International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 356581, 11 pages
doi:10.1155/2010/356581
Research Article

(L,M)-Fuzzy σ-Algebras

Fu-Gui Shi

Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China

Received 23 August 2009; Revised 19 December 2009; Accepted 19 January 2010

Academic Editor: Andrei Volodin

Copyright © 2010 Fu-Gui Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The notion of (L,M)-fuzzy σ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzy σ-algebras. In our definition of (L,M)-fuzzy σ-algebras, each L-fuzzy subset can be regarded as an L-measurable set to some degree.