NPTEL : NOC:Approximate Reasoning using Fuzzy Set Theory (Mathematics)

Co-ordinators : Prof. Balasubramaniam Jayaram


Lecture 1 - Flow of the Course: A not-so-sneak peek

Lecture 2 - Fuzzy Sets - The Necessity

Lecture 3 - Fuzzy Sets - Representations

Lecture 4 - Fuzziness vs Probability

Lecture 5 - Fuzzy Sets - Some Important Notions

Lecture 6 - Operations on Fuzzy Sets

Lecture 7 - Posets on Fuzzy Sets

Lecture 8 - Lattice of Fuzzy Sets

Lecture 9 - Boolean Algebra of Sets

Lecture 10 - Algebras on Fuzzy Sets

Lecture 11 - Triangular Norms

Lecture 12 - Triangular Norms: Analytical Aspects

Lecture 13 - Triangular Norms: Algebraic Aspects

Lecture 14 - T-Norms: Construction and Representations

Lecture 15 - T-Norms:Complementation and Duality

Lecture 16 - Fuzzy Implications

Lecture 17 - Fuzzy Implications - Desirable Properties

Lecture 18 - Construction of Fuzzy Implication - I

Lecture 19 - Construction of Fuzzy Implication - II

Lecture 20 - Construction of Fuzzy Implication - II

Lecture 21 - Construction of Fuzzy Implication - III

Lecture 22 - Construction of Fuzzy Implication - IV

Lecture 23 - (N, T, I)- An Organic Relationship

Lecture 24 - Fuzzy Relations

Lecture 25 - Composition of Fuzzy Relations

Lecture 26 - Similarity and Compatibility Classes

Lecture 27 - On the Transitivity of Fuzzy Relations - I

Lecture 28 - On the Transitivity of Fuzzy Relations - II

Lecture 29 - Fuzzy Propositions: Some Interpretations

Lecture 30 - Fuzzy If-Then Rules

Lecture 31 - Fuzzy Relational Inference

Lecture 32 - Fuzzy Relational Inference - MISO Case

Lecture 33 - Fuzzy Relational Inference - Multiple Rules

Lecture 34 - Fuzzy Inferencing Schemes - A Visual Illustration

Lecture 35 - Similarity Based Reasoning

Lecture 36 - SBR : Mamdani Fuzzy Systems

Lecture 37 - Introduction to Building a Mamdani FIS

Lecture 38 - Contrast Enhancement in Images: An FIS Approach

Lecture 39 - Takagi-Sugeno-Kang Fuzzy Systems

Lecture 40 - Fuzzy Inference Systems - Interpolativity

Lecture 41 - Interpolativity of FRI - Single SISO Rule

Lecture 42 - Fuzzy Relational Equations

Lecture 43 - Interpolativity of FRI - Multiple SISO Rules

Lecture 44 - Similarity Based Reasoning- Interpolativity

Lecture 45 - FRI~SBR : FITA~FATI : Some Connections

Lecture 46 - Continuous Models of FRI

Lecture 47 - Continuous Models of CRI and BKS

Lecture 48 - Continuous Models of SBR

Lecture 49 - Extensionality of a Fuzzy Set

Lecture 50 - Robustness of CRI

Lecture 51 - Robustness of BKS

Lecture 52 - Robustness of SBR

Lecture 53 - Monotonicity of an FIS

Lecture 54 - Monotonicity of an FRI

Lecture 55 - Monotonicity of an SBR

Lecture 56 - Functional (In)Equalities involving FLCs

Lecture 57 - Suitability of BKS with Yager's Implications

Lecture 58 - Law of Importation and Hierarchical CRI