Search results for: inverse models of data envelopment analysis

Authors: Yakin Hajlaoui, Richard Labib, Jean-François Plante, Michel Gamache

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This study introduces the Multi-Layer Inverse Distance Weighting Model (ML-IDW), inspired by the mathematical formulation of both multi-layer neural networks (ML-NNs) and Inverse Distance Weighting model (IDW). ML-IDW leverages ML-NNs' processing capabilities, characterized by compositions of learnable non-linear functions applied to input features, and incorporates IDW's ability to learn anisotropic spatial dependencies, presenting a promising solution for nonlinear spatial interpolation and learning from complex spatial data. it employ gradient descent and backpropagation to train ML-IDW, comparing its performance against conventional spatial interpolation models such as Kriging and standard IDW on regression and classification tasks using simulated spatial datasets of varying complexity. the results highlight the efficacy of ML-IDW, particularly in handling complex spatial datasets, exhibiting lower mean square error in regression and higher F1 score in classification.

Keywords: deep learning, multi-layer neural networks, gradient descent, spatial interpolation, inverse distance weighting

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Authors: Sherly M. A., Varsha Vijaykumar, Subhankar Karmakar, Terence Chan, Christian Rau

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This study aims at proposing an indicator-based framework for assessing social vulnerability of any coastal megacity to floods. The final set of indicators of social vulnerability are chosen from a set of feasible and available indicators which are prepared using a Geographic Information System (GIS) framework on a smaller scale considering 1-km grid cell to provide an insight into the spatial variability of vulnerability. The optimal weight for each individual indicator is assigned using data envelopment analysis (DEA) as it avoids subjective weights and improves the confidence on the results obtained. In order to de-correlate and reduce the dimension of multivariate data, principal component analysis (PCA) has been applied. The proposed methodology is demonstrated on twenty four wards of Mumbai under the jurisdiction of Municipal Corporation of Greater Mumbai (MCGM). This framework of vulnerability assessment is not limited to the present study area, and may be applied to other urban damage centers.

Keywords: urban floods, vulnerability, data envelopment analysis, principal component analysis

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Authors: Bahram Fathi, Mahdi Khodaparast Mashhadi, Masuod Homayounifar

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Global awareness on energy security and climate change has created much interest in assessing energy efficiency performance. A number of previous studies have contributed to evaluate energy efficiency performance using different analytical techniques among which data envelopment analysis (DEA) has recently received increasing attention. Most of DEA-related energy efficiency studies do not consider undesirable outputs such as CO2 emissions in their modeling framework, which may lead to biased energy efficiency values. Within a joint production frame work of desirable and undesirable outputs, in this paper we construct energy efficiency performance index for measuring energy efficiency performance by using environmental DEA model with CO2 emissions. We finally apply the index proposed to assess the energy efficiency performance in OPEC over time.

Keywords: energy efficiency, environmental, OPEC, data envelopment analysis

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Authors: Ioanna Pagoni, Annitsa Koumoutsidi

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The aim of this paper is to estimate the efficiency of airports that are located in touristic regions. It focuses on the regional airports of Greece, which are located at the mainland and the islands that constitute touristic destinations. Most of these airports share the following characteristics. They operate at levels below capacity with a high level of seasonality to their traffic. In addition, in such airports, the operation of charter and low-cost airlines is significant. The efficiency of the study airports is calculated by using the non-parametric data envelopment analysis during the period of 2010-2016. The selected inputs include several airport infrastructure measures such as passenger terminal size, aircraft parking area, runway length, and the number of check-in counters, while the number of employees in each airport is also used. The number of passengers and aircraft movements are selected as outputs. The effect of seasonality, as well as the operation of charter airlines and low-cost carriers on airport efficiency, is estimated by running proper regression models. Preliminary findings indicate that low-cost and charter airlines contribute to increasing airport efficiency for most of the study airports. The results of this research could be useful for airlines, airport operators, hotel businesses, and other tourism-related operators.

