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Data envelopment analysis (DEA) obtains the relative efficiency 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 efficiency 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 efficiency. In this paper, we presented the semi-additive production technology in DEA in the presence of flexible 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 flexible 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 different approaches for measuring the efficiency of DMUs in the presence of flexible measures in semi-additive production technology. These two approaches allocate flexible measure as input or output in such a way that the efficiency of the unit under evaluation is maximized. Also, we use the proposed approach to evaluate the efficiency of data sets related to academic units. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some n-tuple fixed point and n-tuple coincidence point results in C*-algebra-valued metric spaces using the concept of an α-series applied to a series of mappings. At the end of the paper, we give an example and an application to support our main results. [ABSTRACT FROM AUTHOR]

Fuzzy analytical hierarchy process (FAHP) is one of the most popular multi-criteria decision making (MCDM) techniques in which the weights of criteria and the evaluation measures of alternatives are generated based on fuzzy pairwise comparisons. There are many approaches for determining the weights from pairwise comparison matrices (PCM). Some of them have calculated the interval weights at all alphacuts. However, in some MCDM techniques (like technique for order preference by similarity to ideal solution (TOPSIS), vlsekriterijumska optimizacija i kompromisno resenje (VIKOR), and FAHP), it is needed to calculate normalized crisp weights. In this paper, the authors extend an index where interval weights obtained at all alphacuts are converted into the crisp weight. Finally, several illustrative examples in the literature are considered to show the verification of the proposed index and the obtained results are then compared with weights extracted by fuzzy preference programming (FPP). The results show that our approach is suitable for obtaining the crisp weights and also, has the similar ranking orders with those of the others. [ABSTRACT FROM AUTHOR]

This paper presents a new inventory model for deteriorating items, allowable shortages, and stochastic inationary conditions, considering a belief-rule-base inventory control (BRB-IC) method. This is a new insight in comparison with the previous research, which considers a belief-rule-based inventory control under nonstationary demand. The Genetic Algorithm and exact methods have been considered for minimizing the objective function. The numerical example and a sensitivity analysis provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

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 five-pronged axioms in DEA model to be integer values for the first time in the field. An additional effort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the first phase produces more precise efficiency values and the best benchmark in its second phase, i.e. the nearest integer point to the efficiency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of efficiency 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. [ABSTRACT FROM AUTHOR]

Benchmarking is a tool for evaluating organizational performance with a learning approach from oth)ers. The importance of benchmarking in every industry is clear for anyone. In the automotive industry, the performance of after-sales service agencies in Iran is evaluated every year by Iran Standard and Quality Inspection company. One of the ways to continuously improve in after-sales service agencies is benchmarking of successful and efficient examples in the network. In this paper, a benchmarking model is developed considering that the repair index and customer satisfaction are interdependent. To improve the accuracy and operationality of benchmarking, some constraints have been added to the model with the opinion of experts. Considering the dependent parameters, a data envelopment analysis model has been proposed and this model has been implemented to benchmark 20 after-sales service agencies of a car company. By solving the model and comparing it with the results of the original model, it was observed that the considered conditions changed the benchmarking and in)creased the accuracy. This paper discusses the concept of the impact and importance of dependent parameters in benchmarking, and with this concept, a benchmarking model for automotive after-sales service agencies is presented. [ABSTRACT FROM AUTHOR]

This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the main problem becomes a system of algebraic equations that we can solve numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical tests are provided to demonstrate the generality, efficiency, accuracy of presented scheme and the flexibility of this technique. The numerical experiments compared it with other existing methods such as Reproducing Kernel Hilbert Space method (RKHSM). Comparing the results of these methods as well as comparing the current method (NSJOM) with the true solution, indicating the validity and efficiency of this scheme. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated. [ABSTRACT FROM AUTHOR]

Benchmarking is a tool for evaluating organizational performance with a learning approach from others. The importance of benchmarking in every industry is clear for anyone. In the automotive industry, the performance of after-sales service agencies in Iran is evaluated every year by Iran Standard and Quality Inspection company. One of the ways to continuously improve in after-sales service agencies is benchmarking of successful and efficient examples in the network. In this paper, a benchmarking model is developed considering that the repair index and customer satisfaction are interdependent. To improve the accuracy and operationality of benchmarking, some constraints have been added to the model with the opinion of experts. Considering the dependent parameters, a data envelopment analysis model has been proposed and this model has been implemented to benchmark 20 after-sales service agencies of a car company. By solving the model and comparing it with the results of the original model, it was observed that the considered conditions changed the benchmarking and increased the accuracy. This paper discusses the concept of the impact and importance of dependent parameters in benchmarking, and with this concept, a benchmarking model for automotive after-sales service agencies is presented. [ABSTRACT FROM AUTHOR]

