“…Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. …”
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“…Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. …”
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“…Number Systems The Real Numbers The Complex Numbers Sequences Convergence of Sequences Subsequences Limsup and Liminf Some Special Sequences Series of Numbers Convergence of Series Elementary Convergence Tests Advanced Convergence Tests Some Special Series Operations on Series Basic Topology Open and Closed Sets Further Properties of Open and Closed Sets Compact Sets The Cantor SetConnected and Disconnected Sets Perfect Sets Limits and Continuity of Functions Basic Properties of the Limit of a Function Continuous Functions Topological Properties and Continuity Classifying Discontinuities and Monotonicity Differentiation of Functions The Concept of Derivative The Mean Value Theorem and Applications More on the Theory of Differentiation The Integral Partitions and the Concept of Integral Properties of the Riemann IntegralSequences and Series of Functions Convergence of a Sequence of Functions More on Uniform Convergence Series of Functions The Weierstrass Approximation Theorem Elementary Transcendental Functions Power Series More on Power Series: Convergence Issues The Exponential and Trigonometric Functions Logarithms and Powers of Real Numbers Appendix I: Elementary Number Systems Appendix II: Logic and Set Theory Table of Notation Glossary Bibliography Index.…”
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“…It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. …”
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“…Rough Set TheoryBasic concepts and properties of rough sets Rough Membership Rough Intervals Rough FunctionApplications of Rough SetsMultiple Objective Rough Decision Making Reverse Logistics Problem with Rough Interval Parameters MODM based Rough Approximation for Feasible RegionEVRMCCRMDCRM Reverse Logistics Network Design Problem of Suji Renewable Resource MarketBilevel Multiple Objective Rough Decision Making Hierarchical Supply Chain Planning Problem with Rough Interval Parameters Bilevel Decision Making ModelBL-EVRM BL-CCRMBL-DCRMApplication to Supply Chain Planning of Mianyang Co., LtdStochastic Multiple Objective Rough Decision Multi-Objective Resource-Constrained Project Scheduling UnderRough Random EnvironmentRandom Variable Stochastic EVRM Stochastic CCRM Stochastic DCRM Multi-Objective rc-PSP/mM/Ro-Ra for Longtan Hydropower StationFuzzy Multiple Objective Rough Decision Making Allocation Problem under Fuzzy Environment Fuzzy Variable Fu-EVRM Fu-CCRM Fu-DCRM Earth-Rock Work Allocation Problem.…”
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“…The book is entirely self-contained, with all necessary background in point set topology, model theory, "non"standard analysis, and set theory provided in full.…”
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“…Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. …”
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“…Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. …”
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“…The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. …”
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“…This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. …”
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“…The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.…”
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“…Some of these topics include: Mathematical and structural induction Set theory Combinatorics Functions, relations, and ordered sets Boolean algebra and Boolean functions Graph theory Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.…”
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“…Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.…”
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“…I quantify the impact of late-time halo mergers using excursion set theory, and argue that the associated uncertainty in the boost of energy injection is limited for the CMB, but can have serious consequences for late time probes (i.e. for the 21-cm signal). …”
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“…In the year (1879–1884), George Cantor coined few problems and consequences in the field of set theory. One of them was the Cantor ternary set as a classical example of fractals. …”
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“…Compared to other methods, the concept of multiple vehicle cooperative localization with spatial registration is first proposed under Random Finite Set Theory. In addition, the proposed solution also addresses the challenges for multiple vehicle cooperative localization, e.g., the communication bandwidth issue and data association uncertainty. …”
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“…In this paper, we initiate the study of soft congruence relations by using the soft set theory. The notions of soft quotient rings, generalized soft ideals and generalized soft quotient rings, are introduced, and several related properties are investigated. …”
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“…Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. …”
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“…Classical rough set theory is a technique of granular computing for handling the uncertainty, vagueness, and granularity in information systems. …”
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“…In fuzzy set theory, it is well known that a triangular fuzzy number can be uniquely determined through its position and entropies. …”
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