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The purpose of this study is to estimate inputs (outputs) and flexible measures when outputs (inputs) are changed provided that the relative efficiency values remain without change.

A novel inverse data envelopment analysis (DEA) approach with flexible measures is proposed in this research to assess inputs (outputs) and flexible measures when outputs (inputs) are perturbed on condition that the relative efficiency scores remain unchanged. Furthermore, flexible inverse DEA approaches proposed in this study are used for a numerical example from the literature and an application of Iranian banking industry to clarify and validate them.

The findings show that including flexible measures into the investigation effects on the changes of performance measures estimated and leads to more reasonable achievements.

The traditional inverse DEA models usually investigate the changes of some determinate input-output factors for the changes of other given input-output indicators assuming that the efficiency values are preserved. However, there are situations that the changes of performance measures should be tackled while some measures, called flexible measures, can play either input or output roles. Accordingly, inverse DEA optimization models with flexible measures are rendered in this paper to address these issues.

In order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.

Based on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R²) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.

The model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.

This study aims to introduce a multi-configuration, three-finger dexterous hand with integrated high-dimensional sensors and provides an analysis of its design, modeling and kinematics.

A mechanical design scheme of the three-finger dexterous hand with a reconfigurable palm is proposed based on the existing research on dexterous hands. The reconfigurable palm design enables the dexterous hand to achieve four grasping modes to adapt to multiple grasping tasks. To further enhance perception, two six-axis force and torque sensors are integrated into each finger. The forward and inverse kinematics equations of the dexterous hand are derived using the D-H method for kinematics modeling, thus providing a theoretical model for index analysis. The performance is evaluated using three widely applied indicators: workspace, interactivity of fingers and manipulability.

The results of kinematics analysis show that the proposed hand has excellent dexterity. Additionally, three different experiments are conducted based on the proposed hand. The performance of the dexterous hand is also verified by fingertip force, motion accuracy test, grasping and in-hand manipulation experiments based on Feix taxonomy. The results show that the dexterous hand has good grasping ability, reproducing 82% of the natural movement of the human hand in daily grasping activities and achieving in-hand manipulations such as translation and rotation.

A novel three-finger dexterous hand with multi-configuration and integrated high-dimensional sensors is proposed. It performs better than the previously designed dexterous hand in actual experiments and kinematic performance analysis.

This paper aims to discuss the inverse problems that arise in various practical heat transfer processes. The purpose of this paper is to provide an identification method for predicting the internal boundary conditions for thermal analysis of mechanical structure. A few examples of heat transfer systems are given to illustrate the applicability of the method and the challenges that must be addressed in solving the inverse problem.

In this paper, the thermal network method and the finite difference method are used to model the two-dimensional heat conduction inverse problem of the tube structure, and the heat balance equation is arranged into an explicit form for heat load prediction. To solve the matrix ill-conditioned problem in the process of solving the inverse problem, a Tikhonov regularization parameter selection method based on the inverse computation-contrast-adjustment-approach was proposed.

The applicability of the proposed method is illustrated by numerical examples for different dynamically varying heat source functions. It is proved that the method can predict dynamic heat source with different complexity.

The modeling calculation method described in this paper can be used to predict the boundary conditions for the inner wall of the heat transfer tube, where the temperature sensor cannot be placed.

This paper presents a general method for the direct prediction of heat sources or boundary conditions in mechanical structure. It can directly obtain the time-varying heat flux load and thtemperature field of the machine structure.

This paper presents a review concerning the analytical and inverse methods of small punch creep test (SPCT) in order to evaluate the mechanical property of component material at elevated temperature.

In this work, the effects of temperature, specimen size and shape on material properties are mainly discussed using the finite element (FE) method. The analytical approaches including membrane stretching, empirical or semi-empirical solutions that are currently used for data interpretation have been presented.

The state-of-the-art research progress on the inverse method, such as non-linear optimization program and neutral network, is critically reviewed. The capabilities of the inverse technique, the uniqueness of the solution and future development are discussed.

The state-of-the-art research progress on the inverse method such as non-linear optimization program and neutral network is critically reviewed. The capabilities of the inverse technique, the uniqueness of the solution and future development are discussed.

Assessing inputs and outputs is a significant aspect of taking decisions while there are complex and multistage processes in many examinations. Due to the presence of interval performance measures in various real-world studies, the purpose of this study is to address the changes of interval inputs of two-stage processes for the perturbations of interval outputs of two-stage systems, given that the overall efficiency scores are maintained.