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 five-pronged axioms in DEA model to be integer values for the first time in the field. An additional effort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the first phase produces more precise efficiency values and the best benchmark in its second phase, i.e. the nearest integer point to the efficiency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of efficiency 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. [ABSTRACT FROM AUTHOR]

This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the main problem becomes a system of algebraic equations that we can solve numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical tests are provided to demonstrate the generality, efficiency, accuracy of presented scheme and the flexibility of this technique. The numerical experiments compared it with other existing methods such as Reproducing Kernel Hilbert Space method (RKHSM). Comparing the results of these methods as well as comparing the current method (NSJOM) with the true solution, indicating the validity and efficiency of this scheme. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated. [ABSTRACT FROM AUTHOR]

Standard Data Envelopment Analysis (DEA) supposes that the performance measure status from the point of view of input or output is known. Nevertheless, in some situations, determining the status of a performance measure in two-stage network is not easy. Measures with unknown status of input/output are called exible measures. In all of the previous studies did not point to classify exible measures in two-stage network DEA. In this paper we propose FNDEA models based on the multiplier model under constant returns to scale (CRS) and variable returns to scale (VRS) in general two-stage network structures. Our models classify exible measures, in which each one of the exible measure is treated as either input or output to maximize the overall network efficiency of the DMU under evaluation. The current paper develops an additive efficiency decomposition approach wherein the overall efficiency is expressed as a (weighted) sum of the efficiencies of the individual stages. This approach can be applied under both CRS and (VRS) assumptions. Numerical examples are used to illustrate the procedures. [ABSTRACT FROM AUTHOR]

This paper proposes a DEA-based model for analyze the fuzzy risk in project selection. We used concept semi-variance for measure upper and downside risk and a DEA model for classification desirable and undesirable risk. Firstly, the proposed model includes new desirable and undesirable risk-return indexes. Thus a novel DEA model is presented for evaluation and classification desirable and undesirable risks and finally, is extend to fuzzy DEA model for project portfolio selection. An applied example is used to explain the proposed approach and usefulness and applicability of this approach have been illustrated using the 37 available projects. [ABSTRACT FROM AUTHOR]

This paper deals with benchmarking for a three-stage DMU. After investigating and eliminating congestion, adjustment of intermediate products and initial inputs have achieved by utilizing an Inverse DEA model, which dominates the current vectors and serve as a benchmark that is to the best of this paper knowledge. This process has two cases. First, the overall efficiency stays fixed, and the second case, is corresponded to the overall efficiency improvement. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of second-order fuzzy initial value problems that are known as the Cauchy-Euler differential equations, in the crisp case. This work begins by studying the structure of solution function in the crisp case and providing a requirement space of the generalized differentiable functions. In sequel, the process of production and construction of the solution formula are discussed, in details. Finally, the obtained formulas are applied and illustrated by solving some examples. [ABSTRACT FROM AUTHOR]

Identification of various sources of inefficiency plays an important role in the performance analysis aimed at developing plans for the improvement of decision making. In this regard, not only technical, cost, and allocative efficiency can be estimated by information on inputs and outputs and their prices, but losses due to the lack of profit and revenue and optimal cost can also be calculated based on the relevant inefficiency. The present paper aimed at providing new estimation of cost efficiency and sources of losses in the total efficiency in a non-competitive environment where there is the possibility of change in prices of inputs and outputs from one DMU to another. In line with studies (K. Tone, A Strange Case of the Cost and Allocative Efficiencies in DEA, Journal of the Operational Research Society 53 (2002) 1225-1231) and (K. Tone et al., Ecomposition of Cost Efficiency and its Application to Japanese-Us Electric Utility Comparisons, Socio-Economic Planning Sciences 47 (2007) 91-106), the present study sought to introduce new sources of inefficiency and related losses by presenting new price-based and cost-based production possibility set. [ABSTRACT FROM AUTHOR]

