Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Fuzzy systems and applications (17.D0M21Z)

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Year: 2, Semester: Winter)

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 fundamental knowledge about the selected topics in mathematics such as data bases, pattern recognition, image processing, decision theory and the application of fuzzy systems in these fields. The character of the course is applicative. Thus, the students should master the techniques of creating appropriate mathematical models that will be used in solving practical problems from applicative domains.

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.

Theoretical part (lectures). Fuzzy and ordinary sets.Approximate reasoning. Fuzzy systems. Fuzzy data bases. Pattern recognition. Image processing. Shape analysis. Fuzzy decision theory. Engineering applications. Application of fuzzy systems in medicine, economics, actuarial, ecology. Computer use – fuzzy toolbox. 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 choose in coordination with the course teacher 1-3 areas and can also take partial exams in each of these areas during the course. A student is expected to write a seminar paper in one of these subject areas which is presented orally. During the course the students do a project-program (C,Pascal,Matlab,Mathematica) for a given problem. 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
Wang, Z., Klir J. G.	Fuzzy Measure Theory	1992	Plenum Press, New York and London	English
V. P. Maslov, S. N. Samborskij (eds.)	Idempotent Analysis	1992	Adv. in Soviet Math.13, Amer.Math.Soc., Provi.	English
Klir, G.J., Yuan, B.	Fuzzy Sets and Fuzzy Logic: Theory and Applications	1995	Prentice Hall, Upper Saddle River, New Jersey	English
P. Klement, R. Mesiar, E. Pap	Triangular norms	2000	Kluwer Academic Publishers, Dordrecht	English
Grabisch M., Nguyen H. Walker E. A.	Fundamentals of Uncertainty Calculi with Application to Fuzzy Inference	1995	KluwerAcademicPublishers, Dordrecht-Boston-London	English