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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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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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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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Wasserstein Distance
A fundamental problem in metric algebraic geometry is distance minimization.
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Condition Numbers
The concept of a condition number has its origin in numerical analysis. It measures how much the output value of a function we wish to evaluate can...
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Critical Equations
The following optimization problem arises in many applications, and we shall revisit it again and again throughout this book.
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Reach and Offset
In this chapter, we study the medial axis, bottlenecks, and offset hypersurfaces. These notions are intuitive and important for many applications....
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Assessing the Potential of Gene Tree Parsimony for Microbial Phylogenomics
A key challenge in microbial phylogenomics is that microbial gene families are often affected by extensive horizontal gene transfer (HGT). As a...
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Evidence of Increased Adaptation of Omicron SARS-CoV-2 Codons to Humans
Viruses are highly dependent on their hosts to carry out cellular mechanisms and cause productive infection. Thus, they undergo extensive adaptations...
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Revisiting the Effects of MDR1 Variants Using Computational Approaches
P-glycoprotein, encoded by the MDR1 gene, is an ATP-dependent pump that exports various substances out of cells. Its overexpression is related to...
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Maximum Alternating Balanced Cycle Decomposition and Applications in Sorting by Intergenic Operations Problems
In the literature on genome rearrangement, several approaches use different structures to improve the results of genome rearrangement problems. In...
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Gene Tree Parsimony in the Presence of Gene Duplication, Loss, and Incomplete Lineage Sorting
Inferring species trees from multi-locus data needs to account for gene tree discordance due to various biological processes, including incomplete...
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From moving masses to bending spaces: an excursion in metric geometry
Welcome to the Springer Math Podcast. In this month’s podcast, Camillo De Lellis, a researcher at the Institute for Advanced Study in Princeton,...
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Matrix Algebra
The need to understand matrix algebra in the context of underlying applications is paramount. Rank one projections are the building tools and they...