Distance-based clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian Density Distance (GDD) approach was proposed to optimize local criteria in terms of Distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and Distance properties of remaining unclustered samples. Here, we introduce Adaptive GDD (AGDD), which eliminates the inappropriate effect of clustered samples by adaptively updating the parameters during clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The Distance metrics calculating the dissimilarity between samples can affect the clustering performance. The effect of different Distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known clustering methods.

In this research, By using data envelopment analysis method and output Distance Functions to decomposes energy productivity change into four components; technical efficiency change, technological change, changes in capital to energy ratio and labor in energy ratio In the industrial sector of the country Iran during the period 2014-2004. To this end, the output-axis data envelope analysis method has been used with the assumption of constant returns to scale. The results show that the effect of changing the ratio of capital to energy is a major factor in reducing the of energy intensity in the industrial sector of the Iran, changes technological progress, changes labor-energy ratio and changes technical efficiency drove up energy intensity in most industries.

In this paper, we evaluate the aggregation of Farrell's efficiency indices. Due to this fact that the industry minimum cost is equal to the sum of minimum unit costs, we find conditions on this aggregation. Some conditions are introduced under which the industry efficiency can be obtained from the efficiency of individual firms.

Regarding environmental importance and the lack of analytical methods for environmental policies, in this paper, shadow price for NOx and SOx emissions has been estimated for the Iranian electric industry. Input Distance Function is used for estimating shadow prices. The estimated shadow prices have revealed that the cost of Iranian electric industry for reducing one KG of NOx and Sox is 14991 and 17687 Rials, respectively. Estimated shadow prices in this study are greater than the amount offered by EPO (Environment Protection Organization) and World Bank. So it is recommended that any fine should be taken according to the emission shadow price.

In conventional DEA methods, all Inputs and outputs are assumed to be continuous. However, the implied presumption of continuous data may not maintain an acceptable level of precision in practical data. Many practical situations such as number of teachers in a school, number of students in a college, or research papers only take integer values. Presented work presumes subsets of Input and output variables in traditional , ve-pronged axioms in DEA model to be integer values for the , rst time in the , eld. An additional e, ort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the , rst phase produces more precise e, ciency values and the best benchmark in its second phase, i. e. the nearest integer point to the e, ciency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of e, ciency values obtained with this model compared to prior models that is show in table 1. And in Table 2, the values of the slack are compared with each other.

Iran is one of the most energy-rich countries subsidizing energy carriers, especially in the agricultural sector, to the extent that the resulting growth is at the expense of the environment. This study tries to investigate the potential impacts of energy price reform on the agro-environment, based on the Marginal Abatement Costs (MACs) of emissions. Firstly, the energy demand Function of the agricultural sector and the probable reaction of Inputs and outputs to the reform were estimated. Then, using an Input Distance Function (IDF), the country and provincial-wide MAC were simulated through counterfactual reform scenarios. The results indicated that energy price reform would increase the MAC of emissions and socio-environmental benefits. However, the reform adversely affected the income of farmers. Also, the results provided detailed information both at a nationwide and provincial scale. Finally, it was recommended to implement complementary policies alongside reforms to compensate for the reduction in farmers’ income.