http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Mathematical Foundations of Fuzzy Sets Introduce yourself to the foundations of fuzzy logic with this easy-to-use guide Many fields studied are defined by imprecise information or high degrees of uncertainty. When this uncertainty derives from randomness, traditional probabilistic statistical methods are adequate to address it; more everyday forms of vagueness and imprecision, however, require the toolkit associated with 'fuzzy sets' and 'fuzzy logic'. Engineering and mathematical fields related to artificial intelligence, operations research and decision theory are now strongly driven by fuzzy set theory. Mathematical Foundations of Fuzzy Sets introduces readers to the theoretical background and practical techniques required to apply fuzzy logic to engineering and mathematical problems. It introduces the mathematical foundations of fuzzy sets as well as the current cutting edge of fuzzy-set operations and arithmetic, offering a rounded introduction to this essential field of applied mathematics. The result can be used either as a textbook or as an invaluable reference for working researchers and professionals. Mathematical Foundations of Fuzzy Sets offers thereader: Detailed coverage of set operations, fuzzification of crisp operations, and more Logical structure in which each chapter builds carefully on previous results Intuitive structure, divided into 'basic' and 'advanced' sections, to facilitate use in one- or two-semester courses Mathematical Foundations of Fuzzy Sets is essential for graduate students and academics in engineering and applied mathematics, particularly those doing work in artificial intelligence, decision theory, operations research, and related fields.
8.1.2.1 The Inner Product A˜⊛DT⋄B˜ -- 8.1.2.2 The Inner Product A˜⊛DT⋆B˜ -- 8.1.2.3 The Inner Product A˜⊛DT†B˜ -- 8.1.3 The Equivalences and Fuzziness -- 8.2 The Second Type of Inner Product -- 8.2.1 Using the Extension Principle -- 8.2.2 Using the Expression in the Decomposition Theorem -- 8.2.3 Comparison of Fuzziness -- Chapter 9 Gradual Elements and Gradual Sets -- 9.1 Gradual Elements and Gradual Sets -- 9.2 Fuzzification Using Gradual Numbers -- 9.3 Elements and Subsets of Fuzzy Intervals -- 9.4 Set Operations Using Gradual Elements -- 9.4.1 Complement Set -- 9.4.2 Intersection and Union -- 9.4.3 Associativity -- 9.4.4 Equivalence with the Conventional Situation -- 9.5 Arithmetics Using Gradual Numbers -- Chapter 10 Duality in Fuzzy Sets -- 10.1 Lower and Upper Level Sets -- 10.2 Dual Fuzzy Sets -- 10.3 Dual Extension Principle -- 10.4 Dual Arithmetics of Fuzzy Sets -- 10.5 Representation Theorem for Dual-Fuzzified Function -- Bibliography -- Mathematical Notations -- Index -- EULA.
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