Keywords: airport efficiency, data envelopment analysis, low-cost carriers, charter airlines, seasonality

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Authors: Raziyeh Shamsi

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In this paper, we present a multiple objective linear programming (MOLP) problem in full fuzzy case and find Data Envelopment Analysis(DEA) targets. In the presented model, we are seeking the least inputs and the most outputs in the production possibility set (PPS) with the variable return to scale (VRS) assumption, so that the efficiency projection is obtained for all decision making units (DMUs). Then, we provide an algorithm for finding DEA targets interactively in the full fuzzy case, which solves the full fuzzy problem without defuzzification. Owing to the use of interactive methods, the targets obtained by our algorithm are more applicable, more realistic, and they are according to the wish of the decision maker. Finally, an application of the algorithm in 21 educational institutions is provided.

Keywords: DEA, MOLP, full fuzzy, target

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Authors: Abdon Choque-Rivero

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The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: inverse scattering, discrete system, transmission eigenvalues, Marchenko method

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Authors: Sheetal Kumar Parwar, J. Deb Barma, A. Majumder

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Submerged arc welding is a very complex process. It is a very efficient and high performance welding process. In this present study an attempt have been done to reduce the welding distortion by increased amount of oxide flux through TiO2 in submerged arc welding process. Care has been taken to avoid the excessiveness of the adding agent for attainment of significant results. Data Envelopment Analysis (DEA) based BAT algorithm is used for the parametric optimization purpose in which DEA Data Envelopment Analysis is used to convert multi response parameters into a single response parameter. The present study also helps to know the effectiveness of the addition of TiO2 in active flux during submerged arc welding process.

Keywords: BAT algorithm, design of experiment, optimization, submerged arc welding

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Saleh Alotaibi, Mohammed Quddus, Craig Morton, Jobair Bin Alam

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This paper explores the role of large-scale investment in transport sectors and the impact of increased railway accessibility on the efficiency of the regional economic productivity in the Kingdom of Saudi Arabia (KSA). There are considerable differences among the KSA regions in terms of their levels of investment and productivity due to their geographical scale and location, which in turn greatly affect their relative efficiency. The study used a non-parametric linear programming technique - Data Envelopment Analysis (DEA) - to measure the regional efficiency change over time and determine the drivers of inefficiency and their scope of improvement. In addition, Window DEA analysis is carried out to compare the efficiency performance change for various time periods. Malmquist index (MI) is also analyzed to identify the sources of productivity change between two subsequent years. The analysis involves spatial and temporal panel data collected from 1999 to 2018 for the 13 regions of the country. Outcomes reveal that transport investment and improved railway accessibility, in general, have significantly contributed to regional economic development. Moreover, the endowment of the new railway stations has spill-over effects. The DEA Window analysis confirmed the dynamic improvement in the average regional efficiency over the study periods. MI showed that the technical efficiency change was the main source of regional productivity improvement. However, there is evidence of investment allocation discrepancy among regions which could limit the achievement of development goals in the long term. These relevant findings will assist the Saudi government in developing better strategic decisions for future transport investments and their allocation at the regional level.

Keywords: data envelopment analysis, transport investment, railway accessibility, efficiency

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Panos Xenos, Milton Nektarios, John Yfantopoulos

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Background: Policy makers, professional organizations and payers have introduced a variety of initiatives and reforms for the health systems worldwide, aimed at improving hospital efficiency. Their efforts are concentrated in two main categories: to constrain increasing healthcare costs and to enhance quality of services provided. Research Objectives: This study examines the efficiency of 112 Greek public hospitals for the year 2009, evaluates the importance of bootstrapping techniques and investigates the effect of contextual factors on hospital efficiency. Furthermore, the effect of qualitative evidence, on hospital efficiency is explored using data from 28 large hospitals. Methods: We applied Data Envelopment Analysis, augmented by bootstrapping techniques, to estimate efficiency scores. In order to measure the effect of environmental factors on hospital efficiency we used Tobit regression analysis. The significance of our models is evaluated using statistical tests to compare distributions. Results: The Kolmogorov-Smirnov test between the original and the bootstrap-corrected efficiency indicates that their distributions are significantly different (p-value<0.01). The environmental factors, that seem to influence efficiency, are Occupancy Rating and the ratio between Outpatient Visits and Inpatient Days. Results indicate that the inclusion of the quality variable in DEA modelling generates statistically significant variations in efficiency scores (p-value<0.05). Conclusions: The inclusion of quality variables and the use of bootstrap resampling in efficiency analysis impose a statistically significant effect on the distribution of efficiency scores. As a policy conclusion we highlight the importance of these methods on hospital efficiency analysis and, by implication, on healthcare resource allocation.

