Course11110616257 lectures
Approximate Reasoning using Fuzzy Set Theory
Prof. Balasubramaniam Jayaram · IIT Hyderabad
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
- Flow of the Course: A not-so-sneak peek
- Fuzzy Sets - The Necessity
- Fuzzy Sets - Representations
- Fuzziness vs Probability
- Fuzzy Sets - Some Important Notions
Week 2
- Operations on Fuzzy Sets
- Posets on Fuzzy Sets
- Lattice of Fuzzy Sets
- Boolean Algebra of Sets
- Algebras on Fuzzy Sets
Week 3
- Triangular Norms
- Triangular Norms: Analytical Aspects
- Triangular Norms: Algebraic Aspects
- T-Norms: Construction and Representations
- T-Norms:Complementation and Duality
Week 4
- Fuzzy Implications
- Fuzzy Implications - Desirable Properties
- Construction of Fuzzy Implication - l
- Construction of Fuzzy Implication - ll
- Construction of Fuzzy Implication - lll
- Construction of Fuzzy Implications - IV
- (N, T, I)- An Organic Relationship
Week 5
- Fuzzy Relations
- Composition of Fuzzy Relations
- Similarity & Compatibility Classes
- On the Transitivity of Fuzzy Relations - I
- On the Transitivity of Fuzzy Relations - II
Week 6
- Fuzzy Propositions: Some Interpretations
- Fuzzy If-Then Rules
- Fuzzy Relational Inference
- Fuzzy Relational Inference - MISO Case
- Fuzzy Relational Inference - Multiple Rules
Week 7
- Fuzzy Inferencing Schemes - A Visual Illustration
- Similarity Based Reasoning
- SBR : Mamdani Fuzzy Systems
- Introduction to Building a Mamdani FIS
- Contrast Enhancement in Images: An FIS Approach
- Takagi-Sugeno-Kang Fuzzy Systems
Week 8
- Fuzzy Inference Systems- Interpolativity
- Interpolativity of FRI - Single SISO Rule
- Fuzzy Relational Equations
- Interpolativity of FRI - Multiple SISO Rules
- Similarity Based Reasoning- Interpolativity
Week 9
- FRI ~ SBR : FITA ~ FATI :Some Connections
- Continuous Models of FRI
- Continuous Models of CRI and BKS
- Continuous Models of SBR
Week 10
Week 11
Week 12
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.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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