Iranian Journal of

In the present time, evaluating the performance of banks is one of the important subjects for societies and the bank managers who want to expand the scope of their operation. One of the non-parametric approaches for evaluating efficiency is data envelopment analysis(DEA). By a mathematical programming model, DEA provides an estimation of efficiency surfaces. A major problem faced by DEA is that the frontier calculated by DEA may be slightly distorted if the data is affected by statistical noises. In recent years, using the neural networks is a powerful non-parametric approach for modeling the nonlinear relations in a wide variety of decision making applications. The radial basis function neural networks (RBFNN) have proved significantly beneficial in the evaluation and assessment of complex systems. Clustering is a method by which a large set of data is grouped into clusters of smaller sets of similar data. In this paper, we proposed RBFNN with the K-means clustering method for the efficiency evaluation of a large set of branches for an Iranian bank. This approach leads to an appropriate classification of branches. The results are compared with the conventional DEA results. It is shown that, using the hybrid learning method, the weights of the neural network are convergent.

In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p-cuts and small cuts. In particular, we prove some overspill and underspill properties for them.

In this paper, we introduce a new class of (semi)hypergroup from a given (partially) quasi-ordered (semi)hypergroup as a generalization of {it "$El$--hyperstructures"}. Then, we study some basic properties and important elements belong to this class.