Data Envelopment Analysis is a technique based on mathematical planning for specifying the efficiency of decision making units (DMUs). DMUs are units which produce similar outputs using similar inputs. So far, the issue of allocating a new resource to decision-making units has been discussed as a challenging issue in several articles. In some cases, manager is not going to add a new resource but to reallocate one of the previous resources. Reallocating a resource may be done for different purposes and has different benefits. For example, without adding a new resource and only using the same resources, is it possible to increase the efficiency of one unit or even increase the efficiency of the whole system? This is the main idea of the present article. In this paper, a mathematical model is presented that can be used to reallocate one of the previous available resources between units in such a way that the total efficiency of decision-making units reaches the maximum possible value. In this model, in order to prevent excessive reduction of the share of each unit of the desired source, restrictions have been considered. In these constraints, a lower bound for the share of each unit is specified. Also, reallocating a resource is likely to lead some changes in output values of decision-making units. Fortunately, this issue has not been neglected in our model. In the presented model, some constraints are considered that specify an upper bound for outputs produced by the units. There are other restrictions in this model. The first is that the total share of units from the desired resource should not exceed the amount available of it and the second is that the total output produced by all units should be at least equal to the total output produced before reallocation. The model presented in this article, in addition to considering the restrictions described, all of which are unavoidable, has been transformed into a linear programming model that can be solved by many existing software. Finally the mentioned model has been utilized in two examples. The first example is numerical and the second one is related to Tehran stock exchange. In both examples, after the reallocation of the resource in question, the total efficiency of the units has increased significantly. [ABSTRACT FROM AUTHOR]

In this paper, the problem of determining heat transfer from convecting-radiating fin of rectangular shape is investigated. We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. It is demonstrated that the governing fin equation, a nonlinear second-order differential equation, is exactly solvable. The exact, closed-form analytical solutions in implicit form are convenient for physical interpretation and optimization for maximum heat transfer. Additionally, exact analytical expressions for heat transfer rate and the fin efficiency are provided. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method for solving nonlinear fractional integral equations (NFIE) is introduced. This method is based on the new basis functions (NFs) introduced in [M. Paripour and et al., Numerical solution of nonlinear Volterra Fredholm integral equations by using new basis functions, Communications in Numerical Analysis, (2013)]. Since the conventional operational matrices for fractional kernels are singular, the definition of these matrices is modified. In order to increase the accuracy of approximating integrals, the operational matrices are exactly calculated and parametrically presented. Then, the solution procedure is proposed and applied on NFIE. Furthermore, the error analysis is performed and rate of convergence is obtained. In addition, various numerical examples are provided for a wide range of fractional orders and nonlinearity of integral equations. Comparison of the results with the exact solutions and those reported in previous studies indicate the capability, salient accuracy, and superiority of the proposed method over similar ones. [ABSTRACT FROM AUTHOR]

The finite semigroups are applicable in several branches of sciences. The power graph of such semigroups is also an strategic tool in demonstrating the properties of semigroups. The completeness and the 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 necessary and 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?" [ABSTRACT FROM AUTHOR]

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 (ViT -- 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. [ABSTRACT FROM AUTHOR]

In this paper, we present some characterizations of prime and maximal filters. Moreover, we introduce ∩-irreducible filters of an equality algebra, investigate some results about them and relations between maximal, prime, V-irreducible and ∩-irreducible filters in equality algebra. Also, we introduce spec- trum of an equality algebra and prove that the spectrum endowed with Zariski topology is a compact T0 topological space and maximal spectrum (as a subspace of that) is a compact T1 topological space. [ABSTRACT FROM AUTHOR]

This study proposes a method for solving mixed integer multi-objective fractional signomial geometric programming (MIMOFSGP) problems. In this paper we firstly convert a multi-objective fractional signomial programming into a non-fractional problem by a new convenient reformulation strategy. Then the fuzzy programming technique is applied to find the optimal compromise solution and a convex relaxation is used to reach a global solution. A mixed integer compromise optimal solution of the convex programming problem can finally be found by use of nonlinear branch and bound algorithm. Then on using the Spacial branch and bound algorithm, we obtain a solution that has the shortest distance from the solution of the original problem. Finally two examples are included to demonstrate the correctness and effciency of the proposed approach. [ABSTRACT FROM AUTHOR]