Keywords: hospitals, efficiency, quality, data envelopment analysis, Greek public hospital sector

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Authors: Songul Cinaroglu

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Regional planning in health has gained speed for developing countries in recent years. In Turkey, 89 different Public Hospital Unions (PHUs) were conducted based on provincial levels. In this study technical efficiencies of 89 PHUs were examined by using Data Envelopment Analysis (DEA) and machine learning techniques by dividing them into two clusters in terms of similarities of input and output indicators. Number of beds, physicians and nurses determined as input variables and number of outpatients, inpatients and surgical operations determined as output indicators. Before performing DEA, PHUs were grouped into two clusters. It is seen that the first cluster represents PHUs which have higher population, demand and service density than the others. The difference between clusters was statistically significant in terms of all study variables (p ˂ 0.001). After clustering, DEA was performed for general and for two clusters separately. It was found that 11% of PHUs were efficient in general, additionally 21% and 17% of them were efficient for the first and second clusters respectively. It is seen that PHUs, which are representing urban parts of the country and have higher population and service density, are more efficient than others. Random forest decision tree graph shows that number of inpatients is a determinative factor of efficiency of PHUs, which is a measure of service density. It is advisable for public health policy makers to use statistical learning methods in resource planning decisions to improve efficiency in health care.

Keywords: public hospital unions, efficiency, data envelopment analysis, random forest

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Authors: Juan F. P. Ramírez, Jésica A. L. Isaza, Benjamín A. Rojano

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This study proposes a novel use of a method to determine the mechanical properties of fruits by the use of the indentation tests. The method combines experimental results with a numerical finite elements model. The results presented correspond to a simplified numerical modeling of banana. The banana was assumed as one-layer material with an isotropic linear elastic mechanical behavior, the Young’s modulus found is 0.3Mpa. The method will be extended to multilayer models in further studies.

Keywords: finite element method, fruits, inverse analysis, mechanical properties

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Authors: Pornpimol Chaiwuttisak

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The study aims to compare the performance of the logistics for Thailand’s wholesale and retail trade industries (except motor vehicles, motorcycle, and stalls) by using data (data envelopment analysis). Thailand Standard Industrial Classification in 2009 (TSIC - 2009) categories that industries into sub-group no. 45: wholesale and retail trade (except for the repair of motor vehicles and motorcycles), sub-group no. 46: wholesale trade (except motor vehicles and motorcycles), and sub-group no. 47: retail trade (except motor vehicles and motorcycles. Data used in the study is collected by the National Statistical Office, Thailand. The study consisted of four input factors include the number of companies, the number of personnel in logistics, the training cost in logistics, and outsourcing logistics management. Output factor includes the percentage of enterprises having inventory management. The results showed that the average relative efficiency of small-sized enterprises equals to 27.87 percent and 49.68 percent for the medium-sized enterprises.

Keywords: DEA, wholesales and retails, logistics, Thailand

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Authors: Fatemeh Abbasi, Sahand Daneshvar

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Productivity is one of the essential goals of companies to improve performance, which as a strategy-oriented method, determines the basis of the company's economic growth. The history of productivity goes back centuries, but most researchers defined productivity as the relationship between a product and the factors used in production in the early twentieth century. Productivity as the optimal use of available resources means that "more output using less input" can increase companies' economic growth and prosperity capacity. Also, having a quality life based on economic progress depends on productivity growth in that society. Therefore, productivity is a national priority for any developed country. There are several methods for calculating productivity growth measurements that can be divided into parametric and non-parametric methods. Parametric methods rely on the existence of a function in their hypotheses, while non-parametric methods do not require a function based on empirical evidence. One of the most popular non-parametric methods is Data Envelopment Analysis (DEA), which measures changes in productivity over time. The DEA evaluates the productivity of decision-making units (DMUs) based on mathematical models. This method uses multiple inputs and outputs to compare the productivity of similar DMUs such as banks, government agencies, companies, airports, Etc. Non-parametric methods are themselves divided into the frontier and non frontier approaches. The Malmquist productivity index (MPI) proposed by Caves, Christensen, and Diewert (1982), the Hicks–Moorsteen productivity index (HMPI) proposed by Bjurek (1996), or the Luenberger productivity indicator (LPI) proposed by Chambers (2002) are powerful tools for measuring productivity changes over time. This study will compare the Malmquist, Hicks–Moorsteen, and Luenberger indices theoretically and empirically based on DEA models and review their strengths and weaknesses.

