy Sets
Statistical models for observations which are numbers or vectors are random variables and random vectors, respectively. Similarly, if the... -
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... -
Aspects of stochastic control theory
In the present chapter, we introduce linear stochastic control systems and the corresponding notions of stability, stabilizability and detectability.... -
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... -
Aqueous Sulfur Sols
Sulfur Sulfur sols are colloidal colloidal solutions of elemental sulfur or of...