Since the change of conditional value at risk (CVaR) in different confidence levels is very effective in portfolio optimization, the meta-Malmquist index (MMI) is utilized. For this purpose, mean-CVaR models by MMI in the presence of negative data are introduced. Like Markowitz theory in mean)variance framework, we use CVaR as a risk measure and propose our models without considering the skewness and kurtosis of assets return. In our study there are some negative data, so our models is based on Range Directional Measure (RDM) model that can be taken positive and negative data. In this paper efficiencies are obtained in all confidence levels by mean-CVaR models and MMI is calculated on confidence levels as periods in the presence of negative data. This method could help the investors to construct their profitable portfolio by using MMI index. We, also carry out an empirical study within Iran stock exchange market. [ABSTRACT FROM AUTHOR]

In the latest decade, the concepts of service delivery and software-as-a-service have evolved into two important evolution paradigms that have affected the information systems area. A paradigm shift in software development has been triggered by this change, in which software is developed through the use of ready-made services in the cloud. Since service composition in the cloud environment must be done on-the-fly, realizing this requires a trade-off between the optimality of the composite service and the time it takes. As QoS-aware service composition has several potential solutions, some of which are usually considered optimal, which should be considered an NP-hard problem. A growing number of services leads to a larger problem search space, which is why in recent years many researchers have looked into methods that use meta-heuristic algorithms to solve the problem of service composition in a cloud environment. Thus, it is crucial that researchers have access to up-to-date and specialized review articles. Based on a systematic review of the research literature, the paper aims to extract important questions that are relevant to meta-heuristic QoS-aware service composition methods. Then, after classifying the studies and studying the proposed methods, goals, and priorities of researchers in articles, useful results and statistics for future research in this field are presented. [ABSTRACT FROM AUTHOR]

The goal of this paper is to calculate the order reduction of the generalized mKdV equation with constant-coefficients (gmKdVcc) and the generalized mKdV equation with variable-coefficients (gmKdVvc) using the µ-symmetry method. Moreover we obtain Lagrangian and µ-conservation law of the gmKdVcc equation and the gmKdVvc equation using the variational problem method. [ABSTRACT FROM AUTHOR]

Since the change of conditional value at risk (CVaR) in different confidence levels is very effective in portfolio optimization, the meta-Malmquist index (MMI) is utilized. For this purpose, mean-CVaR models by MMI in the presence of negative data are introduced. Like Markowitz theory in mean-variance framework, we use CVaR as a risk measure and propose our models without considering the skewness and kurtosis of assets return. In our study there are some negative data, so our models is based on Range Directional Measure (RDM) model that can be taken positive and negative data. In this paper efficiencies are obtained in all confidence levels by mean-CVaR models and MMI is calculated on confidence levels as periods in the presence of negative data. This method could help the investors to construct their profitable portfolio by using MMI index. We, also carry out an empirical study within Iran stock exchange market. [ABSTRACT FROM AUTHOR]

In the latest decade, the concepts of service delivery and software-as-a-service have evolved into two important evolution paradigms that have affected the information systems area. A paradigm shift in software development has been triggered by this change, in which software is developed through the use of ready-made services in the cloud. Since service composition in the cloud environment must be done on-the-fly, realizing this requires a trade-off between the optimality of the composite service and the time it takes. As QoS-aware service composition has several potential solutions, some of which are usually considered optimal, which should be considered an NP-hard problem. A growing number of services leads to a larger problem search space, which is why in recent years many researchers have looked into methods that use meta-heuristic algorithms to solve the problem of service composition in a cloud environment. Thus, it is crucial that researchers have access to up-to-date and specialized review articles. Based on a systematic review of the research literature, the paper aims to extract important questions that are relevant to meta-heuristic QoS-aware service composition methods. Then, after classifying the studies and studying the proposed methods, goals, and priorities of researchers in articles, useful results and statistics for future research in this field are presented. [ABSTRACT FROM AUTHOR]

The goal of this paper is to calculate the order reduction of the generalized mKdV equation with constant-coeffcients (gmKdVcc) and the generalized mKdV equation with variable-coefficients (gmKdVvc) using the μ-symmetry method. Moreover we obtain Lagrangian and μ-conservation law of the gmKdVcc equation and the gmKdVvc equation using the variational problem method. [ABSTRACT FROM AUTHOR]

