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Fuzzy Discrete Structures 2000 ed. [Kietas viršelis]

  • Formatas: Hardback, 266 pages, aukštis x plotis: 235x155 mm, weight: 1270 g, XIV, 266 p., 1 Hardback
  • Serija: Studies in Fuzziness and Soft Computing 58
  • Išleidimo metai: 04-Oct-2000
  • Leidėjas: Physica-Verlag GmbH & Co
  • ISBN-10: 3790813354
  • ISBN-13: 9783790813357
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 266 pages, aukštis x plotis: 235x155 mm, weight: 1270 g, XIV, 266 p., 1 Hardback
  • Serija: Studies in Fuzziness and Soft Computing 58
  • Išleidimo metai: 04-Oct-2000
  • Leidėjas: Physica-Verlag GmbH & Co
  • ISBN-10: 3790813354
  • ISBN-13: 9783790813357
Kitos knygos pagal šią temą:
This ambitious exposition by Malik and Mordeson on the fuzzification of discrete structures not only supplies a solid basic text on this key topic, but also serves as a viable tool for learning basic fuzzy set concepts "from the ground up" due to its unusual lucidity of exposition. While the entire presentation of this book is in a completely traditional setting, with all propositions and theorems provided totally rigorous proofs, the readability of the presentation is not compromised in any way; in fact, the many ex­ cellently chosen examples illustrate the often tricky concepts the authors address. The book's specific topics - including fuzzy versions of decision trees, networks, graphs, automata, etc. - are so well presented, that it is clear that even those researchers not primarily interested in these topics will, after a cursory reading, choose to return to a more in-depth viewing of its pages. Naturally, when I come across such a well-written book, I not only think of how much better I could have written my co-authored monographs, but naturally, how this work, as distant as it seems to be from my own area of interest, could nevertheless connect with such. Before presenting the briefest of some ideas in this direction, let me state that my interest in fuzzy set theory (FST) has been, since about 1975, in connecting aspects of FST directly with corresponding probability concepts. One chief vehicle in carrying this out involves the concept of random sets.
Foreword vii
Preface xi
Fuzzy Logic Functions
1(40)
Sets
1(1)
Relations
2(3)
Functions
5(2)
Fuzzy Sets
7(1)
Semigroups
8(4)
Fuzzy Logic
12(4)
Fuzzy Functions and Decomposition
16(17)
Solution of Fuzzy Logic Inequalities
33(7)
References
40(1)
Decision Trees
41(16)
Decision Trees
41(3)
Fuzzy Decision Tree Algorithms
44(9)
Analysis of the BBB Algorithm
53(2)
References
55(2)
Networks
57(50)
Network Models
57(2)
A Maximum Flow Algorithm
59(6)
The Max Flow, Min Cut Theorem
65(2)
Maximum Flow in a Network with Fuzzy Arc Capacities
67(7)
The Maximum Flow with Integer Values
74(2)
Integer Flows in Network with Two-Sided Fuzzy Capacity Constraints
76(7)
Real-Valued Flows in a Network with Fuzzy Arc Capacities
83(8)
Petri Nets
91(4)
Fuzzy Petri Nets for Rule-Based Decisionmaking
95(8)
References
103(4)
Fuzzy Graphs and Shortest Paths
107(32)
Fuzzy Shortest Paths
107(9)
Analysis of the Fuzzy Path Models
116(4)
On Valuation and Optimization Problems
120(14)
References
134(5)
Fuzzy Machines, Languages, and Grammars
139(58)
Max-Product Machines
139(6)
Irreducibility and Minimality
145(3)
On Reductions of Maximin Machines
148(17)
Context-Free Max-Product Grammars
165(3)
Context-Free Fuzzy Languages
168(5)
Deterministic Acceptors of Regular Fuzzy Languages
173(6)
Fuzzy Languages on a Free Monoid
179(3)
Algebraic Character and Properties of F-Regular Languages
182(13)
Refernces
195(2)
Algebraic Fuzzy Automata
197(50)
Semigroups of Fuzzy Finite State Machines
197(4)
Homomorphisms
201(2)
Admissible Relations
203(2)
Fuzzy Transformation Semigroups
205(4)
Submachines
209(4)
Retrievability, Separability and Connectivity
213(3)
Decomposition of Fuzzy Finite State Machines
216(3)
Admissible Partitions
219(8)
On Fuzzy Recognizers
227(12)
Minimal Fuzzy Recognizers
239(6)
References
245(2)
Appendix 247(8)
BBB
247(8)
Index 255(6)
List of Symbols 261