Introduction to Fuzzy Set Theory, Arithmetic and Logic

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 SciencePREREQUISITES: Nil

Syllabus

Week 1: Introduction to Fuzzy sets , Crisp vs Fuzzy Types of Fuzzy sets, Membership functions , Alpha cuts Contd alpha cutsWeek 2: Operation on fuzzy sets, t-norm, complements t-conorm, combination of operartions continuedWeek 3: Introduction to Fuzzy arithmetic Interval arithmeticWeek 4: +,-,,* using alpha cuts MIN and MAX fuzzy numbersWeek 5: Fuzzy arithmetic using Alpha cuts continued Decomposition principleWeek 6: Extension principle Fuzzy arithmetic using Extension Principle Fuzzy EquationsWeek 7: Relations, Introduction to fuzzy relations Projections, Equivalence relation, transitive closure, compatibility relationWeek 8: Introduction to propositional Logic, Boolean Algebra Multi valued logicWeek 9: Fuzzy Logic, Linguistic hedges, Fuzzy propositions (conditional and unconditional)Week 10: Inference from conditional and qualified fuzzy propositionsWeek 11: Fuzzy Quantifiers, Inference from quantified fuzzy propositionsWeek 12: Introduction to possibility theory Possibility vs probability Belief and Plausibility, Dempsters rule