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“…Hugh Woodin is a leading figure in modern set theory, having made many deep and lasting contributions to the field, in particular to descriptive set theory and large cardinals. …”
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“…This special book is dedicated to the memory of Professor Zdzisław Pawlak, the father of rough set theory, in order to commemorate both the 10th anniversary of his passing and 35 years of rough set theory. …”
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“…There are many mathematical formal models have been proposed to handle conflict situations and one of the most popular is rough set theory. With the ability to handle vagueness from the conflict data set, rough set theory has been successfully used. …”
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“…Two examples of ‘decision making problems’ with complete solutions are presented out of which one example will show the dominance of the application potential of intuitionistic fuzzy set theory over fuzzy set theory, and the other will show the converse i.e. the dominance of the application potential of fuzzy set theory over intuitionistic fuzzy set theory in some cases. …”
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“…Syntactic models of the set theory.…”
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“…Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. …”
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“…Regional concepts and regionalization, spatial preference-utility-choice structures, spatial optimization with single and multiple objectives, dynamic spatial systems and their controls are analyzed in sequence.The analytical framework is based on fuzzy set theory. Basic concepts of fuzzy set theory are first discussed. …”
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“…This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). …”
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“…Contents of this issue: Workshops on SPM themes; Second workshop on Coverings, Selections and Games in Topology (SPM05); Analysis and Descriptive Set Theory Workshop; Descriptive set theory: Effective methods, equivalence relations; Analysis: typical functions, level sets structure; Organizational and additional details; Research announcements; Cardinal restrictions on some homogeneous compacta; Filters: Topological congruence relations on groups; Inverse Limits and Function Algebras; Ultrafilters and partial products of infinite cyclic groups; More on regular reduced products; Consistency of ``the ideal of null restricted to some A is kappa-complete not kappa^+-complete, kappa weakly inaccessible and cov(M)=aleph_1''; On removing one point from a compact space; Problems from earlier issues.…”
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“…This book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. …”
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“…The book starts with a presentation of naive set theory, the theory of sets that mathematicians use on a daily basis. …”
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“…Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. …”
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“…Attribute reduction as an important preprocessing step for data mining, and has become a hot research topic in rough set theory. Neighborhood rough set theory can overcome the shortcoming that classical rough set theory may lose some useful information in the process of discretization for continuous-valued data sets. …”
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“…Salient Features Mathematical logic, fundamental concepts, proofs and mathematical induction (Chapter 1) Set theory, fundamental concepts, theorems, proofs, Venn diagrams, product of sets, application of set theory and fundamental products (Chapter 2) An introduction to binary relations and concepts, graphs, arrow diagrams, relation matrix, composition of relations, types of relation, partial order relations, total order relation, closure of relations, poset, equivalence classes and partitions. …”
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