# Approximate Reasoning using Fuzzy Set Theory

- Institution: IIT Hyderabad
- Department: Mathematics
- Teacher: Prof. Balasubramaniam Jayaram
- Level: Graduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106162)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106162)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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.

Prerequisites: 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: https://nptel.ac.in/courses/108104157https://nptel.ac.in/courses/111102130

## Lectures

1. [Flow of the Course: A not-so-sneak peek](https://invisiblenetwork.ai/learn/nptel/111106162/4a7892cecfeb) (YouTube)
2. [Fuzzy Sets - The Necessity](https://invisiblenetwork.ai/learn/nptel/111106162/378b6d250c5f) (YouTube)
3. [Fuzzy Sets - Representations](https://invisiblenetwork.ai/learn/nptel/111106162/ea54be89d9cc) (YouTube)
4. [Fuzziness vs Probability](https://invisiblenetwork.ai/learn/nptel/111106162/87b6ef222448) (YouTube)
5. [Fuzzy Sets - Some Important Notions](https://invisiblenetwork.ai/learn/nptel/111106162/6916836a91ca) (YouTube)
6. [Operations on Fuzzy Sets](https://invisiblenetwork.ai/learn/nptel/111106162/0f9abf863739) (YouTube)
7. [Posets on Fuzzy Sets](https://invisiblenetwork.ai/learn/nptel/111106162/644c3577f16c) (YouTube)
8. [Lattice of Fuzzy Sets](https://invisiblenetwork.ai/learn/nptel/111106162/2b6198d5b22d) (YouTube)
9. [Boolean Algebra of Sets](https://invisiblenetwork.ai/learn/nptel/111106162/ff09d4a183f7) (YouTube)
10. [Algebras on Fuzzy Sets](https://invisiblenetwork.ai/learn/nptel/111106162/dd291a814a27) (YouTube)
11. [Triangular Norms](https://invisiblenetwork.ai/learn/nptel/111106162/8ae1c71698c0) (YouTube)
12. [Triangular Norms: Analytical Aspects](https://invisiblenetwork.ai/learn/nptel/111106162/651d2e8d5fe2) (YouTube)
13. [Triangular Norms: Algebraic Aspects](https://invisiblenetwork.ai/learn/nptel/111106162/8defba1807c2) (YouTube)
14. [T-Norms: Construction and Representations](https://invisiblenetwork.ai/learn/nptel/111106162/48e9df28b0ac) (YouTube)
15. [T-Norms:Complementation and Duality](https://invisiblenetwork.ai/learn/nptel/111106162/e9482bc36ea8) (YouTube)
16. [Fuzzy Implications](https://invisiblenetwork.ai/learn/nptel/111106162/3009add6c594) (YouTube)
17. [Fuzzy Implications - Desirable Properties](https://invisiblenetwork.ai/learn/nptel/111106162/9a844c02a98b) (YouTube)
18. [Construction of Fuzzy Implication - l](https://invisiblenetwork.ai/learn/nptel/111106162/e8cc9bbf2854) (YouTube)
19. [Construction of Fuzzy Implication - ll](https://invisiblenetwork.ai/learn/nptel/111106162/64b8e2016d36) (YouTube)
20. [Construction of Fuzzy Implication - lll](https://invisiblenetwork.ai/learn/nptel/111106162/f25ce3413ea4) (YouTube)
21. [Construction of Fuzzy Implications - IV](https://invisiblenetwork.ai/learn/nptel/111106162/bd59c76f9a9a) (YouTube)
22. [(N, T, I)- An Organic Relationship](https://invisiblenetwork.ai/learn/nptel/111106162/fc7768e1bbf8) (YouTube)
23. [Fuzzy Relations](https://invisiblenetwork.ai/learn/nptel/111106162/8a3cecd8d301) (YouTube)
24. [Composition of Fuzzy Relations](https://invisiblenetwork.ai/learn/nptel/111106162/d511dde590e9) (YouTube)
25. [Similarity & Compatibility Classes](https://invisiblenetwork.ai/learn/nptel/111106162/fde12b244d43) (YouTube)
26. [On the Transitivity of Fuzzy Relations - I](https://invisiblenetwork.ai/learn/nptel/111106162/7ca770970057) (YouTube)
