# Introduction to Fuzzy Set Theory, Arithmetic and Logic

By Prof. Niladri Chatterjee   |   IIT Delhi
Learners enrolled: 1130
The primary purpose of this course is to introduce students to the important areas of fuzzy set theory and fuzzy logic. No previous knowledge is needed regarding fuzzy set theory or fuzzy logic. But familiarity with classical set theory, and two-valued logic will be helpful. In most real-life applications of any decision making one needs to face many types on uncertainty. While as humans we can deal with this uncertainty with our reasoning prowess it is not clear how to deal with this uncertainty in a system. Fuzzy sets and fuzzy logic gives us one way of representing this uncertainty and reasoning with them. This course is aimed at providing a strong background for the subject. This course will be useful as an elective course for senior undergraduates, and master degree students. Weekly assignments will be provided and their solutions will be given in the following week to help students to solve the problems.

INTENDED AUDIENCE: M.Sc Mathematics, M.Sc Computer Science
PREREQUISITES:          Nil
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Start Date : 26 Jul 2021 End Date : 15 Oct 2021 Exam Date : 23 Oct 2021 IST Enrollment Ends : 09 Aug 2021 Category : Mathematics Credit Points : 3 Level : Undergraduate/Postgraduate

### Course layout

Week 1: Introduction to Fuzzy sets , Crisp vs Fuzzy Types of Fuzzy sets, Membership functions , Alpha cuts Contd alpha cuts
Week 2: Operation on fuzzy sets, t-norm, complements t-conorm, combination of operartions continued
Week 3: Introduction to Fuzzy arithmetic Interval arithmetic
Week 4: +,-,,* using alpha cuts MIN and MAX fuzzy numbers
Week 5: Fuzzy arithmetic using Alpha cuts continued Decomposition principle
Week 6: Extension principle Fuzzy arithmetic using Extension Principle Fuzzy Equations
Week 7: Relations, Introduction to fuzzy relations Projections, Equivalence relation, transitive closure, compatibility relation
Week 8: Introduction to propositional Logic, Boolean Algebra Multi valued logic
Week 9: Fuzzy Logic, Linguistic hedges, Fuzzy propositions (conditional and unconditional)
Week 10: Inference from conditional and qualified fuzzy propositions
Week 11: Fuzzy Quantifiers, Inference from quantified fuzzy propositions
Week 12: Introduction to possibility theory Possibility vs probability Belief and Plausibility, Dempsters rule

### Books and references

1. Fuzzy Sets and Fuzzy Logic, Geoge J. Klir and Bo Yuan
2. Fuzzy Mathematical Models in Engineering and Management Science, A. Kaufmann and M.M. Gupta
3. Fuzzy Logic, Timothy J. Ross
4. Fuzzy Set Theory, H.J. Zimmermann
5. Introduction to Fuzzy Logic and Fuzzy Sets, J.J. Buckley and E. Eslami

### Instructor bio

IIT Delhi
Prof. Niladri Chatterjee is a professor of Department of Mathematics, IIT Delhi. He is B.Stat and M.Stat from Indian Statistical Institute Kolkata. He is an M.Tech in Computer Science and PhD in Computer science from University College London. His major research interests are Artificial Intelligence, Machine Learning, Natural Language Processing, Statistical Modeling among others. He has more than 30 years of research and teaching experience. He is also member of several Government committees related to AI and Machine Learning.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team