Amenability of groups and semigroups characterized by‎ ‎configuration

‎In 2005‎, ‎Abdollahi and Rejali‎, ‎studied the relations between‎ ‎paradoxical decompositions and configurations for semigroups‎. ‎In‎ ‎the present paper‎, ‎we introduce another concept of amenability on‎ ‎semigroups and groups which includes amenability of semigroups and‎ ‎inner-amenability of groups‎. ‎We have the previous known results to‎ ‎semigroups and groups satisfying this concept.