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To present a new parallel method for solving differential equations that describe transient states in physical systems.

The proposed speculative method first solves a differential equation with a large integration step to determine initial data for parallel computations in sub‐intervals of time, then speculatively computes in parallel solutions in all the sub‐intervals with a smaller integration step and finally composes the final solution from the speculatively computed ones. The basic numerical method applied is the well‐known Runge‐Kutta algorithm.

The speculative method allows important reduction of the computation time of sequential algorithms. The speed‐up of the speculative method that we propose, as compared to the sequential execution, depends on the number of sub‐intervals that are defined inside the total analysed time interval. The speed‐up increases almost linearly with the number of sub‐intervals. The good accuracy of computations in the presented example was obtained.

The proposed method can be applied to non‐linear systems without discontinuity points and to stable systems (i.e. systems insensitive to the selection of initial conditions).

The method can be especially applied for long‐lasting computations with a slow convergence of state variables values along with the decrease of integration steps.

The paper presents an original parallel method for solving differential equations, which significantly speeds up transient states analysis in physical systems.

The purpose of this paper is to present a new warranty model to improve warranty management. As a case study, the developed model has been applied on an industrial vehicle manufacturing company. The model is composed of quality function deployment (QFD) and interval-based analytical hierarchy process (i-AHP). The i-AHP is an extension of the concept of analytical hierarchy process (AHP) that takes the benefits of interval computations in order to mitigate the shortcomings of AHP and fuzzy AHP.

Using a combination of i-AHP and QFD, the authors analyzed the several options and alternatives available, weighting each one by means of an interval pair-wise comparison. Using collected data, the authors have shown how to map the capability of each option against each alternative and thereby build a relationship matrix under the QFD approach based on interval computations.

The use of i-AHP&QFD integrated methodology helps to identify the best options to solve several decision problems in diverse fields and could be applied successfully in warranty management. This methodology is especially useful when dealing with several options and equal numbers of alternatives for each warranty option.

The case study includes competitiveness analysis at the first house of quality (HOQ), but not at the subsequent HOQ, due to a lack of information from the relevant competitors. However, the paper demonstrates the kind of competitiveness analysis at the first HOQ which can be extended to all subsequent HOQs.

The research would be useful to academics and practitioners in developing integrated versions of the QFD and i-AHP methodologies to improve warranties.

This study contributes to the diffusion of a new form of integrated warranty model, through the presentation of practical examples of industrial vehicle warranty management. Also, the model presents the i-AHP in order to quantify and compare variables via the use of geometrical averages and to synthesize a subsequent solution.

This paper aims to develop an efficient numerical method for nonlinear transient heat conduction problems with local radiation boundary conditions and nonlinear heat sources.

Based on the physical characteristic of the transient heat conduction and the distribution characteristic of the Green’s function, a quasi-superposition principle is presented for the transient heat conduction problems with local nonlinearities. Then, an efficient method is developed, which indicates that the solution of the original nonlinear problem can be derived by solving some nonlinear problems with small structures and a linear problem with the original structure. These problems are independent of each other and can be solved simultaneously by the parallel computing technique.

Within a small time step, the nonlinear thermal loads can only induce significant temperature responses of the regions near the positions of the nonlinear thermal loads, whereas the temperature responses of the remaining regions are very close to zero. According to the above physical characteristic, the original nonlinear problem can be transformed into some nonlinear problems with small structures and a linear problem with the original structure.

An efficient and accurate numerical method is presented for transient heat conduction problems with local nonlinearities, and some numerical examples demonstrate the high efficiency and accuracy of the proposed method.

The purpose of this paper is to evaluate the reliability and structure function of refrigeration complex system consisted of four components in complex manner.

Although, a variety of methodologies have been used to assess the refrigeration system's reliability function that has proven to be effective, the universal generating function approach is the basis of this research study, which is used in the calculation of a domestic refrigeration system with four separate components that are related in series and parallel with a corresponding sample to form a complex machine.