In this paper an improved version of the collocation method is proposed to solve ordinary differential equations with initial conditions. Our proposed algorithm is described by applying it to some well-known IVPs. The results are compared with basic collocation algorithms to show the advantages, applicability and efficiency of the proposed method. Based on numerical results, the proposed algorithm has better accuracy and execution time. [ABSTRACT FROM AUTHOR]

In this paper a new method of parameter estimation was employed for extended Burr XII parameters using the principle of maximum entropy (POME) based on k-record values. Exact solutions for expectations were obtained. Monte Carlo simulation method were applied to assess the performance of this method. [ABSTRACT FROM AUTHOR]

The primary aim of this paper is to investigate useful generalizations of the classical concept of action of a hyperstructure on a non-empty set. The main goal is to develop the theory of dynamical system to the theory of n-ary dynamical hypersystem. We also give some principal properties of an n-ary dynamical hypersystem. [ABSTRACT FROM AUTHOR]

This paper aims to propose a constructive methodology for determining the matrix sign function for a stable variant of the Kung-Traub method. It analytically shows that the new scheme is asymptotically stable. Different numerical experiments compare the new scheme's behavior with the existing matrix iteration of the same type. Finally, the given approach applies to solve the algebraic Riccati equation and the Sylvester equation. [ABSTRACT FROM AUTHOR]

Dynamical systems with delay are widespread in nature. The study of time-delay induced changes in the collective behavior of systems of coupled nonlinear oscillators is a subject of great interest, both because of its fundamental importance from the point of view of dynamical systems and because of its practical applications. In this paper, an explicit technique is proposed for numerical solution of nonlocal dynamical systems with time delay. The proposed method is adopted quadratic spline interpolation. Then, the error analysis of the developed method is discussed. It is exploited in the discussion of nonlocal delay Ikeda and Hutchinson models. Finally, the performance of the presented approach is verified by applying the error and convergence study for different values of fractional order parameters. [ABSTRACT FROM AUTHOR]

The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper we propose a new method for numerical solution of linear integral equations of third kind. The proposed method is based on the approximation of the unknown function with Krall-Laguerre polynomials. This method has a simple computation with a quite acceptable approximate solution. Moreover, we obtain an estimate of the error bound for suggested method. Two examples are also presented to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Our aim at this paper is to estimate the parameters of extended Burr XII (EBXII) based on k-records with corrected bias. To get this goal maximum likelihood estimator (MLE) is applied and bias correction for ML estimation is considered to get better and improved estimator. Numerical results for comparison of performances of estimators are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness and multiplicity of the solutions of a strongly nonlinear mathematical model arising from chemical reactor theory. The analysis is based on the reproducing kernel Hilbert space method. The main aim of this work is to find how much information can be predicted using numerical computations. The dependence of the number of solutions on the parameters of the model is also studied. Furthermore, the analytical approximations of all branches of solutions can be calculated by the proposed method. The convergence of the proposed method is proved. Some numerical simulations are presented.. [ABSTRACT FROM AUTHOR]

There are numerous models of data envelopment analysis (DEA) for solving the efficiency evaluation a set of homogeneous Decision-Making Units (DMUs) that use similar sources to produce similar outputs. However, the efficiency boundary in these models is very sensitive to outliers and random factors. In this way, researchers have always sought a method that, in addition to having the high exibility of nonparametric methods, compensates for the weaknesses of this view. The approach suggested by scholars in this regard is the use of a combination of Artificial Neural Network (ANN) and DEA. In this paper, a new method of combining ANN and DEA (ANN-DEA) presented in which the input and output values for a large number of DMUs determined as neural network inputs. It can be seen that the use of the neural network to solve the data envelopment analysis problem does not require solving the model for each DMU, and therefore compared with the conventional method, in the proposed algorithm processing time and memory usage significantly reduced. We have also compared the new model with the existing approach of ANN-DEA. To illustrate the ability of the proposed methodology some case studies are used, including a set of 500 Iranian bank branches. The results indicate a high accuracy and less computational time of the proposed hybrid model and have practical outcomes for decision makers. [ABSTRACT FROM AUTHOR]

