Fuzzy Systems

There will be no lectures on May 30th and June 6th.



This page contains information about the lecture "Fuzzy Systems" that is read by Prof. Dr. Rudolf Kruse in summer 2019. 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.


Lectures and Tutorials



 Lecture:  Thursdays 9:15-10:45 in G29-E037

 Exercise Class 1: Monday 3pm-5am in G29-K059

 Exercise Class 2: Wednesday, 3pm - 5pm in G29-K059


Conditions for Exams


A new assignment sheet containing written and programming assignments is published on this web page every week. The written assignments must me ticked off at the beginning of every exercise. Ticking off an assignment means that you are willing and able to explain and present the assignment and your solution proposal (which does not need 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 Alexander Dockhorn. Latest submission is possible until four days before the corresponding exercise day at 8:00 a.m. Later submissions will not be accepted. The programs must run properly in the programming language discussed in the exercise. Submissions can be performed as teams of up to three students, as long as all team members are named in the submission and every single team member is able to present the solution.

The graded certificate for this course is issued to students who

  • regularly contribute well in the exercises,
  • tick off at least one half of all written assignments,
  • present at least twice a solution to a written assignment during the exercise (this number is reduced in case not everybody can present twice due to the number of exercises)
  • finally pass the exam after the course.

Note that graded exams have to be officially announced to the examination office. The date of the written exam is not yet fixed. When this is the case, it will be announced here.




0 Introduction PDF The lecture will start on April 4th, the first lecture will be held in G02-311
1 Fuzzy Sets and Fuzzy Logic PDF updated \sim operator
 2 Approximate Reasoning  PDF Updated on June 27, renamed the chapter
3 Fuzzy Control PDF  
4 Fuzzy Data Analysis PDF  
5 Learning Fuzzy Systems PDF  updated ANFIS Model figure



You should have some background knowledge about

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


Exercise Sheets Assignments:

There will be no exercise class on 29 May due to the Day of Teaching. The Wednesday exercise will be discussed a week later.

ID Topic       Due Date per Group      Exercise Sheet
         Monday       Wednesday   
1 Set Theory and Boolean Algebra 15.04. 17.04. PDF
2 Boolean Algebra, Linguistic Terms 29.04. 24.04. PDF
3 Alpha-cuts 06.05. 08.05. PDF
4 Fuzzy Set Operations 13.05. 15.05. PDF
5 Fuzzy Implication, Extension Principle 20.05.  22.05. PDF
6 Fuzzy Relations  27.05.  05.06. PDF
7 Fuzzy Relational Equations  03.06. 12.06. PDF
8 Mamdani-Assilian Control  17.06. 19.06. PDF
9 Quantifiers, Takagi-Sugeno Control  24.06.  26.06. PDF
10 Summary  01.07.  03.07. PDF


 Past Exams:






Last Modification: 04.07.2019 - Contact Person: Webmaster