This course concentrates on fuzzy set theory and its application. This includes the concepts, and techniques from fuzzy sets and fuzzy logic to enhance machine learning techniques.

To review the concepts of fuzzy set theory
To understand the fuzzy set theory techniques
To use the theory in optimization problems
To apply the theory to enhance machine learning techniques

1. Crisp sets and Fuzzy sets - Introduction - crisp sets an overview-the notion of fuzzy sets-basic concepts of fuzzy sets- membership functions - methods of generating membership functions-Defuzzification methods-operations on fuzzy sets- fuzzy complement- fuzzy union- fuzzy intersection- combinations of operations-General aggregation operation

2. Fuzzy arithmetic and Fuzzy relations-Fuzzy numbers-arithmetic operations on intervals-arithmetic operations on fuzzy numbers-fuzzy equations- crisp and fuzzy relations-binary relations- binary relations on a single set - equivalence and similarity relations- compatibility or tolerance relation

3. Fuzzy measures - Fuzzy measures - belief and plausibility measure - probability measures -possibility and necessity measures- possibility distribution- relationship among classes of fuzzy measures.

4. Fuzzy Applications-Fuzzy approximate reasoning- Fuzzy Expert System-Fuzzy systems-Fuzzy controllers-Fuzzy Neural Networks- Fuzzy automata-Fuzzy Dynamic systems

5. Fuzzy Clustering-Fuzzy Pattern Recognition-Fuzzy image processing - Fuzzy data bases and information retrieval-Fuzzy Decision making - Fuzzy systems and Genetic algorithms - Fuzzy regression.

1. George J Klir and Tina AFolger: Fuzzy Sets, Uncertainty and Information, Fuzzy Sets, Uncertainty and Information Pearson Education; 1st edition , 2015
2. George J Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications Pearson Education; 1stedition, 2015.
3. Timothy J Ross: Fuzzy logic with Engineering Applications; 3rdEdition,Wiley, 2011.
4. H. J. Zimmerman: Fuzzy Set theory and its Applications;4thEdition, Springer,2001.