Fuzzy Systems

Winter 2012/13


  • The inspection of the written exams from 7 February 2013 will take place in G29-019 on 8 April 2013 from 9:00 to 11:00 a.m.


General Information

This page contains information about the lecture "Fuzzy Systems" that is read by Prof. Dr. Rudolf Kruse in the winter 2012/13. It is updated during the course.

Fuzzy set theory is an extension of the classical set theory that can model imprecise and vague expressions of natural language such as big, small, hot, cold, etc. Fuzzy logic allows to formalize rules that contain such expressions of natural language. These rules can be utilized to support decision processes. The lecture "Fuzzy Systems" offers an introduction to both fuzzy set theory and fuzzy logic. Moreover it deals with applications of control engineering, approximate inference and data analysis.

Note that since "Fuzzy Systems" is a master course, both lecture and exercise will be given in English. There might be German assignment sheets on request.

back to top

Schedule and Rooms

back to top


If you have questions regarding the lecture or exercise, please contact (via e-mail if possible) one of the persons named below.

back to top

Conditions for Certificate ("Schein") and Exam

A new assignment sheet containing written and programming assignments is published on this web page every week. The written assignments must me ticked of at the beginning of every exercise. Ticking off an assignment you agree to be able to explain and present the assignment and your solution proposal (which need not to be completely correct. However, you should be prepared thoroughly in order to solve the assignment).

Programming assignments must be submitted in electronic form to Christian Moewes before 8 o'clock in the morning of the corresponding exercise day. Late assignments will not be accepted. The programs must run properly on the SUN pool machines in the faculty of computer science.

The certificate for this course is issued to students who

  • regularly contribute well in the exercises,
  • tick off at least two third of all written assignments,
  • present at least twice a solution to a written assignment during the exercise,
  • submit at least twice a running implementation of a programming assignment, and
  • finally pass the written exam after the course.

Students who want to finish the course with an exam or a marked certificate must

  • regularly contribute well in the exercises,
  • tick off at least half of all written assignments,
  • present at least twice a solution to a written assignment during the exercise,
  • officially announce the exam to the examination office by using HISQIS.
  • finally pass the written exam after the course.

The written exam is scheduled on Thursday, February 7, 2013 in the FIN auditorium (G29-307) from 12:30 until 14:30 o'clock.

back to top


You do not need but should have background knowledge about

  • mathematics (especially algebra and convex optimization theory),
  • computer science (algorithms, data structures, etc.) and
  • machine learning or data mining.
back to top

Slides from the Lecture

The slides from the lecture will be published here incrementally as the course proceeds.

back top top


The collection of assignment sheets will be updated weekly at this location.

  • assignment sheet 01 due 09/10/2012 (Set Theory and Boolean Algebra)
  • assignment sheet 02 due 16/10/2012 (Basics of Fuzzy Sets)
  • assignment sheet 03 due 23/10/2012 (Boolean Algebra, alpha-cuts)
  • There was no assignment sheet for 30/10/2012 due to the missing lecture on 22/10/2012.
  • assignment sheet 04 due 06/11/2012 (Fuzzy Set Operations)
  • assignment sheet 05 due 13/11/2012 (Fuzzy Implications, Extension Principle) This assignment sheet was discussed on 20/11/2012.
  • assignment sheet 06 due 20/11/2012 (Fuzzy Relations) This assignment sheet was discussed on 27/11/2012.
  • assignment sheet 07 due 27/11/2012 (Fuzzy Set Operations, Set Representation, Quantifiers, Linguistic Variables)
  • assignment sheet 08 due 04/12/2012 (Fuzzy Arithmetics, Quantifiers, Mamdani-Assilian Controller)
  • assignment sheet 09 due 11/12/2012 (Mamdani-Assilian and Takagi-Sugeno Control)
  • assignment sheet 10 due 18/12/2012 (Fuzzy Control based on Relational Equations, System of Relational Equations, Similarity Relations)
  • There was not any assignment sheet for 08/01/2013 due to the missing lecture on 07/01/2013.
  • assignment sheet 11 due 15/01/2013 (Fuzzy Clustering, Noise Clustering)
  • assignment sheet 12 due 22/01/2013 (Theory of Evolution, Evolutionary Fuzzy System)
back top top

Additional Material

Feel free to check out the following supplementary material that augment the lecture and exercise.

back to top


  • about fuzzy systems
    • R. Kruse, C. Borgelt, P. Held, C. Moewes, M. Steinbrecher (2012). Computational Intelligence. Springer, New York (to appear).
    • R. Kruse, C. Borgelt, F. Klawonn, C. Moewes, G. Ruß, M. Steinbrecher (2011). Computational Intelligence. Vieweg+Teubner, Wiesbaden.
    • C. Borgelt, F. Klawonn, R. Kruse, D. Nauck (2003). Neuro-Fuzzy-Systeme (3rd edition). Vieweg, Braunschweig/Wiesbaden.
    • G.J. Klir and B. Yuan (1995). Fuzzy Sets and Fuzzy Logic - Theory and Applications. Prentice Hall, Upper Saddle River, NJ.
    • R. Kruse, J. Gebhardt, and F. Klawonn (1994). Fuzzy-Systeme (2nd edition). Teubner, Stuttgart.
    • R. Kruse, J. Gebhardt, and F. Klawonn (1994). Foundations of Fuzzy Systems. Wiley, Chichester.
    • K. Michels, F. Klawonn, R. Kruse, and A. N├╝rnberger (2002). Fuzzy-Regelung. Springer-Verlag, Heidelberg.
  • about machine learning and data mining
    • D. Hand and M. Berthold (2002). Intelligent Data Analysis: An Introduction (2nd edition). Springer-Verlag, Berlin.
    • T. Mitchell (1997). Machine Learning. McGraw Hill, New York, NY.
back to top


back to top
en lang icon de lang icon Printable View - Recent Changes
Page last modified on March 26, 2013, at 04:03 PM by cmoewes