Keywords: data envelopment analysis, Hicks–Moorsteen productivity index, Leuenberger productivity indicator, malmquist productivity index

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Authors: Kyugneun Lee, Ikjin Lee

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Parameter estimation with inverse problem often suffers from unfavorable conditions in the real world. Useless data and many input parameters make the problem complicated or insoluble. Data refinement and reformulation of the problem can solve that kind of difficulties. In this research, a method to solve the rank deficient inverse problem is suggested. A multi-physics system which has rank deficiency caused by response correlation is treated. Impeditive information is removed and the problem is reformulated to sequential estimations using Bayesian network (BN) and subset groups. At first, subset grouping of the responses is performed. Feature selection with singular value decomposition (SVD) is used for the grouping. Next, BN inference is used for sequential conditional estimation according to the group hierarchy. Directed acyclic graph (DAG) structure is organized to maximize the estimation ability. Variance ratio of response to noise is used to pairing the estimable parameters by each response.

Keywords: Bayesian network, feature selection, rank deficiency, statistical inverse analysis

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Shivi Agarwal, Trilok Mathur

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This paper proposes the method to measure the total factor productivity (TFP) change by credibility theory for fuzzy input and output variables. Total factor productivity change has been widely studied with crisp input and output variables, however, in some cases, input and output data of decision-making units (DMUs) can be measured with uncertainty. These data can be represented as linguistic variable characterized by fuzzy numbers. Malmquist productivity index (MPI) is widely used to estimate the TFP change by calculating the total factor productivity of a DMU for different time periods using data envelopment analysis (DEA). The fuzzy DEA (FDEA) model is solved using the credibility theory. The results of FDEA is used to measure the TFP change for fuzzy input and output variables. Finally, numerical examples are presented to illustrate the proposed method to measure the TFP change input and output variables. The suggested methodology can be utilized for performance evaluation of DMUs and help to assess the level of integration. The methodology can also apply to rank the DMUs and can find out the DMUs that are lagging behind and make recommendations as to how they can improve their performance to bring them at par with other DMUs.

Keywords: chance-constrained programming, credibility theory, data envelopment analysis, fuzzy data, Malmquist productivity index

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Authors: Maatoug Hassine, Mourad Hrizi

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In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: geometric inverse source problem, heat equation, topological optimization, topological sensitivity, Kohn-Vogelius formulation

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Authors: Ekrem Erdem, Can Tansel Tugcu

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Improved resource efficiency of production is a key requirement for sustainable growth, worldwide. In this regards, by considering the energy and tourism as the extra inputs to the classical Coub-Douglas production function, this study aims at investigating the efficiency changes in the North African countries. To this end, the study uses panel data for the period 1995-2010 and adopts the Malmquist index based on the data envelopment analysis. Results show that tourism increases technical and scale efficiencies, while it decreases technological and total factor productivity changes. On the other hand, when the production function is augmented by the energy input, technical efficiency change decreases, while the technological change, scale efficiency change and total factor productivity change increase. Thus, in order to satisfy the needs for sustainable growth, North African governments should take some measures for increasing the contribution that the tourism makes to economic growth and some others for efficient use of resources in the energy sector.