In this paper, signature reliability of the refrigeration system has been evaluated with the universal generating function technique. There are four components present in the proposed system in complex (series and parallel) manner. The tail signature, signature, Barlow–Proschan index, expected lifetime and expected cost of independent identically distributed are all computed.

This is the first study of domestic refrigeration system to examine the signature reliability with the help of universal generating function techniques with various measures. Refrigeration systems are an essential process in industries and home applications as they perform cooling or the maintain temperature at the desired value. A cycle of refrigeration consists of four main components such as, heat exchange, compression and expansion with a refrigerant flowing through the units within the cycle.

Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in an electrostatic system efficiently with interval parameters.

The Taylor series expansion is proposed for evaluating the upper and lower bounds of electric potentials in an electrostatic system with interval parameters. The uncertain parameters of the electrostatic system are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained using the equilibrium governing equation and by using the properties of interval mathematics, the upper and lower bounds of the electric potentials of an electrostatic system can be calculated.

To evaluate the accuracy and efficiency of the proposed method, the upper and lower bounds of the electric potentials and the computation time of the proposed method are compared with those obtained using the Monte Carlo simulation, which is referred to as a reference solution. Numerical examples illustrate that the bounds of electric potentials of this method are consistent with those obtained using the Monte Carlo simulation. Moreover, the proposed method is significantly more time-saving.

This paper provides a rapid computational method to estimate the upper and lower bounds of electric potentials in electrostatics analysis with interval parameters. The precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.

The purpose of this paper is to suggest a polynomial complexity method for determining the range of the active and reactive power consumed in AC uncertain parameter circuits whose uncertain parameters are given as intervals.

First, the original problem is formulated as a corresponding interval quadratic range determination (IQRD) problem. Next, it is shown that the IQRD problem can be transformed equivalently into an interval linear range determination (ILRD) problem.

An efficient numerical method for solving the associated ILRD problem has been developed, capable of tackling the present active (or reactive) power range problem. It is based on the use of the outer solution y of an associated interval linear system defining the constraints in the ILRD problem.

The method yields the exact active and reactive power range if the number of the components y_i of y containing zero is relatively small (which is most often the case); otherwise, it provides tight outer bounds on the ranges sought.

The present method can be an alternative to the widely used Monte‐Carlo method since the former method provides exact (within rounding errors) results or tight outer approximations for lesser computation times.

To the best of the author's knowledge, the present paper suggests, for the first time, a simple interval analysis method of polynomial complexity for solving the problem considered which is inherently a NP‐hard problem (of exponential complexity).

In structural mechanics, systems with damping factor get converted to nonlinear eigenvalue problems (NEPs), namely, quadratic eigenvalue problems. Generally, the parameters of NEPs are considered as crisp values but because of errors in measurement, observation or maintenance-induced errors, the parameters may have uncertain bounds of values, and such uncertain bounds may be considered in terms of closed intervals. As such, this paper aims to deal with solving nonlinear interval eigenvalue problems (NIEPs) with respect to damped spring-mass systems having interval parameters.

Two methods, namely, linear sufficient regularity perturbation (LSRP) and direct sufficient regularity perturbation (DSRP), have been proposed for solving NIEPs based on sufficient regularity perturbation method for intervals. LSRP may be used for solving NIEPs by linearizing the eigenvalue problems into generalized interval eigenvalue problems, and DSRP may be considered as a direct solution procedure for solving NIEPs.

LSRP and DSRP methods help in computing the lower and upper eigenvalue and eigenvector bounds for NIEPs which contain the crisp eigenvalues. Further, the DSRP method is computationally efficient compared to LSRP.

The efficiency of the proposed methods has been validated by example problems of NIEPs. Moreover, the procedures may be extended for other nonlinear interval eigenvalue application problems.