27. [On the Transitivity of Fuzzy Relations - II](https://invisiblenetwork.ai/learn/nptel/111106162/87909fe222f8) (YouTube)
28. [Fuzzy Propositions: Some Interpretations](https://invisiblenetwork.ai/learn/nptel/111106162/91c78033122a) (YouTube)
29. [Fuzzy If-Then Rules](https://invisiblenetwork.ai/learn/nptel/111106162/209a98836ce1) (YouTube)
30. [Fuzzy Relational Inference](https://invisiblenetwork.ai/learn/nptel/111106162/43b100391478) (YouTube)
31. [Fuzzy Relational Inference - MISO Case](https://invisiblenetwork.ai/learn/nptel/111106162/d477613f4a31) (YouTube)
32. [Fuzzy Relational Inference - Multiple Rules](https://invisiblenetwork.ai/learn/nptel/111106162/b36ede3a9490) (YouTube)
33. [Fuzzy Inferencing Schemes - A Visual Illustration](https://invisiblenetwork.ai/learn/nptel/111106162/7b1bcbe2b9c9) (YouTube)
34. [Similarity Based Reasoning](https://invisiblenetwork.ai/learn/nptel/111106162/7ce6e071df5e) (YouTube)
35. [SBR : Mamdani Fuzzy Systems](https://invisiblenetwork.ai/learn/nptel/111106162/0d6c803dfa8a) (YouTube)
36. [Introduction to Building a Mamdani FIS](https://invisiblenetwork.ai/learn/nptel/111106162/a052d4ea675e) (YouTube)
37. [Contrast Enhancement in Images: An FIS Approach](https://invisiblenetwork.ai/learn/nptel/111106162/db64bbe00352) (YouTube)
38. [Takagi-Sugeno-Kang Fuzzy Systems](https://invisiblenetwork.ai/learn/nptel/111106162/5df880a3db99) (YouTube)
39. [Fuzzy Inference Systems- Interpolativity](https://invisiblenetwork.ai/learn/nptel/111106162/0deb1190d113) (YouTube)
40. [Interpolativity of FRI - Single SISO Rule](https://invisiblenetwork.ai/learn/nptel/111106162/476dedd12e3d) (YouTube)
41. [Fuzzy Relational Equations](https://invisiblenetwork.ai/learn/nptel/111106162/ec77f8b9f577) (YouTube)
42. [Interpolativity of FRI - Multiple SISO Rules](https://invisiblenetwork.ai/learn/nptel/111106162/1f12f93dc917) (YouTube)
43. [Similarity Based Reasoning- Interpolativity](https://invisiblenetwork.ai/learn/nptel/111106162/2a5525b1b8d6) (YouTube)
44. [FRI ~ SBR : FITA ~ FATI :Some Connections](https://invisiblenetwork.ai/learn/nptel/111106162/3e62999c3195) (YouTube)
45. [Continuous Models of FRI](https://invisiblenetwork.ai/learn/nptel/111106162/3b340876e35b) (YouTube)
46. [Continuous Models of CRI and BKS](https://invisiblenetwork.ai/learn/nptel/111106162/ba3ed936256c) (YouTube)
47. [Continuous Models of SBR](https://invisiblenetwork.ai/learn/nptel/111106162/c504843c25ed) (YouTube)
48. [Extensionality of a Fuzzy Set](https://invisiblenetwork.ai/learn/nptel/111106162/448ab8d7f40b) (YouTube)
49. [Robustness of CRI](https://invisiblenetwork.ai/learn/nptel/111106162/bd1c4fba1e99) (YouTube)
50. [Robustness of BKS](https://invisiblenetwork.ai/learn/nptel/111106162/ebb87f23c5c9) (YouTube)
51. [Robustness of SBR](https://invisiblenetwork.ai/learn/nptel/111106162/e28ba84a92fb) (YouTube)
52. [Monotonicity of an FIS](https://invisiblenetwork.ai/learn/nptel/111106162/9dffe3e6e3ba) (YouTube)
53. [Monotonicity of an FRI](https://invisiblenetwork.ai/learn/nptel/111106162/38db367a8613) (YouTube)
54. [Monotonicity of an SBR](https://invisiblenetwork.ai/learn/nptel/111106162/b33e1d89e42f) (YouTube)
55. [Functional (In)Equalities involving FLCs](https://invisiblenetwork.ai/learn/nptel/111106162/afd6b5bee4e2) (YouTube)
56. [Suitability of BKS with Yager’s Implications](https://invisiblenetwork.ai/learn/nptel/111106162/a1fa1766b7bc) (YouTube)
57. [Law of Importation and Hierarchical CRI](https://invisiblenetwork.ai/learn/nptel/111106162/d12ad43ac2f9) (YouTube)