Approximate Reasoning using Fuzzy Set Theory

By Prof. Balasubramaniam Jayaram   |   IIT Hyderabad
Learners enrolled: 600
About the course: The main focus of this course is to provide an understanding of and the theoretical underpinning of the different schemes of Approximate Reasoning employing Fuzzy Sets. It is envisaged that the structure and approach of the course will be to make a student of Math appreciate how the different structural constructs, often consigned to theoretical studies, play a role in propping up working engineering models, and a student of engineering understand the variety of theoretical explorations that allow for some basic guarantees to their embedded models.

A basic understanding of analysis and algebra is required, while the basics of fuzzy set theory, while being useful will also be covered as we go along. Thus it should be accessible to final year undergrads and any post-graduate student in Math / CSE or EE.

INTENDED AUDIENCE: This course will be accessible to Science / Engineering students upwards of 4th year undergraduate. Specifically, 4th year B.Tech / BE (CSE / EE), M.Sc (Mathematics / Stats / Computing), M. Tech (CSE, EE)

INDUSRTY SUPPORT: Industries dealing with Data Analysis and Inference, Control Systems, Aerospace.

PRE-REQUISITE: An understanding of basic concepts of analysis and algebra at the level of an undergrad course is required. Familiarity with the following courses on NPTEL would be of added value:
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Postgraduate
Start Date : 25 Jul 2022
End Date : 14 Oct 2022
Enrollment Ends : 08 Aug 2022
Exam Date : 30 Oct 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Fuzzy Sets – Preliminaries
Week 2: Fuzzy Set Theoretic Connectives – Algebra of Fuzzy Sets
Week 3: Fuzzy Set Theoretic Connectives – Triangular Norms
Week 4: Fuzzy Set Theoretic Connectives – Fuzzy Implications
Week 5: Fuzzy Inference Mechanisms – Fuzzy Relations
Week 6: Fuzzy Inference Mechanisms – Fuzzy Relational Inference
Week 7: Fuzzy Inference Mechanisms – Similarity Based Reasoning
Week 8: Fuzzy Inference Mechanisms – Hands-On with Fuzzy Logic Toolbox in Matlab
Week 9: Properties of an FIS - Interpolativity
Week 10: Properties of an FIS - Continuity
Week 11: Properties of an FIS - Robustness
Week 12: Properties of an FIS – Monotonicity

Books and references

1. V Novák, I Perfilieva, J Mockor, Mathematical principles of fuzzy logic, Springer, Heidelberg, 2012.
2. M Grabisch, JL Marichal, R Mesiar, E Pap, Aggregation functions, Cambridge University Press, 2009.
3. M Baczynski, B Jayaram, Fuzzy implications, Springer, Heidelberg, 2008.
4. EP Klement, R Mesiar, E Pap, Triangular norms, Kluwer Academic, 2000.

Instructor bio

Prof. Balasubramaniam Jayaram

IIT Hyderabad
Prof. Balasubramaniam Jayaram received his PhD in Mathematics from the Sri Sathya Sai Institute of Higher Learning, India in 2004. After having been a visiting researcher with universities in Germany, Austria, Slovakia, and Czech Republic, he is currently a full professor in the Department of Mathematics, Indian Institute of Technology Hyderabad, India (https://people.iith.ac.in/jbala/).

Prof. Jayaram's research interests are at the intersection of Math and Data Engineering, especially to study the theory behind practical and working models for inference, searching and reasoning. His contributions to fuzzy set theory are in the areas of aggregation operations - specifically, triangular norms and fuzzy implications, and approximate reasoning - specifically, dealing with their efficacy and efficiency. He has co-authored the only research monograph on Fuzzy Implications (https://link.springer.com/book/10.1007/978-3-540-69082-5) and is the author or co-author of nearly 100 refereed journal and conference papers.  He is also a 4-time recipient of the “Excellence in Teaching” award at IIT Hyderabad.

Prof. Jayaram is an experienced research fellow of the Alexander von Humboldt Foundation. He is on the editorial board of many of the leading journals in the field of fuzzy set theory, viz.  IEEE Transactions on Fuzzy Systems (2014-),  Fuzzy Sets and Systems (2016-), International Journal of Approximate Reasoning (2019 - ) and Kybernetika (2020 - ). He also continues to serve on the program committees of some of the top tier conferences in the field of fuzzy set theory like AGOP, IPMU, IFSA-EUSFLAT, FSTA, ISCAMI. 

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: October 30, 2022 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.


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 Hyderabad. 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

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