Non-atomicity for fuzzy and non-fuzzy multivalued set functions
In this paper, we extend the concept of set-valued fuzzy measures (introduced and studied by Guo and Zhang [2004. On set-valued fuzzy measures. Information Sciences 160 (2004) 13-25]) to the class of multivalued set functions taking values in the family of non-empty closed subsets of a real normed space. Also. we introduce the notions of atom and non-atomicity of a multivalued set function and present some of their properties. We also establish an extension result by preserving non-atomicity for a fuzzy multisubmeasure/multimeasure. (C) 2008 Elsevier B.V. All rights reserved.
non-atomic atom multisubmeasure multimeasure fuzzy multivalued set function