Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0972.28010
Butnariu, Dan; Klement, Erich Peter
Measures on triangular norm-based tribes: Properties and integral representations. (English)
[A] Grabisch, Michel (ed.) et al., Fuzzy measures and integrals. Theory and applications. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 40, 233-246 (2000). ISBN 3-7908-1258-7/hbk

The paper gives an overview about real-valued measures on triangular norm-based tribes. The domain of these measures are certain classes of fuzzy sets (i.e., $[0,1]$-valued functions) which are proper generalizations of $\sigma$-algebras and where the set theoretical operations are derived from triangular norms. The authors first present several particular triangular norms $T$ and discuss the corresponding $T$-tribes. For measures on $T$-tribes with respect to particular triangular norms $T$, the paper contains integral representations, a Jordan decomposition theorem and a Lyapunov type theorem. The paper concludes with several open problems some of which are related to the article of {\it G. Barbieri} and {\it H. Weber} [J. Math. Anal. Appl. 244, No. 2, 408-424 (2000; Zbl 0965.28010)].
[Hans Weber (Udine)]

MSC 2000:: *28E10 Fuzzy measures

Keywords: Lyapunov theorem; triangular norm-based tribes; integral representations; Jordan decomposition

Citations: Zbl 0965.28010

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]