Keywords: data envelopment analysis, economic efficiency, North African countries, sustainable growth

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Authors: Mesbaholdin Salami, Farzad Movahedi Sobhani, Mohammad Sadegh Ghazizadeh

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Evaluation of organizational performance is among the most important measures that help organizations and entities continuously improve their efficiency. Organizations can use the existing data and results from the comparison of units under investigation to obtain an estimation of their performance. The Malmquist Productivity Index (MPI) is an important index in the evaluation of overall productivity, which considers technological developments and technical efficiency at the same time. This article proposed a model based on the multistage MPI, considering limited data (Grey’s theory). This model can evaluate the performance of units using limited and uncertain data in a multistage process. It was applied by the electricity market manager to Iran’s electric power supply chain (EPSC), which contains uncertain data, to evaluate the performance of its actors. Results from solving the model showed an improvement in the accuracy of future performance of the units under investigation, using the Grey’s system theory. This model can be used in all case studies, in which MPI is used and there are limited or uncertain data.

Keywords: Malmquist Index, Grey's Theory, CCR Model, network data envelopment analysis, Iran electricity power chain

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Authors: Sumei Cai, Hong Li

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Either during water or gas injection into reservoir, in order to understand the areal flow pressure distribution underground, associated bounding deformation is prevalently monitored by ground or downhole tiltmeters. In this paper, an inverse solution to elastic response of far field displacements induced by reservoir pressure change due to flow injection was studied. Furthermore, the fundamental theory on inverse solution to elastic problem as well as its spatial smoothing approach is presented. Taking advantage of source code development based on Boundary Element Method, numerical analysis on the monitoring data of ground surface displacements to further understand the behavior of reservoir process was developed. Numerical examples were also conducted to verify the effectiveness.

Keywords: remote displacement, inverse problem, boundary element method, BEM, reservoir process

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Authors: Faisal Yousafzai, Murad-ul-Islam Khan, Kar Ping Shum

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We introduce the concept of partially inverse AG**-groupoids which is almost parallel to the concepts of E-inversive semigroups and E-inversive E-semigroups. Some characterization problems are provided on partially inverse AG**-groupoids. We give necessary and sufficient conditions for a partially inverse AG**-subgroupoid E to be a rectangular band. Furthermore, we determine the unitary congruence η on a partially inverse AG**-groupoid and show that each partially inverse AG**-groupoid possesses an idempotent separating congruence μ. We also study anti-separative commutative image of a locally associative AG**-groupoid. Finally, we give the concept of completely N-inverse AG**-groupoid and characterize a maximum idempotent separating congruence.

Keywords: AG**-groupoids, congruences, inverses, rectangular band

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Authors: Yu Menshikov

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In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solution are analyzed. Several methods for remove the influence of uncontrollable inaccuracy have been suggested.

Keywords: inverse problems, filtration, uncontrollable inaccuracy

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Authors: Ali Anwar, Hu Qinglei, Li Bo, Muhammad Taha Ali

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In this paper a generic model of perturbed nonlinear systems is considered which is affected by hard backlash nonlinearity at the input. The nonlinearity is modelled by a dynamic differential equation which presents a more precise shape as compared to the existing linear models and is compatible with nonlinear design technique such as backstepping. Moreover, a novel backstepping based nonlinear control law is designed which explicitly incorporates a continuous-time adaptive backlash inverse model. It provides a significant flexibility to control engineers, whereby they can use the estimated backlash spacing value specified on actuators such as gears etc. in the adaptive Backlash Inverse model during the control design. It ensures not only global stability but also stringent transient performance with desired precision. It is also robust to external disturbances upon which the bounds are taken as unknown and traverses the backlash spacing efficiently with underestimated information about the actual value. The continuous-time backlash inverse model is distinguished in the sense that other models are either discrete-time or involve complex computations. Furthermore, numerical simulations are presented which not only illustrate the effectiveness of proposed control law but also its comparison with PID and other backstepping controllers.

