Fuzzy measures and integrals | Faculty of Technical Sciences

Subject: Fuzzy measures and integrals (17.D0M50Z)

Native organizations units: Department of Fundamentals Sciences

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

General information:

Category	Professional-applicative
Scientific or art field	Teorijska i primenjena matematika
ECTS	10

The students learn about theoretical overview, methods and applications of fuzzy measures and integrals.

The students are capable of independent scientific work. The acquired knowledge can be used in solving practical problems using mathematical models based on fuzzy integrals.

The course content includes the following topics. Non-additive set functions. Fuzzy measures. Generalized fuzzy measures (fuzzy bi-measures, real fuzzy measures). Co-monotone functions. Fuzzy measures based integrals. (Choquet integral, Sugeno integral, Shilkret integral). Convergence theorems. Symmetric and asymmetric extension of fuzzy integrals. Applications of fuzzy integrals and their extensions in decision theory, mathematical psychology and pattern recognition. Study and research work includes relevant scientific literature.

Lectures. Consultations. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. Through homework assignments, work with the course teacher and study of the scientific journals and other relevant literature, the students are prepared for independent work on writing a scientific paper.

Authors	Title	Year	Publisher	Language
M. Grabisch, T. Murofushi, M. Sugeno, editors	Fuzzy Measures and Integrals-Theory and Applications	2000	Physica-Verlag	English
E. Pap, editor	Handbook of Measure Theory	2002	Elsevier	English
D. Denneberg	Non-Additive Measure and Integral	1994	Kluwer Academic Publishers	English
E. Pap	Null-additive Set Functions	1995	Kluwer Academic Publishers	English