“…Fraenkel was a world-renowned mathematician in pre–Second World War Germany, whose work on set theory was fundamental to the development of modern mathematics. …”
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“…The (occasional) reliance on extensions of basic set theory is clearly laid out. The book concludes with a set of open problems.…”
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“…The topic is essentially interdisciplinary and will be of interest to mathematicians working in geometric functional analysis, topological and ergodic dynamics, Ramsey theory, logic and descriptive set theory, representation theory, topological groups, and operator algebras.…”
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“…Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. …”
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“…We screen highly discriminative genes and gene pairs to create simple prediction models involved in single genes or gene pairs on the basis of soft computing approach and rough set theory. Accurate cancerous prediction is obtained when we apply the simple prediction models for four cancerous gene expression datasets: CNS tumor, colon tumor, lung cancer and DLBCL. …”
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“…This class includes the recently introduced “games in phenotype space” and “evolutionary set theory.” There can be local interactions for determining the relative fitness of individuals, but we require global updating, which means all individuals compete uniformly for reproduction. …”
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“…According to graph-set theory the descriptor on the binary level is C (2) (1)(8). …”
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“…In this paper, we propose a novel feature extraction algorithm called membership-degree preserving discriminant analysis (MPDA) based on the fisher criterion and fuzzy set theory for face recognition. In the proposed algorithm, the membership degree of each sample to particular classes is firstly calculated by the fuzzy k-nearest neighbor (FKNN) algorithm to characterize the similarity between each sample and class centers, and then the membership degree is incorporated into the definition of the between-class scatter and the within-class scatter. …”
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“…In case of vagueness situation, fuzzy set theory is then incorporated onto the HDMSOW's. To determine the objective weight for each attribute, the fuzzy Shannon's entropy is considered. …”
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“…In this paper, the neighborhood hypergraph is presented, combining rough set theory and hypergraph. After that, a novel classification algorithm for imbalance data based on neighborhood hypergraph is developed, which is composed of three steps: initialization of hyperedge, classification of training data set, and substitution of hyperedge. …”
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“…Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue that it supports the opposing view, i.e., the widespread intuition “if you need a non-measurable function, it is physically irrelevant”.…”
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“…An event tree analysis method based on fuzzy set theory is proposed to calculate the dam failure probability. …”
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“…A stochastic model is required to capture functional promiscuity, redundant sequence motifs, dynamic interactions, or conformational heterogeneity, which facilitate the decision-making in regulatory processes, ranging from enzymes to membraneless cellular compartments. The fuzzy set theory offers a quantitative framework to address these problems. …”
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“…Rough random theory, generally applied to statistics, decision-making, and so on, is an extension of rough set theory and probability theory, in which a rough random variable is described as a random variable taking “rough variable” values. …”
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“…In this article, we propose an original matching procedure for multiple treatment frameworks based on partially ordered set theory (poset). In our proposal, called matching on poset‐based average rank for multiple treatments (MARMoT), poset theory is used to summarize individuals' confounders and the relative average rank is used to balance confounders and match individuals in different treatment groups. …”
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“…The aim of this paper was the assessment of the particular soft computing methods’ (e.g., Self-Organizing Maps, Rough Set Theory) usefulness for selecting a representative property model. …”
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“…Alfred Tarski (1901–1983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic, and universal algebra. …”
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“…Self-contained, with coverage of topology, measure theory, and integration, it offers a thorough elaboration of major theorems, notions, and constructions needed not only by mathematics students but also by students of statistics and probability, operations research, physics, and engineering.Structured logically and flexibly through the author''s many years of teaching experience, the material is presented in three main sections:Part 1, chapters 1through 3, covers the preliminaries of set theory and the fundamentals of metric spaces and topology. …”
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“…Chapter III presents the basic concepts and mathematical operations of fuzzy set theory with simple numerical examples in a easy-to-read and easy-to-follow manner. …”
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“…In light of this it is natural that fuzzy set theory has become a topic of intensive interest in many areas of geographical research and applications This volume, Fuzzy Modeling with Spatial Information for Geographic Problems, provides many stimulating examples of advances in geographical research based on approaches using fuzzy sets and related technologies.…”
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