Mathematical basis of the fuzzy systems | Faculty of Technical Sciences

Subject: Mathematical basis of the fuzzy systems (17.D0M07L)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Year: 1, Semester: Summer)

General information:

Category	Scientific-professional
Scientific or art field	Applied Computer Science and Informatics Teorijska i primenjena matematika
ECTS	10

Enabling students to develop abstract thinking and acquire knowledge about the theory of fuzzy systems. The goal is to develop in the student the way of thinking that will enable recognizing the possibility of application of the theory of fuzzy systems in various scientific disciplines.

To use the acquired knowledge in engineering subjects and in practice, postulate and solve mathematical models in engineering subjects using the knowledge about fuzzy systems. These models usually stem from practice and often require multidisciplinary knowledge for their successful solving.

Theoretical part of the course (lectures): Fuzzy sets. Fuzzy arithmetic. Fuzzy logic. Fuzzi topological spaces. Fuzzy metric spaces. Fuzzy measures and integrals. Fuzzy statistics. Part of the course is organized in the form of independent study and research work in the field of mathematics. The study and research work is based on active study of primary scientific sources, organization and performing of experiments, and statistical processing of data, numerical simulations, with the option of writing a paper in the field of mathematics.

Lectures. Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. In addition to lectures there are regular consultations. The students can take partial exams during the course. A part of the course material (which represents a unit of course subject matter) is presented orally and submitted as a written seminar paper. The oral part of the final examination is eliminatory. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Authors	Title	Year	Publisher	Language
V. P. Maslov, S. N. Samborskij (eds.)	Idempotent Analysis	1992	Adv. in Soviet Math.13, Amer.Math.Soc.,Provid.	English
Grabisch M., Nguyen H. Walker E. A.	Fundamentals of Uncertainty Calculi with Application to Fuzzy Inference	1995	KluwerAcademicPublishers,Dordrecht-Boston-London	English
Klir, G.J., Yuan, B.	Fuzzy Sets and Fuzzy Logic: Theory and Applications	1995	Prentice Hall, Upper Saddle River, New Jersey	English
Wang, Z., Klir J. G.	Fuzzy Measure Theory	1992	Plenum Press, New York and London	English
P. Klement, R. Mesiar, E. Pap	Triangular norms	2000	Kluwer Academic Publishers, Dordrecht	English

Course activity	Pre-examination	Obligations	Number of points
Lecture attendance	Yes	Yes	5.00
Practical part of the exam - tasks	No	Yes	25.00
Theoretical part of the exam	No	Yes	40.00
Project defence	Yes	Yes	10.00
Term paper	Yes	Yes	20.00