Abstract and Applied Analysis
Volume 2012 (2012), Article ID 260457, 11 pages
http://dx.doi.org/10.1155/2012/260457
Research Article

Generalized Caratheodory Extension Theorem on Fuzzy Measure Space

Mehmet Şahin, Necati Olgun, F. Talay Akyıldız, and Ali Karakuş

Department of Mathematics, Faculty of Arts and Sciences, University of Gaziantep, 27310 Gaziantep, Turkey

Received 23 April 2012; Revised 28 June 2012; Accepted 10 October 2012

Academic Editor: Alberto D'Onofrio

Copyright © 2012 Mehmet Şahin et al. 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

Lattice-valued fuzzy measures are lattice-valued set functions which assign the bottom element of the lattice to the empty set and the top element of the lattice to the entire universe, satisfying the additive properties and the property of monotonicity. In this paper, we use the lattice-valued fuzzy measures and outer measure definitions and generalize the Caratheodory extension theorem for lattice-valued fuzzy measures.