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98.705 FUZZY SYSTEMS (TA) 3-2-0

Module I
Introduction to Fuzzy sets and systems. Basics of fuzzy sets membership function, support of a fuzzy set, height - normalised fuzzy set, a - cuts (decomposition of a fuzzy set), set theoretic definitions on fuzzy sets, complement, intersection and union equality, subsethood - basic definition based on membership functions. The law of the excluded middle and law of contradiction on fuzzy sets. Properties of fuzzy sets operations (logical proof only). Extension of fuzzy sets concepts - type-2 and level 2 fuzzy sets - examples.

Module II
Operations on fuzzy sets - intersection, algebraic sum - product, bounded sum - product, drastic sum product, t-norms and t-conorms(s - norms) on fuzzy sets, typical parameterised t - norms and s-norms(with simplified proof). Extension principle and its applications. Fuzzy relation. Resolution form of a binary fuzzy relation. Operations on fuzzy relations - projection, max.-min. and min and max, compositions cylindric extension. Similarity relations - reflexivity, symmetry, transitivity.

Module III
Further operations on fuzzy sets and proposed by Zadeh - concentration dilation, contrast Intensification, a linguistic hedges, computation of the meaning of values of a linguistic variable, fuzzy algorithms, fuzzy engineering - applications of fuzzy controls, case studies.

Text Books : -

Module I & II
Ref (1) (ch 1, 2 & 3)
Module III
Ref (1) (ch 1, 2 & 3)
Ref (2) & Ref (3)

References : -

1. C.T lin & C S George Lee. Neural Fuzzy Systems, Prentice Hall .
2. Earl Cox. Fuzzy Systems Handbook, Associated Press
3. Klir and Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall of India.
4. IEEE Trans on Systems, Man & Cybernetics, vol. SMC - 3, No.1, January 1973, pp 28-44
5. Bart Kosko. Fuzzy Engineering, Prentice Hall.
6. Bart Kosko. Fuzzy Thinking , Hooper Collins Publications.

Question Paper : -

The question paper will consist of two parts. Part I is to cover the entire syllabus, and carries 40 marks. This will contain 10 compulsory questions of 4 marks each. Part II is to cover 3 modules, and carries 60 marks. There will be 3 questions from each module (10 marks each) out of which 2 are to be answered.