06CS766 - Fuzzy Logic |
PART – A |
UNIT 1 |
INTRODUCTION, CLASSICAL SETS AND FUZZY SETS:
Background, Uncertainty and Imprecision, Statistics and Random Processes,
Uncertainty in Information, Fuzzy Sets and Membership, Chance versus
Ambiguity. Classical Sets - Operations on Classical Sets, Properties of
Classical (Crisp) Sets, Mapping of Classical Sets to Functions. Fuzzy Sets -
Fuzzy Set operations, Properties of Fuzzy Sets. Sets as Points in Hypercubes. |
UNIT 2 |
CLASSICAL RELATIONS AND FUZZY RELATIONS: Cartesian
Product, Crisp Relations - Cardinality of Crisp Relations, Operations on
Crisp Relations, Properties of Crisp Relations, Composition. Fuzzy Relations
- Cardinality of Fuzzy Relations, Operations on Fuzzy Relations, Properties
of Fuzzy Relations, Fuzzy Cartesian Product and Composition, Noninteractive
Fuzzy Sets. Tolerance and Equivalence Relations - Crisp
Equivalence Relation, Crisp Tolerance Relation, Fuzzy Tolerance and
Equivalence Relations. Value Assignments - Cosine Amplitude, Max-min
Method, Other Similarity methods. |
UNIT 3 |
MEMBERSHIP FUNCTIONS: Features of the Membership Function,
Standard Forms and Boundaries, Fuzzification, Membership Value
Assignments – Intuition, Inference, Rank Ordering, Angular Fuzzy Sets,
Neural Networks, Genetic Algorithms, Inductive Reasoning. |
UNIT 4 |
FUZZY-TO-CRISP CONVERSIONS, FUZZY ARITHMETIC: Lambda-Cuts for Fuzzy Sets, Lambda-Cuts for Fuzzy Relations,
Defuzzification Methods. Extension Principle - Crisp Functions, Mapping
and Relations, Functions of fuzzy Sets – Extension Principle, Fuzzy
Transform (Mapping), Practical Considerations. Fuzzy Numbers Interval
Analysis in Arithmetic, Approximate Methods of Extension - Vertex method,
DSW Algorithm, Restricted DSW Algorithm, Comparisons. Fuzzy Vectors. |
PART – B |
UNIT 5 |
CLASSICAL LOGIC AND FUZZY LOGIC: Classical Predicate Logic –
Tautologies, Contradictions, Equivalence, Exclusive Or and Exclusive Nor,
Logical Proofs, Deductive Inferences. Fuzzy Logic, Approximate Reasoning,
Fuzzy Tautologies, Contradictions, Equivalence and Logical Proofs, Other
forms of the Implication Operation, Other forms of the Composition
Operation. |
UNIT 6 |
FUZZY RULE- BASED SYSTEMS: Natural Language, Linguistic
Hedges, Rule-Based Systems - Canonical Rule Forms, Decomposition of
Compound Rules, Likelihood and Truth Qualification, Aggregation of Fuzzy
Rules. Graphical Techniques of Inference. |
UNIT 7 |
FUZZY DECISION MAKING: Fuzzy Synthetic Evaluation, Fuzzy
Ordering, Preference and consensus, Multiobjective Decision Making, Fuzzy
Bayesian Decision Method, Decision Making under Fuzzy States and Fuzzy
Actions. |
UNIT 8 |
FUZZY CLASSIFICATION: Classification by Equivalence Relations -
Crisp Relations, Fuzzy Relations. Cluster Analysis, Cluster Validity, c-
Means Clustering - Hard c-Means (HCM), Fuzzy c-Means (FCM).
Classification Metric, Hardening the Fuzzy c-Partition, Similarity Relations
from Clustering. |
REFERENCE |
TEXT BOOKS: |
1. Fuzzy Logic with Engineering Applications – Timothy J. Ross,
McGraw-Hill, 1997.
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Reference Books |
1. Neural Networks and Fuzzy systems: A Dynamical System
Approach – B Kosko, Prentice Hall, 1991. |
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