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Course11110616257 lectures

Approximate Reasoning using Fuzzy Set Theory

Prof. Balasubramaniam Jayaram · IIT Hyderabad

Start with lecture 1 At NPTEL

About

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

Week 1

  1. Flow of the Course: A not-so-sneak peek YouTube
  2. Fuzzy Sets - The Necessity YouTube
  3. Fuzzy Sets - Representations YouTube
  4. Fuzziness vs Probability YouTube
  5. Fuzzy Sets - Some Important Notions YouTube

Week 2

  1. Operations on Fuzzy Sets YouTube
  2. Posets on Fuzzy Sets YouTube
  3. Lattice of Fuzzy Sets YouTube
  4. Boolean Algebra of Sets YouTube
  5. Algebras on Fuzzy Sets YouTube

Week 3

  1. Triangular Norms YouTube
  2. Triangular Norms: Analytical Aspects YouTube
  3. Triangular Norms: Algebraic Aspects YouTube
  4. T-Norms: Construction and Representations YouTube
  5. T-Norms:Complementation and Duality YouTube

Week 4

  1. Fuzzy Implications YouTube
  2. Fuzzy Implications - Desirable Properties YouTube
  3. Construction of Fuzzy Implication - l YouTube
  4. Construction of Fuzzy Implication - ll YouTube
  5. Construction of Fuzzy Implication - lll YouTube
  6. Construction of Fuzzy Implications - IV YouTube
  7. (N, T, I)- An Organic Relationship YouTube

Week 5

  1. Fuzzy Relations YouTube
  2. Composition of Fuzzy Relations YouTube
  3. Similarity & Compatibility Classes YouTube
  4. On the Transitivity of Fuzzy Relations - I YouTube
  5. On the Transitivity of Fuzzy Relations - II YouTube

Week 6

  1. Fuzzy Propositions: Some Interpretations YouTube
  2. Fuzzy If-Then Rules YouTube
  3. Fuzzy Relational Inference YouTube
  4. Fuzzy Relational Inference - MISO Case YouTube
  5. Fuzzy Relational Inference - Multiple Rules YouTube

Week 7

  1. Fuzzy Inferencing Schemes - A Visual Illustration YouTube
  2. Similarity Based Reasoning YouTube
  3. SBR : Mamdani Fuzzy Systems YouTube
  4. Introduction to Building a Mamdani FIS YouTube
  5. Contrast Enhancement in Images: An FIS Approach YouTube
  6. Takagi-Sugeno-Kang Fuzzy Systems YouTube

Week 8

  1. Fuzzy Inference Systems- Interpolativity YouTube
  2. Interpolativity of FRI - Single SISO Rule YouTube
  3. Fuzzy Relational Equations YouTube
  4. Interpolativity of FRI - Multiple SISO Rules YouTube
  5. Similarity Based Reasoning- Interpolativity YouTube

Week 9

  1. FRI ~ SBR : FITA ~ FATI :Some Connections YouTube
  2. Continuous Models of FRI YouTube
  3. Continuous Models of CRI and BKS YouTube
  4. Continuous Models of SBR YouTube

Week 10

  1. Extensionality of a Fuzzy Set YouTube
  2. Robustness of CRI YouTube
  3. Robustness of BKS YouTube
  4. Robustness of SBR YouTube

Week 11

  1. Monotonicity of an FIS YouTube
  2. Monotonicity of an FRI YouTube
  3. Monotonicity of an SBR YouTube

Week 12

  1. Functional (In)Equalities involving FLCs YouTube
  2. Suitability of BKS with Yager’s Implications YouTube
  3. Law of Importation and Hierarchical CRI YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Hyderabad
Department
Mathematics
Teacher
Prof. Balasubramaniam Jayaram
Level
Graduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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