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HIGER & APPLIED AREA MINOR COURSES:

Math.414 Fuzzy Set Theory 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is:
 To describe various types of soft computing techniques, and applications of soft
computing.
 To describe the fuzzy sets and fuzzy logic.
 To describe the fuzzy controller and fuzzy rule base and approximate reasoning.

LEARNING OUTCOMES:

After the completion of the course, students are able to:
 Understand the basic tools of soft computing.
 Understand the fuzzy sets and crisp sets, fuzzy set theory and operations.
 Understand the fuzzy controller and fuzzy rule base and approximate reasoning.

THEORY (45 Hours)

UNIT I: (15 Hours)
Introduction, soft computing vs. hard computing, various types of soft computing techniques, and
applications of soft computing. Basic tools of soft computing - Fuzzy logic, neural network,
evolutionary computing. Introduction: Neural networks, application scope of neural networks,
fuzzy logic, genetic algorithm, and hybrid systems. Concepts of Fuzzy Set, Standard Operations
of Fuzzy Set, Fuzzy Complement, Fuzzy Union, Fuzzy Intersection, Other Operations in Fuzzy
Set, T- norms and T- conorms. Interval, Fuzzy Number, Operation of Interval, Operation of - cut
Interval, Examples of Fuzzy Number Operation.

UNIT-II: (10 Hours)
Definition of Triangular Fuzzy Number, Operation of Triangular Fuzzy Number, Operation of
General Fuzzy Numbers. Approximation of Triangular Fuzzy Number, Operations of Trapezoidal
Fuzzy Number, Bell Shape Fuzzy Number. Function with Fuzzy Constraint, Propagation of
Fuzziness by Crisp Function, Fuzzifying Function of Crisp Variable, Maximizing and Minimizing
Set, Maximum Value of Crisp Function.

UNIT-III: (10 Hours)
Integration and Differentiation of Fuzzy Function Product Set, Definition of Relation,
Characteristics of Relation, Representation Methods of Relations, Operations on Relations, Path
and Connectivity in Graph, Fundamental Properties, Equivalence Relation, Compatibility
Relation, Pre-order Relation, Order Relation, Definition and Examples of Fuzzy Relation, Fuzzy
Matrix, Operations on Fuzzy Relation.

UNIT-IV: (10 Hours)
Composition of Fuzzy Relation, - cut of Fuzzy Relation, Projection and Cylindrical Extension,
Extension by Relation, Extension Principle, Extension by Fuzzy Relation, Fuzzy distance between
Fuzzy Sets. Graph and Fuzzy Graph, Fuzzy Graph and Fuzzy Relation.

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