International Journal of Industrial Mathematics
Volume:15 Issue: 3, Summer 2023

The current research intends to apply an extended version of articial neural networks approach for solving a linear fractional Volterra integro-dierential equation. More precisely, our main discussion in this study is to answer this fundamental question practically: That is, would it be possible to speed up the convergence of a given neural network structure by substituting the standard rst-order derivative with a fractional order one. It is worth mentioning that, there is no certain geometric interpretation for fractional order derivative of a continuous function at a point in the domain. But, we strongly believe that this derivative calculus might help us to discover an ecient iterative technique to approximate solution of the earlier mentioned math problem. In this way, two simple but typical comparative test problems are given, and the related salient features of this technique are also discussed.

Diagnosis of covid-19 using deep learning on CT scan images can play an important role in helping doctors. In this paper, by combining EfficientNet-B2 and vision transformers (V iT − 1 − 32) neural networks a new deep transfer learning is proposed. For evaluation, con-fusion matrix, precision, accuracy, recall, and F1 score are used. The experimental results are 0.9838 for validation accuracy, 0.9667 for test accuracy, and 0.9839 for accuracy.

The particle size distribution provides important information about soil engineering properties. Finer particles are usually determined by classical sedimentation methods such as hydrometer tests. These methods are based on simplifying assumptions and despite operational complexities, the obtained results are not precise. At this time, Image Processing methods were used in dierent industries to obtain various information about size distributions and particle shape analysis. The present research suggests the image processing method based on the analysis of microscopic images of stable particles (static method) for determining the size and shape distribution of the ne-grained fraction of the soil. The images of ne-grained soil particles prepared with optical microscopes were analyzed to generate information about particle size and shape. By comparing gradation curves obtained with image processing and hydrometric methods, we found that there is more adaptation in the range of 40 to 70 microns of particle sizes. Investigations have shown that in this range, the shape of the particles has less diversity and is closer to the perfect sphere form. This study found that image processing while reducing costs, could provide more comprehensive information and would be expected to be used in geotechnical laboratories.

Data envelopment analysis (DEA) obtains the relative eciency of decision-making units (DMUs) based on their inputs and outputs. In many situations, some variables can play the role of input or output for a DMU. It is important to provide a suitable model that can maximize the eciency of the unit under evaluation by correctly choosing the role of these variables. One of the production technologies in DEA is semi-additive production technology. In addition to the observed DMUs, this technology also considers the set of all aggregations corresponding to these DMUs in the evaluation of eciency. In this paper, we presented the semi-additive production technology in DEA in the presence of exible measures. This technology is created based on the observed DMUs and their corresponding aggregations DMUs. We have shown that we can provide semi-additive production technology in the presence of exible measures based only on the observed DMUs by removing the region with decreasing returns to scale from the production possibility set (PPS). In the following, we present two dierent approaches for measuring the eciency of DMUs in the presence of exible measures in semi-additive production technology. These two approaches allocate exible measure as input or output in such a way that the eciency of the unit under evaluation is maximized. Also, we use the proposed approach to evaluate the eciency of data sets related to academic units.

This research aims to evaluate the efficiency of a two-stage network structure by examining the impact of contextual variables on its performance. To accomplish this, a two-stage approach is implemented, which involves network data envelopment analysis (NDEA) in the first step and ordinary least squares (OLS) analysis in the second step. In the first step, a non-cooperative (Leader-Follower) model is employed to assess the efficiency of each sub-section within the two-stage process based on their inputs and outputs. In the second step, the logarithm of the estimated efficiency scores is regressed on the contextual variables to refine the network-specific efficiency. The performance of various Spanish airports is analyzed to demonstrate the effectiveness of this approach.

An important and core issue for the managers of banking sector is to evaluate and rank the branches of a bank. In this study, a typical multi-criteria ranking problem for the Tose’e Ta’avon bank branches in Khuzestan province of Iran as a case study is defined and solved. For this aim, first a set of important criteria for evaluating banking sector are selected from the literature and experts of the field. Then, for coping with the uncertain nature of the real-life problems, the data of the bank branches in the selected criteria for the past years are obtained and represented as interval values. A decision framework consisting of two phases are proposed to rank the given bank branches. In the first phase the criteria are weighted by the methods such experts’ opinions, interval Shannon’s entropy, and linear combination of these two methods. In the second phase, the classical PROMETHEE approach is extended to its interval form and applied to rank the bank branches. By implementing the proposed solution methodology on the case study, several rankings are obtained and their similarities are compared to each other. The decision maker can consider any of the rankings for further managerial decisions.

The study of finite semigroups is of interest because of its application inseveral branches of science, for instance, its uses and advantages in mathematics, computer science and finite machines are well-known. The power graph associated to such semigroups is also an applicable tool in demonstrating the properties of semigroups. The completeness and Eulerianity of power graphs associated to finite commutative semigroups and finite non-commutative epigroups are studied in this paper. We show that these graphs may be non-complete for the monogenic semigroups and we gives a necessaryand sufficient condition for such graphs to be complete when finite regular epigroups are considered. This study answers in part the natural question”Is there any non-isomorphic non-group semigroups with the same complete power graph?”