The subject of the book could be described as fuzzy discrete structures. The book deals with fuzzy logic, fuzzy switching functions, fuzzy decision trees, fuzzy networks, fuzzy petri nets, fuzzy path problems, fuzzy automata, and fuzzy languages. The notion of a fuzzy decision tree and a branch-bound-backtrack algorithm is presented. In the Appendix, this algorithm is described in C++. Network flow problems with various capacities are examined. Fuzzy shortest path techniques are presented whereby there is an actual path which corresponds to the fuzzy shortest path. Recent results on fuzzy automata and fuzzy languages are also presented.
Table of Contents
Foreword.- Preface.- Fuzzy Logic Functions: Sets. Relations. Functions. Fuzzy Sets. Semigroups. Fuzzy Logic. Fuzzy Functions and Decomposition. Solution of Fuzzy Logic Inequalities. References.- Decision Trees: Decision Trees. Fuzzy Decision Tree Algorithms. Analysis of the BBB Algorithm. References.- Networks: Network Models. A Maximum Flow Algorithm. The Max Flow, Min Cut Theorem. Maximum Flow in a Network with Fuzzy Arc Capacities. The Maximum Flow with Integer Values. Integer Flows in Network with Two-Sided Fuzzy Capacities Constraints. Real-Valued Flows in a Network with Fuzzy Arc Capacities. Petri Nets. Fuzzy Petri Nets for Rule-Based Decisionmaking. References. - Fuzzy Graphs and Shortest Paths.- Fuzzy Shortest Paths. Analysis of the Fuzzy Path Models. On Valuation and Optimization Problems. References.- Fuzzy Machines, Languages, and Grammars: Max-Product Machines. Irreducibility and Minimality. On Reductions of Maximin Machines. Context-Free Max-Product Grammars. Context-Free Fuzzy Languages. Deterministic Acceptors of Regular Fuzzy Languages. Fuzzy Languages on a Free Monoid. Algebraic Character and Properties of F-Regular Languages. References.- Algebraic Fuzzy Automata. Semigroups of Fuzzy Finite State Machines. Homomorphisms. Admissible Relations. Fuzzy Transformation Semigroups. Submachines. Retrievability, Separability and Connectivity. Decomposition of Fuzzy Finite State Machines. Admissible Partitions. On Fuzzy Recognizers. Minimal Fuzzy Recognizers. References.- Appendix.- Index.- List of Symbols.