This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness according to the principle of grey numbers operation. The domain means the emerging background of interval grey numbers, it is vital for the operational mechanism of such interval grey numbers. However, the criteria of selection of domain always remain same that is not only for the calculated grey numbers but also for the resultant grey numbers, which can be assumed as unrealistic up to a certain extent.

The existence of interval grey number operation based on kernel and the degree of greyness containing two calculation aspects, which are kernel and the degree of greyness. For the degree of greyness, it includes concepts of domain and calculation of the domain. The concepts of a domain are defined. The enhanced algorithm is also comprised of four deductive theorems and eight rules that are linked to the properties of the enhanced algorithm of the interval grey numbers based on the kernel and the degree of greyness.

Aiming to improve the algorithm of the degree of greyness for interval grey numbers, based on the variation of domain in the operation process, the degree of greyness of the operation result is defined in this paper, and the specific expressions for algebraic operations are given, which is relevant to the kernel, the degree of greyness and the domain. Then, these expressions are used to the algorithm of interval grey numbers based on the kernel and the degree of greyness, improving the accuracy of the operation results.

The enhanced algorithm in this paper can effectively reduce the loss of information in the operation process, so as to avoid the situation where the decision values are the same and scientific decisions cannot be made during the grey evaluation and decision-making process.

Users are the key players in an online social network (OSN), so the behavior of the OSN is strongly related to their behavior. User weight refers to the influence of the users on the OSN. The purpose of this paper is to propose a method to identify the user weight based on a new metric for defining the time intervals.

The behavior of an OSN changes over time, thus the user weight in the OSN is different in each time frame. Therefore, a good metric for estimating the user weight in an OSN depends on the accuracy of the metric used to define the time interval. New metric for defining the time intervals is based on the standard deviation and identifies that the user weight is based on a simple exponential smoothing model.

The results show that the proposed method covers the maximum behavioral changes of the OSN and is able to identify the influential users in the OSN more accurately than existing methods.

In event detection, when a terrorist attack occurs as an event, knowing the influential users help us to know the leader of the attack. Knowing the influential user in each time interval based on this study can help us to detect communities which formed around these people. Finally, in marketing, this issue helps us to have a targeted advertising.

User effect is a significant issue in many OSN domain problems, such as community detection, event detection and recommender systems.

Previous studies do not give priority to the recent time intervals in identifying the relative importance of users. Thus, defining a metric to compute a time interval that covers the maximum changes in the network is a major shortcoming of earlier studies. Some experiments were conducted on six different data sets to test the performance of the proposed model in terms of the computed time intervals and user weights.

For some specific multi-criteria decision-making (MCDM) problems, especially in emergency situations, because of the feature of criteria and other fuzzy factors, it is more appropriate that values of different criteria are expressed in their correspondingly appropriate value types. The purpose of this paper is to build a multi-criteria group decision-making (MCGDM) model dealing with heterogeneous information based on distance-based VIKOR to solve emergency supplier selection in practice appropriately and flexibly, where a compromise solution is more acceptable and suitable.

This paper extends the classical VIKOR to a generalized distance-based VIKOR to handle heterogeneous information containing crisp number, interval number, intuitionistic fuzzy number and hesitant fuzzy linguistic value, and develops an MCGDM model based on the distance-based VIKOR to handle the multi-criteria heterogeneous information in practice. This paper also introduces a parameter called non-fuzzy degree for each type of heterogeneous value to moderate the computation on aggregating heterogeneous hybrid distances.

The proposed distance-based model can handle the heterogeneous information appropriately and flexibly because the computational process is directly operated on the heterogeneous information based on generalized distance without a transformation process, which can improve the decision-making efficiency and reduce information loss. An example of emergency supplier selection is given to illustrate the proposed method.

This paper develops an MCGDM model based on the distance-based VIKOR to handle heterogeneous information appropriately and flexibly. In emergency supplier selection situations, the proposed decision-making model allows the decision-makers to express their judgments on criteria in their appropriate value types.