Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43619991130Entropy of a semigroup of maps from a set-valued view182118351067ENB.HouCollege of Mathematics, Jilin university, 130012, Changchun, P. R. China.X.WangCollege of Mathematics, Jilin university, 130012, Changchun, P. R. China.Journal Article19991130In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreover, some notions of chaos are also well generalized for finitely generated semigroups from a set-valued view.http://bims.iranjournals.ir/article_1067_479aa58a4bb53422d87b5956ff62afe4.pdf