06EC836 - FUZZY LOGIC |
PART – A |
UNIT – I |
INTRODUCTION: Background, Uncertainty and imprecision, Statistics and
random processes, Uncertainty in information, Fuzzy sets and membership,
Chance versus ambiguity, Classical sets - operations on classical sets to functions, Fuzzy sets-fuzzy set operations, Properties of fuzzy sets. Sets as
points in hypercubes. |
UNIT – II |
CLASSICAL RELATIONS AND FUZZY RELATIONS: Cartesian
product, Crisp relations-cardinality of crisp relations, Operations on crisp
relations, Properties of crisp relations, Compositions, Fuzzy relationscardinality
of fuzzy relations, Operations on fuzzy relations, Properties of
fuzzy relations, Fuzzy Cartesian product and composition, Non interactive
fuzzy sets, Tolerance and equivalence relations-crisp equivalence relation,
Crisp tolerance relation, Fuzzy tolerance, Max-min Method, other similarity
methods. |
UNIT – III |
MEMBERSHIP FUNCTIONS: Features of the membership function,
Standards forms and boundaries, fuzzification, Membership value
assignments-intuition, Inference, Rank ordering, Angular fuzzy sets. Neural
networks, Genetic algorithms, Inductive reasoning. |
UNIT – IV |
FUZZY-TO-CRISP CONVERSIONS AND 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, and Fuzzy numbers Interval analysis in Arithmetic,
Approximate methods of extension-vertex method, DSW algorithm,
Restricted DSW algorithm, Comparisons, Fuzzy vectors. |
PART – B |
UNIT – V |
CLASSICAL LOGIC AND FUZZY LOGIC: Classical predicate logictautologies,
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 – VI |
FUZZY RULE-BASED SYSTEMS: Natural language, Linguistic hedges,
Rule-based system-canonical rule forms, Decomposition of compound rules,
Likelihood and truth qualification, Aggregation of fuzzy rules, Graphical
techniques of inference. |
UNIT – VII |
FUZZY DECISION MAKING: Fuzzy synthetic evaluation, Fuzzy
ordering, Preference and consensus, Multiobjective decision making under
fuzzy states and fuzzy actions. |
UNIT – VIII |
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. |
Reference Books |
1. Nural networks and fuzzy systems: A dynamical system
approach, B. Kosko, Peasrson Edu. 1991. |
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