JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2015 | Volume:1 | Issue:2|Papers Count:6

In this paper, approximately amenable modulo an ideal of Banach algebras, approximately amenable modulo an ideal of second dual of Banach algebras are investigated. Also, using the obtained results, it is shown that l1 (s)** is approximately amenable modulo Is** if and only if S/s is finite where Is is the induced ideal for the least group congruence s on S.

The role of non-Archimedean in the DEA models has been clarified, so that the associated linear programs can be infeasible (for the multiplier side) and unbounded (for the envelopment side) with an unsuitable choice of . This paper shows that the overall assurance interval for in DEA models is unique by the concept of extreme directions. Also, it presents an assurance value for using only simple computations on inputs and outputs of DMUs.

In this paper, we present an integrated version of the Ng model and Zhou and Fan model [W. L. Ng, A simple classifier for multiple criteria ABC analysis, European Journal of Operation Research, 177 (2007) 344-353; P. Zhou & L. Fan, A note on multi-criteria ABC inventory classification using weighted linear optimization, European Journal of Operation Research, 182 (2007) 148-18491]. The model that Ng [1] offered, hereafter called the Ng-model, in spite of its advantages may lead to a situation in which the weights of some criteria in relation to an item would not play any role in determining overall score that item. Also, the scale transformation that he applied for transforming the measures of items under criteria into interval 0-1 is not suitable for the small-scale measures. On the other hand, for the R inventory item, the Zhou and Fan model [2], hereafter called the ZF-model, should be solved through a linear optimizer 2R times in which an inventory manager might has no any background in regard with optimizer. Furthermore, when number of items is large, the computing time would increase. Therefore, in order to remove drawbacks of both the approaches, an integrated model is presented in which objective functions are the same ZF-method but its constraints is similar to Ng model. At last, results obtained from applying the proposed model in an illustrative example are compared with Ng and ZF-models.

In Data Envelopment Analysis (DEA), it is assumed that the role of each factor is known as input or output. However, in some cases, there are shared factors that their input versus output status is not clearly known. These are flexible measures. In such cases, determining whether a factor is input or output is ambiguous. Therefore, using fuzzy concept seems to be necessary.In this paper, a two phase procedure is proposed to fuzzy classification of flexible measures. In the first phase, applying the existing classification methods, an orientation of flexible measures to aid in the definition of inputs and outputs is achieved. Through defining a membership function in second phase, the input versus output status of a factor is expressed by fuzzy notion. By the proposed method, the efficiency of a decision mating unit is defended by a membership degree. We illustrate the proposed model in a practical problem setting.

One way to rank DMUs in DEA is the cross efficiency method. In this method, the efficiency of each DMU is calculated by other DMUs optimum weights, which makes the ranking more acceptable for managers. Existing alternative optimum weights in cross efficiency method lead to several ranks for DMUs. Several secondary goals have introduced to avoid this problem, till now. In this paper, a new model is presented, that would be satisfying and acceptable for all DMUs. Therefore, by solving this model, the optimum weights are agreeable and fairy for DMUs.

This study examines the productivity changes of decision making units in situation where input price vectors are varying between them and inputs are heterogeneous; that is a non-competitive market. We present a directional measure of cost Malmquist productivity index where incorporates the decision maker's preference over productivity change over time. A simple numerical example is designed to illustrate the new measure of the cost Malmquist index.