In this paper, the first, second and third Zagreb indices, the first and second multiplicative Zagreb indices, the F-index and F-polynomial of benzyl ether dendrimer with C60H core and benzyl ether dendrimer with porphyrin core are calculated. In addition, the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices of these graphs are computed as well. Finally, the multiplicative Zagreb index of these graphs is computed through the link of graphs. [ABSTRACT FROM AUTHOR]

In this research paper, a numerical method is presented for solving second-order hybrid fuzzy dif- ferential equations by using fuzzy Taylor expansion under generalized Hukuhara differentiability and also with convergence theorem. Also, the method is illustrated by solving several numerical examples. The final results showed that the solution of the second-order hybrid fuzzy differential equations. [ABSTRACT FROM AUTHOR]

In the real word, the decision maker may want to use revenue and cost eficiency analysis for existing units compared to virtual units, traditional DEA models can no longer be used and FDH models must be used to evaluate the efficiency of decision-making units. In this paper, we develop the revenue and cost efficiency models based on the FDH model and obtain the efficiency scores based on pair wise comparisons. In the following, we will develop the proposed models for the two-stage network structure and obtain the desired scores of inputs and outputs by considering the input and output prices. An algorithm for measuring the revenue and cost efficiency is presented based on the ratio of inputs and outputs. Finally, we use the proposed algorithm to evaluate the efficiency of 13 airports in Iran with a two-stage network structure without considering the constraint of convexity and present the results of the research. [ABSTRACT FROM AUTHOR]

Vehicular communications have been considered to be an enabler for numerous vehicle safety and information applications.Vehicle Social Networks (VSNs) are a type of ad-hoc networks which allows wireless communication between two adjacent vehicles. Routing and communicating with adjacent nodes are one of the problems in VSNs. A literature review indicated that the time limit to transmit data and route is a problem due to the geographical distance and speed of the vehicles. The present paper aims to provide an innovative near-optimal solution with minimal delay for the routing problem in these networks, using the optimization algorithm of fire y applicable in dynamic and geographi- cally extensive environments. Vehicles and their movements are considered to be fire ies and their absorption, respectively. The two factors of mean distance and the possibility of two vehicles reaching each other were examined for car absorption and routing. In addition, the number of vehicles in each area, measured by the different density of vehicles in both urban and suburban areas, is another directly effective factor in the routing accuracy. Finally, the proposed method is simulated in the 5G networks and the results indicated the improvement of the proposed method compared with the dynamic group division algorithm in terms of mean car routing distance, urban, and suburban area separation, light changes, light absorption coefficient variations, random number between zero and one changes, and random initial vehicle mobility changes up to 14.68, 13.63, 2.65, 20.08, 18.39, 17.57, and 18.45, respectively. [ABSTRACT FROM AUTHOR]

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 pro-posed 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is a method for evaluating the performance of a set of homogenous decision-making units (DMUs) with multiple inputs and multiple outputs. There are various models for efficiency calculation in DEA, one of which is based on determining a common set of weights (CSW), which is used extensively by DEA experts. In classical data envelopment analysis, all input and output values are clearly specified. However, this assumption might not always be true in realworld applications. One of the important methods for dealing with imprecise data is to explore the use of stochastic data in DEA. This manuscript extends the CSW model to stochastic inputs and outputs. Next, the stochastic CSW model is transformed into a nonlinear model, and then, the deterministic model is transformed into a quadratic programming model. The efficiency obtained using stochastic data is called stochastic efficiency. Finally, the concept presented in this article is demonstrated through a numerical example involving a number of Iranian banks. [ABSTRACT FROM AUTHOR]

In this article, a fast numerical approach is proposed for finding the solution of nonlinear delay differential equations by using hybrid Taylor and Block-pulse Functions (HTBPFs). Firstly, some features of hybrid functions which are a combination of Block-Pulse functions and Taylor polynomials on the interval are introduced [0; 1) . In this spectral approach, the operational matrices of stretch, derivation and coefficient matrices are utilized. Based on these piecewise functions, we transfer delay differential equations (DDEs) into a system of linear or nonlinear algebraic equations. Also, in this numerical approach, it is shown that these operational matrices are sparse which is an effective advantage of the fast implementation of numerical computation. Then, error analysis is done. Finally, three examples are solved to show that the new proposed approach is comparable with other methods of high accuracy and efficiency. [ABSTRACT FROM AUTHOR]