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Online Course

Introduction to Fuzzy Set Theory, Arithmetic and Logic

Indian Institute of Technology Delhi and NPTEL via Swayam

(0)
13
Found in Mathematics

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Overview

The primary purpose of this course is to introduce students to the important areas of fuzzy set theory and fuzzy logic. No previous knowledge is needed regarding fuzzy set theory or fuzzy logic. But familiarity with classical set theory, and two-valued logic will be helpful. In most real-life applications of any decision making one needs to face many types on uncertainty. While as humans we can deal with this uncertainty with our reasoning prowess it is not clear how to deal with this uncertainty in a system. Fuzzy sets and fuzzy logic gives us one way of representing this uncertainty and reasoning with them. This course is aimed at providing a strong background for the subject. This course will be useful as an elective course for senior undergraduates, and master degree students. Weekly assignments will be provided and their solutions will be given in the following week to help students to solve the problems.

INTENDED AUDIENCE: M.Sc Mathematics, M.Sc Computer Science
PREREQUISITES: Nil

Syllabus

COURSE LAYOUT

Week 1: Introduction to Fuzzy sets , Crisp vs Fuzzy Types of Fuzzy sets, Membership functions , Alpha cuts Contd alpha cuts
Week 2: Operation on fuzzy sets, t-norm, complements t-conorm, combination of operartions continued
Week 3: Introduction to Fuzzy arithmetic Interval arithmetic
Week 4: +,-,,* using alpha cuts MIN and MAX fuzzy numbers
Week 5: Fuzzy arithmetic using Alpha cuts continued Decomposition principle
Week 6: Extension principle Fuzzy arithmetic using Extension Principle Fuzzy Equations
Week 7: Relations, Introduction to fuzzy relations Projections, Equivalence relation, transitive closure, compatibility relation
Week 8: Fuzzy relational equation Solution Methods continued
Week 9: Introduction to possibility theory Possibility vs probability Belief and Plausibility, dempsters rule, Possibility and Necessity
Week 10: Fuzzy Logic, Multi valued logic Fuzzy propositions
Week 11: Linguistic hedges, Inference from propositions continued
Week 12: Inference from fuzzy propositions continued


Taught by

Prof. Niladri Chatterjee

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