Keywords: adaptive control, hysteresis, backlash inverse, nonlinear system, robust control, backstepping

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Authors: Sadegh Abedi, Ali Yaghoubi, Hamidreza Mashatzadegan

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This paper proposes an approach to identify key processes required by an organization in the field of knowledge management and aligning them with organizational objectives. For this purpose, first, organization’s most important non-financial objectives which are impacted by knowledge management processes are identified and then, using a quality house, are linked with knowledge management processes which are regarded as technical elements. Using this method, processes that are in need of improvement and more attention are prioritized based on their significance. This means that if a process has more influence on organization’s objectives and is in a dire situation comparing to others, is prioritized for choice and improvement. In this research process dominance is considered to be an influential element in process ranking (in addition to communication matrix). This is the reason for utilizing DEA techniques for prioritizing processes in quality house. Results of implementing the method in Khuzestan steel company represents this method’s capability of identifying key processes that require improvements in organization’s knowledge management system.

Keywords: knowledge management, organizational performance, fuzzy data, envelopment analysis

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Authors: Abdel Hadi Ebraheim

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This paper introduces a new extension of the Inverse Pareto distribution in the framework of Marshal-Olkin (1997) family of distributions. This model is capable of modeling various shapes of aging and failure data. The statistical properties of the new model are discussed. Several methods are used to estimate the parameters involved. Explicit expressions are derived for different types of moments of value in reliability analysis are obtained. Besides, the order statistics of samples from the new proposed model have been studied. Finally, the usefulness of the new model for modeling reliability data is illustrated using two real data sets with simulation study.

Keywords: pareto distribution, marshal-Olkin, reliability, hazard functions, moments, estimation

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Authors: Jianhua Zhou, Yuwen Zhang

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A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

Keywords: conduction, inverse problems, conjugated gradient method, laser

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Authors: Ranadhir Roy

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Inverse problems arise in medical (molecular) imaging. These problems are characterized by large in three dimensions, and by the diffusion equation which models the physical phenomena within the media. The inverse problems are posed as a nonlinear optimization where the unknown parameters are found by minimizing the difference between the predicted data and the measured data. To obtain a unique and stable solution to an ill-posed inverse problem, a priori information must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov’s regularization method, where the a priori information is introduced via a stabilizing functional, which may be designed to incorporate some relevant information of an inverse problem. Effective determination of the Tikhonov regularization parameter requires knowledge of the true solution, or in the case of optical imaging, the true image. Yet, in, clinically-based imaging, true image is not known. To alleviate these difficulties we have applied the penalty/modified barrier function (PMBF) method instead of Tikhonov regularization technique to make the inverse problems well-posed. Unlike the Tikhonov regularization method, the constrained optimization technique, which is based on simple bounds of the optical parameter properties of the tissue, can easily be implemented in the PMBF method. Imposing the constraints on the optical properties of the tissue explicitly restricts solution sets and can restore uniqueness. Like the Tikhonov regularization method, the PMBF method limits the size of the condition number of the Hessian matrix of the given objective function. The accuracy and the rapid convergence of the PMBF method require a good initial guess of the Lagrange multipliers. To obtain the initial guess of the multipliers, we use a least square unconstrained minimization problem. Three-dimensional images of fluorescence absorption coefficients and lifetimes were reconstructed from contact and noncontact experimentally measured data.

Keywords: constrained minimization, ill-conditioned inverse problems, Tikhonov regularization method, penalty modified barrier function method

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Authors: J. J. Vargas, N. Prieto, L. A. Toro

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Control charts are commonly used to monitor processes involving either variable or attribute of quality characteristics and determining the control limits as a critical task for quality engineers to improve the processes. Nonetheless, in some applications it is necessary to include an estimation of efficiency. In this paper, the ability to define the efficiency of an industrial process was added to a control chart by means of incorporating a data envelopment analysis (DEA) approach. In depth, a Bayesian estimation was performed to calculate the posterior probability distribution of parameters as means and variance and covariance matrix. This technique allows to analyse the data set without the need of using the hypothetical large sample implied in the problem and to be treated as an approximation to the finite sample distribution. A rejection simulation method was carried out to generate random variables from the parameter functions. Each resulting vector was used by stochastic DEA model during several cycles for establishing the distribution of each efficiency measures for each DMU (decision making units). A control limit was calculated with model obtained and if a condition of a low level efficiency of DMU is presented, system efficiency is out of control. In the efficiency calculated a global optimum was reached, which ensures model reliability.

Keywords: data envelopment analysis, DEA, Multivariate control chart, rejection simulation method

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