Actually, an interval inverse two-stage data envelopment analysis (DEA) model is proposed to plan resources. To illustrate, an interval two-stage network DEA model with external interval inputs and outputs and also its inverse problem are suggested to estimate the upper and lower bounds of the entire efficiency and the stages efficiency along with the variations of interval inputs.

An example from the literature and a real case study of the banking industry are applied to demonstrate the introduced approach. The results show the proposed approach is suitable to estimate the resources of two-stage systems when interval measures are presented.

To the best of the authors’ knowledge, there is no study to estimate the fluctuation of imprecise inputs related to network structures for the changes of imprecise outputs while the interval efficiency of network processes is maintained. Accordingly, this paper considers the resource planning problem when there are imprecise and interval measures in two-stage networks.

This research is aimed to mainly be applicable to expediting engineering projects, uses the method of inverse optimization and the double-layer nested genetic algorithm combined with nonlinear programming algorithm, study how to schedule the number of labor in each process at the minimum cost to achieve an extremely short construction period goal.

The method of inverse optimization is mainly used in this study. In the first phase, establish a positive optimization model, according to the existing labor constraints, aiming at the shortest construction period. In the second phase, under the condition that the expected shortest construction period is known, on the basis of the positive optimization model, the inverse optimization method is used to establish the inverse optimization model aiming at the minimum change of the number of workers, and finally the optimal labor allocation scheme that meets the conditions is obtained. Finally, use algorithm to solve and prove with a case.

The case study shows that this method can effectively achieve the extremely short duration goal of the engineering project at the minimum cost, and provide the basis for the decision-making of the engineering project.

The contribution of this paper to the existing knowledge is to carry out a preliminary study on the relatively blank field of the current engineering project with a very short construction period, and provide a path for the vast number of engineering projects with strict requirements on the construction period to achieve a very short construction period, and apply the inverse optimization method to the engineering field. Furthermore, a double-nested genetic algorithm and nonlinear programming algorithm are designed. It can effectively solve various optimization problems.

Literature has widely discussed the relevant role of financial development in determining atmospheric quality. However, there has not been much discussion of how financial inclusion (FIC) plays its role in environmental quality. Thus, this research aims to unveil the role of financial inclusion in determining the CO₂ emissions which serve as a proxy of environmental quality. In addition, this study examines the moderating role of corruption control (CC) in the nexus of FIC-CC.

The empirical results were based on 22 years of annual data from five Brazil, Russia, India, China and South Africa (BRICS) economies, covering the years 1996–2017. The authors use the autoregressive distributed lag (ARDL) model to check regression among variables.

The empirical findings first disclosed the positive impact of FIC whereas CC had an inverse impact on CO₂ emissions. However, the moderating role of CC was observed in mitigating the adverse impact of FIC on ecological quality. In addition, the statistical analysis further showed an inverse impact of economic growth and foreign investment and a positive impact of trade volume and energy consumption on CO₂ emissions.

This analysis states an important policy regarding integrated FIC and green environmental requirements. Additionally, the negative externality of FIC can be controlled by improving the CC.

This study complements the existing literature on FIC and environmental quality by adding the moderating role of CC.

This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source.

The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method.

The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted.

The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

This paper explores the connection between capital structure and financial performance within European listed firms. The primary objective is to demonstrate an inverse U-shaped relationship between these two variables and pinpoint an optimal debt-equity mix.

In this study, we adopt a dynamic modeling approach to investigate the relationship between a firm’s capital structure and financial performance. Drawing on well-established theories and prior empirical studies, our model examines 3,121 dividend-paying firms from 41 European countries over 14 years, from 2008 to 2021. To enhance the reliability of our findings, we employ two distinct estimation techniques: the fixed effect model (FE) and the system generalized method of moments (System-GMM).

This study reveals an inverse U-shaped relationship between the firm’s financial performance, measured by the return on equity (ROE) and its capital structure (total liability to total assets ratio). Furthermore, an optimal capital structure of about 29% is determined for all firms in the sample, and about 21%, 28% and 41% industry-specific capital structure for manufacturing, real estate and wholesale trade, respectively.

This paper contributes to existing knowledge by empirically determining an optimal capital structure for listed firms across various industries in Europe, which very few studies have attempted to do in the past. An optimal capital structure is an invaluable benchmark for managers and other stakeholders, informing their decision-making.