NPTEL Syllabus
Fuzzy Sets and their
Applications - Video course
COURSE OUTLINE
NPTEL
Theory of Fuzzy Sets:
Classical Sets vs Fuzzy Sets (FS) – Types of FS –
Operations on FS – Zadeh’s Extension Principle – Fuzzy
Relations – Fuzzy Relational Equations – Possibility Theory
: Fuzzy Measures.
http://nptel.iitm.ac.in
Mathematics
Some Applications of Fuzzy Sets:
Approximate Reasoning – Fuzzy Relational Inference Fuzzy Controllers – Efficiency and Effectiveness of inference
schemes – Functional Approximation capabilities.
NB: Course along the lines of the syllabus specified by UGC
Pre-requisites:
as an optional course under MM 503 (a & b).
COURSE DETAIL
Basic knowledge of algebra and analysis at the level of
undergraduate studies
Module No.
Topic/s
Lectures
Additional Reading:
Fuzzy Sets : Classical sets vs Fuzzy Sets –
Basics
Need
for
fuzzy sets –
Definition and Mathematical
representations – Level Sets –
F u z z y functions - Zadeh’s
Extension Principle
5
Operations on Operations on [0,1] – Fuzzy
Fuzzy Sets
negation, triangular norms, tconorms, fuzzy implications,
Aggregation
Operations,
Fuzzy Functional Equations
8
Frank Höppner, Frank Klawonn, Rudolf Kruse,
Thomas Runkler, Fuzzy Cluster Analysis: Methods
for Classification, Data Analysis and Image
Recognition, Wiley Publishers, 1999.
E P Klement, R Mesiar and E. Pap, Triangular norms,
Kluwer Academic Press, Dordrecht, 2000.
M Grabisch et al., Aggregation Functions, Series Encyclopedia Of Mathematics And Its Applications,
Cambridge University Press, 2009
Hyperlinks:
1. www.ece.osu.edu/~passino/books.html
Fuzzy
Relations
Fuzzy Binary and n-ary
relations – composition of
fuzzy relations – Fuzzy
Equivalence
Relations
–
Fuzzy Compatibility Relations
– Fuzzy Relational Equations
8
2. http://fuzzy.cs.uni-magdeburg.de/clusterbook/
3. www.mathworks.com/products/fuzzylogic/
4. www.abo.fi/~rfuller/fuzs.html
5. http://jfuzzylogic.sourceforge.net/html/index.html
Possibility
Theory
Fuzzy Measures – Evidence
Theory – Necessity and Belief
Measures
–
Probability
Measures
vs
Possibility
Measures
5
Approximate
Reasoning
Fuzzy Decision Making
Fuzzy Relational Inference
C o m p o s i t i o n a l Rule
Inference - Efficiency
Inference - Hierarchical
–
of
of
7
Fuzzy
Fuzzy If-Then Rule Base –
7
Coordinators:
Dr. Balasubramaniam Jayaram
Department of MathematicsIIT Hyderabad
Controllers
Inference Engine – TakagiSugeno Fuzzy Systems Function Approximation
References:
George J Klir and Bo Yuan, Fuzzy Sets and
Fuzzy Logic : Theory and Applications, Prentice
Hall NJ,1995.
H.J. Zimmermann, Fuzzy Set Theory and its
Applications, Allied Publishers, New Delhi, 1991.
Kevin M Passino and Stephen Yurkovich, Fuzzy
Control, Addison Wesley Longman, 1998.
Michal Baczynski and Balasubramaniam
Jayaram, Fuzzy Implications, Springer Verlag,
Heidelberg, 2008.
A joint venture by IISc and IITs, funded by MHRD, Govt of India
http://nptel.iitm.ac.in