Decompositions and range for additive fuzzy measures
Fuzzy Sets and Systems
Some properties of the variations of non-additive set functions on T-tribes
Fuzzy Sets and Systems
| Hi-index | 0.20 |
In this paper Liapounoff's Theorem for fuzzy measures is proved and it is applied to extend a theorem of Aumann and Shapley [2] concerning the existence of the value for non-atomic games. Precisely, it is proved that the range of any non-atomic n-vector fuzzy measure (in the sense of [6]) is convex and compact and it is shown that this result allows to extend Theorem B from [2, p. 23] from games with unambiguous coalitions to games with fuzzy coalitions (called fuzzy games) defined on @s-algebras of fuzzy sets (which are not necessarily @s-algebras of 'ideal sets').