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In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor "and", sup for "or") to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi fying algebra. This led to my 1971 paper "Fuzzy groups", which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley.
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Contenuti
1 Fuzzy Subsets.- 1.1 Fuzzy Relations.- 1.2 Operations on Fuzzy Relations.- 1.3 Reflexivity, Symmetry and Transitivity.- 1.4 Pattern Classification Based on Fuzzy Relations.- 1.5 Advanced Topics on Fuzzy Relations.- 1.6 References.- 2 Fuzzy Graphs.- 2.1 Paths and Connectedness.- 2.2 Clusters.- 2.3 Cluster Analysis and Modeling of Information Networks.- 2.4 Connectivity in Fuzzy Graphs.- 2.5 Application to Cluster Analysis.- 2.6 Operations on Fuzzy Graphs.- 2.7 Fuzzy Intersection Equations.- 2.8 Fuzzy Graphs in Database Theory.- 2.9 References.- 3 Fuzzy Topological Spaces.- 3.1 Topological Spaces.- 3.2 Metric Spaces and Normed Linear Spaces.- 3.3 Fuzzy Topological Spaces.- 3.4 Sequences of Fuzzy Subsets.- 3.5 F-Continuous Functions.- 3.6 Compact Fuzzy Spaces.- 3.7 Iterated Fuzzy Subset Systems.- 3.8 Chaotic Iterations of Fuzzy Subsets.- 3.9 Starshaped Fuzzy Subsets.- 3.10 References.- 4 Fuzzy Digital Topology.- 4.1 Introduction.- 4.2 Crisp Digital Topology.- 4.3 Fuzzy Connectedness.- 4.4 Fuzzy Components.- 4.5 Fuzzy Surroundedness.- 4.6 Components, Holes, and Surroundedness.- 4.7 Convexity.- 4.8 The Sup Projection.- 4.9 The Integral Projection.- 4.10 Fuzzy Digital Convexity.- 4.11 On Connectivity Properties of Grayscale Pictures.- 4.12 References.- 5 Fuzzy Geometry.- 5.1 Introduction.- 5.2 The Area and Perimeter of a Fuzzy Subset.- 5.3 The Height, Width and Diameter of a Fuzzy Subset.- 5.4 Distances Between Fuzzy Subsets.- 5.5 Fuzzy Rectangles.- 5.6 A Fuzzy Medial Axis Transformation Based on Fuzzy Disks.- 5.7 Fuzzy Triangles.- 5.8 Degree of Adjacency or Surroundedness.- 5.9 Image Enhancement and Thresholding Using Fuzzy Compactness.- 5.10 Fuzzy Plane Geometry: Points and Lines.- 5.11 Fuzzy Plane Geometry: Circles and Polygons.- 5.12 Fuzzy Plane Projective Geometry.- 5.13 A Modified Hausdorff Distance Between Fuzzy Subsets..- 5.14 References.- 6 Fuzzy Abstract Algebra.- 6.1 Crisp Algebraic Structures.- 6.2 Fuzzy Substructures of Algebraic Structures.- 6.3 Fuzzy Submonoids and Automata Theory.- 6.4 Fuzzy Subgroups, Pattern Recognition and Coding Theory.- 6.5 Free Fuzzy Monoids and Coding Theory.- 6.6 Formal Power Series, Regular Fuzzy Languages, and Fuzzy Automata.- 6.7 Nonlinear Systems of Equations of Fuzzy Singletons.- 6.8 Localized Fuzzy Subrings.- 6.9 Local Examination of Fuzzy Intersection Equations.- 6.10 More on Coding Theory.- 6.11 Other Applications.- 6.12 References.- List of Figures.- List of Tables.- List of Symbols.
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- EditorePhysica Verlag
- Data di pubblicazione2001
- ISBN 10 3790814202
- ISBN 13 9783790814200
- RilegaturaCopertina rigida
- LinguaInglese
- Numero di pagine310
- Contatto del produttorenon disponibile
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Fuzzy Mathematics: An Introduction for Engineers and Scientists.
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Heidelberg, Germany Physica-Verlag, 2001
ISBN 10: 3790814202
ISBN 13: 9783790814200
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Gebunden. Condizione: Gut. Gebraucht - Gut Zustand: Gut, Mängelexemplar, XIV, 310 pp. 30 figs., 9 tabs. About this book: The book deals with fuzzy graph theory, fuzzy topology, fuzzy geometry, and fuzzy abstract algebra. It presents the concepts of fuzzy mathematics with applications to engineering, computer science, and mathematics. In this second edition the chapter on geometry is expanded and contains results on the degree of adjacency of two regions and the degree of surroundedness of a region by another. Applications to digital polygons and image description are also given. Furthermore, the new edition includes results on image enhancement and thresholding by optimization of fuzzy compactness as well as results concerning a Hausdorff distance between fuzzy subsets. The most current work on the solution of nonlinear systems of fuzzy intersection equations of fuzzy singletons has been added to the chapter on algebra. The book is written with engineers and computer scientists in mind, but it can also serve as a research guide to interested mathematicians as it involves current results. Written for researchers. Codice articolo 17295
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Fuzzy Mathematics : An Introduction for Engineers and Scientists
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Fuzzy Mathematics
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. With numerous examplesPresentation of concepts of fuzzy mathematics with applications to engineering, computer science, and mathematicsIn the mid-1960 s I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (a. Codice articolo 5310371
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Fuzzy Mathematics: An Introduction for Engineers and Scientists: 20 (Studies in Fuzziness and Soft Computing, 20)
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Condizione: Good. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,650grams, ISBN:9783790814200. Codice articolo 8247734
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ISBN 10: 3790814202
ISBN 13: 9783790814200
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor 'and', sup for 'or') to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi fying algebra. This led to my 1971 paper 'Fuzzy groups', which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley. 314 pp. Englisch. Codice articolo 9783790814200
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Fuzzy Mathematics : An Introduction for Engineers and Scientists
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Buch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor 'and', sup for 'or') to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi fying algebra. This led to my 1971 paper 'Fuzzy groups', which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley. Codice articolo 9783790814200
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Fuzzy Mathematics
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Buch. Condizione: Neu. Neuware -In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor 'and', sup for 'or') to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi fying algebra. This led to my 1971 paper 'Fuzzy groups', which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley.Physica Verlag, Tiergartenstr. 17, 69121 Heidelberg 328 pp. Englisch. Codice articolo 9783790814200
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Fuzzy Mathematics: An Introduction for Engineers and Scientists
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Fuzzy Mathematics: An Introduction for Engineers and Scientists
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Fuzzy Mathematics: An Introduction for Engineers and Scientists
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