فهرست مطالب ساناز اسدی رحمتی

Group  is called metacyclic if it contains a normal cyclic subgroup such that the quotient group  is also cyclic. In this paper, two conjectures proposed by Abdollahi et al. (2006) for a family of finite non-abelian metacyclic prime power groups  were investigated. For this purpose, first, the metacyclic groups were categorized into three Types (families) of the non-isomorphic groups. Next, by using the size of centralizers and also equality of the conjugacy vector type ctv (G) of these groups, the necessary and sufficient conditions under which two non-abelian finite metacyclic prime power groups have the isomorphic non-commuting graphs were determined. The first conjecture of Abdollahi et al. for the three families of the classified groups was proven to be true. Likewise, the second conjecture held for some restrictions on the parameters of group . Finally, it was demonstrated that there were non-isomorphic groups with the same non-commuting graphs.

Data envelopment analysis is taken widespread into consideration in the various science to evaluate the relative efficiency of decision making units that have a multi-stage network structure. In this paper, a bargaining game model is extended to evaluate the efficiency of decision making units with a multi-stage network structure. Moreover, each stage of network data envelopment analysis (DEAN) is considered as a game player. Accordingly, the allocated fixed cost is divided among all the stages such that the best allocation is made to the best stage. With a newer idea, the intermediate stage in the data envelopment analysis of three-stage networks is considered as a common player in the bargaining game, so that the stage plays a significant role in maximizing the performance of network. Next, an alternative approach to allocating a common fixed cost in a multi-stage network based on the bargaining game is proposed. Finally, as direct apllication of the performance of the proposed models some examples are given.

Evaluation of decision-making units is very importantin economic and management systems. Data envelopment analysis is one of the scientific and practical techniques for evaluating decision making units. In the conventional models of data envelopment analysis, the units are divided into efficient and inefficient categories, where the efficiency of each efficient unit is one and there is no distinction between efficient units.This study intends to propose a new way of ranking efficient units based on the concepts of cooperative game. The proposed method is that efficient units are considered as players of a cooperative game. A subset of these players is defined as the coalitionS.Then the sum of the efficiency of the inefficient units according to the production possibility set that is created by the inefficient units and the members of the coalitionS is defined as the characteristic function of S, which is used to determine the marginal effect of the efficient units in the various coalitions. Finally, the Shapley value is used to determine the cooperative game solution and rank the efficient units.In the same way that it is able to rank non-extreme units, inefficient units are also effective in ranking, alsois feasiblein any circumstances of return to scale.