MSc (Mathematics and Computing) Programme:Fuzzy Sets and Applications

Semester I

Real Analysis – I
Linear Algebra
Complex Analysis
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Differential Equations


Semester II

Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Structures
Data Based Management Systems
Operating Systems


Semester III

Topology
Computer Based Optimization Techniques
Computer Networks
Mechanics
Seminar


Semester IV

Functional Analysis
Dissertation


Fuzzy Sets and Applications

Classical and Fuzzy Sets: Overview of Classical Sets, Membership Function, a-cuts,Properties of a-cuts, Decomposition Theorems, Extension Principle.

Operations on Fuzzy Sets: Compliment, Intersections, Unions, Combinations of operations, Aggregation Operations.

Fuzzy Arithmetic: Fuzzy Numbers, Linguistic Variables, Arithmetic Operations on intervals and Numbers, Lattice of Fuzzy Numbers, Fuzzy Equations.

Fuzzy Relations: Crisp and Fuzzy Relations, Projections and Cylindric Extensions, Binary Fuzzy Relations, Binary Relations on single set, Equivalence, Compatibility and Ordering Relations, Morphisms, Fuzzy Relation Equations.

Possibility Theory: Fuzzy Measures, Evidence and Possibility Theory, Possibility versus Probability Theory.

Fuzzy Logic: Classical Logic, Multivalued Logics, Fuzzy Propositions, Fuzzy Qualifiers, Linguistic Hedges.

Uncertainty based Information: Information and Uncertainty, Nonspecificity of Fuzzy and Crisp sets, Fuzziness of Fuzzy Sets.

Applications of Fuzzy Logic