Title:  Mathematical Foundations of Fuzzy Logic 

Code:  IMF 

Ac.Year:  2018/2019 

Sem:  Winter 

Curriculums:  

Language of Instruction:  Czech 

Credits:  5 

Completion:  classified credit 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  0  26  0  0  26 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  0  0  30  0  70 



Guarantor:  Hliněná Dana, doc. RNDr., Ph.D. (DMAT) 

Deputy guarantor:  Havlena Vojtěch, Ing. (DITS) 

Instructor:  Hliněná Dana, doc. RNDr., Ph.D. (DMAT) 

Faculty:  Faculty of Electrical Engineering and Communication BUT 

Department:  Department of Mathematics FEECS BUT 

Prerequisites:  

 Learning objectives: 

  To extend an area of mathematical knowledge with an emphasis of solution searchings and mathematical problems proofs.  Description: 

  At the beginning of semester, students choose from the supplied topics. On the weekly seminars, they present the topics and discuss about them. The final seminar is for assesment of students' performance.  Knowledge and skills required for the course: 

  Knowledge of "IDA  Discrete Mathematics" and "IMA  Mathematical Analysis" courses.  Subject specific learning outcomes and competencies: 

  Successfull students will gain deep knowledge of the selected area of mathematics (depending on the seminar group), and ability to present the studied area and solve problems within it.  Generic learning outcomes and competencies: 

  The ability to understand advanced mathematical texts, the ability to design nontrivial mathematical proofs.  Why is the course taught: 

  Classical logic only describes well the black and white world. Its consistent use in practical situations can lead to problems. This can be solved with multivalued, e.g. fuzzy, logic which is the intuitive basis of any conjecture associated with vague terms. The modeling of fuzzy logic connectives is related to the study of the real variable functions. The mathematical apparatus required for the modeling of fuzzy logic connectives is the content of this course.  Syllabus of numerical exercises: 

  From classical logic to fuzzy logic
 Modelling of vague concepts via fuzzy sets
 Basic operations on fuzzy sets
 Principle of extensionality
 Triangular norms, basic notions, algebraic properties
 Triangular norms, constructions, generators
 Triangular conorms, basic notions and properties
 Negation in fuzzy logic
 Implications in fuzzy logic
 Aggregation operators, basic properties
 Aggregation operators, applications
 Fuzzy relations
 Fuzzy preference structures
 Syllabus  others, projects and individual work of students: 

  Triangular norms, class of třída archimedean tnorms
 Triangular norms, construction of continuous tnorms
 Triangular norms, construction of noncontinuous tnorms
 Triangular conorms
 Fuzzy negations and their properties
 Implications in fuzzy logic
 Aggregation operators, averaging operators
 Aggregation operators, applications
 Fuzzy relations, similarity, fuzzy equality
 Fuzzy preference structures
 Fundamental literature: 

  Alsina, C., Frank, M.J., Schweizer, B., Assocative functions:
Triangular Norms and Copulas, World Scientific Publishing Company, 2006
 Baczynski, M., Jayaram, B., Fuzzy implications, Studies in Fuzziness and Soft Computing, Vol. 231, 2008
 Carlsson,
Ch., Fullér, R., Fuzzy reasoning in decision making and optimization,
Studies in Fuzziness and Soft Computing, Vol. 82, 2002
 Kolesárová, A., Kováčová, M., Fuzzy množiny a ich aplikácie, STU v Bratislave, 2004
 Trillas, E., Eciolaza, L, Fuzzy logicAn introductory course for engineering students, Studies in Fuzziness and Soft Computing, 2015
 Study literature: 

  Alsina, C., Frank, M.J., Schweizer, B., Assocative functions:
Triangular Norms and Copulas, World Scientific Publishing Company, 2006
 Kolesárová, A., Kováčová, M., Fuzzy množiny a ich aplikácie, STU v Bratislave, 2004
 Trillas, E., Eciolaza, L, Fuzzy logicAn introductory course for
engineering students, Studies in Fuzziness and Soft Computing, 2015
 Controlled instruction: 

  Active participation in the exercises (group problem solving, evaluation of the ten exercises): 30 points. Projects: group presentation, 70 points.  Progress assessment: 

  Active participation in the exercises: 30 points. Projects: 70 points.  Exam prerequisites: 

  Students have to get at least 50 points during the semester.  
