MATH-8128               Fuzzy Analysis

Fuzzy Logic is a decision making system. It deals with vague and imprecise information. This is gross oversimplification of the real-world problems and based on degrees of truth rather than usual true/false or 1/0 like Boolean logic. With available dataset rules can be created with membership function developed, solution to to a problem is obtained by taking alpha cuts from membership functions and varying the input parameters and using the developed rule viewer to showcase the possible outcomes. The toolbox can easily be invoked using MATLAB.

Contents

1. Fuzzy Sets,
2. Fuzzy Sets, level sets,
3. Special types of fuzzy sets,
4. Zadeh’s extension principle,
5. Fuzzy functions, sup-min extension principle,
6. Interval arithmetic, fuzzy numbers and fuzzy arithmetic,
7. Fuzzy metric spaces; fuzzy metric spaces, inner product,
8. Support function, embedding results, continuous fuzzy functions,
9. Measurable fuzzy functions, integrable fuzzy functions,
10. Differentiable fuzzy functions.

Recommended Books

1. Barnabas, B., Mathematics of Fuzzy Sets and Fuzzy Logic, (Springer (2013)).
2. Choudary, A. D. R. and Lupulescu, V., Fuzzy Sets and Fuzzy Differential Equations, (Abdus Salam SMS Lahore (2010)).

Suggested Books

1. Lakshmikatham, V., Bhaskar, T.G. and  Devi, J.V., Theory of Set Differential equations in Metric Spaces, Cambridge Scientic, (Cambridge, UK (2006)).
2. Lakshmikantham, V. and Mohapatra, R., Theory of Fuzzy Differential Equations and Inclusions, (Taylor - Francis, London, (2003)).
3. Aubin, J. P. and Frankowska, H.,, Set-Valued Analysis, Birkhäuser, (Berlin (1990)).
4. Negoita, C. and Ralescu, D., Applications of Fuzzy Sets to Systems Analysis, (Wiley, New York, (1975)).

Assessment Criteria

Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04)

Mid-Term Exam:  30

Final-Term Exam: 50

Key Dates and Time of Class Meeting

Monday: 02:00-03:30 PM         

Wednesday: 02:00-03:30 PM

Commencement of Classes                                                    November 02, 2020

Mid Term Examination                                                             December 28, 2020

Final Term Examination                                                           March 01-05, 2021

Declaration of Result                                                               March 12, 2021