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This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function.

To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed.

The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results.

Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.

The purpose of this paper is to determine an extension of the MIN and MAX general analytical expression for triangular fuzzy intervals to trapezoidal ones when Zadeh's extension principle is considered.

In order to determine the MIN and MAX analytical expressions, the paper exhibits the conventional interval relations and their extension in fuzzy case where trapezoidal fuzzy intervals are assumed. The formalization and the justification of the so‐built analytical expressions are then detailed where mathematical mappings are proposed. The potential use of these operators in the framework of uncertain aggregation operators and ranking fuzzy intervals is shown with illustrative examples.

It is discovered that the MIN and MAX operations for fuzzy intervals can be formulated by a general analytical form.

The proposed methodology can be directly applied for ranking fuzzy intervals and implementing a large class of uncertain aggregation operators, especially for two‐additive Choquet integral.

The originality of the proposed technique resides in exploiting the interval relations between supports and kernels to express a general and compact analytical MIN and MAX expressions for fuzzy intervals.

The purpose of this paper is to introduce an interval finite element method (IFEM) to simulate the temperature field of mass concrete under multiple influence uncertainties e.g. environmental temperature, material properties, pouring construction and pipe cooling.

Uncertainties of the significant factors such as the ambient temperature, the adiabatic temperature rise, the placing temperature and the pipe cooling are comprehensively studied and represented as the interval numbers. Then, an IFEM equation is derived and a method for obtaining interval results based on monotonicity is also presented. To verify the proposed method, a non-adiabatic temperature rise test was carried out and subsequently simulated with the method. An excellent agreement is achieved between the simulation results and the monitoring data.

An IFEM method is proposed and a non-adiabatic temperature rise test is simulated to verify the method. The interval results are discussed and compared with monitoring data. The proposed method is found to be feasible and effective.

Compared with the traditional finite element methods, the proposed method taking the uncertainty of various factors into account and it will be helpful for engineers to gain a better understanding of the real condition.

This paper aims to propose a novel statistic energy analysis method with fuzzy parameters to study the dynamic and acoustic responses of coupled system with fuzzy parameters, which can expand the applied range of statistic energy analysis method in engineering to some extent.

On the basis of the property of membership level, the uncertain fuzzy parameters are expressed as the interval forms. Interval mathematics and interval expansion principle are adopted to solve the problem with interval parameters. At last, two numerical examples, which include a two-plate coupled system and a single-partition sound-insulation system, are carried out to demonstrate the feasibility and validity of the presented method.

Interval mathematics and interval expansion principle are adopted to solve the problem with interval parameters.

By integrating the interval analysis, optimization technique and Taylor expansion method, two non-probabilistic, set-theoretical statistical energy analyses are proposed for predicting the dynamical and acoustical response of the complex coupled system with uncertain parameters in high-frequency domain.

The purpose of this paper is to focus on the influences of the uncertain dynamic responses on the reconstruction of loads.

Based on the assumption of unknown-but-bounded (UBB) noise, a time-domain approach to estimate the uncertain time-dependent external loads is presented by combining the inverse system method in modern control theory and interval analysis in interval mathematics. Inspired by the concept of set membership identification in control theory, an interval analysis model of external loads time history, which is indeed a region or feasible set containing all possible loads being consistent with the bounded structural acceleration responses is established and further solved by two interval algorithms.

Unlike traditional loads identification methods which only give a point estimation, an interval estimation of external loads time history, which is a region containing all the possible loads being consistent with the uncertain structural responses, is determined. The correlation characteristics among the responses of acceleration, velocity, and displacement are also discussed in consideration of the UBB uncertainty.

For one hand, the solution of the inverse problem in original system is transformed to the solution of the direct problem in inverse system; for another, the authors deal with the uncertainty by use of interval analysis method, and the identified interval process, which contains any possible external loads time history being consistent with the bounded structural responses can be approximately obtained.

The various approaches to achieving extended drain intervals in vehicle crankcase lubricants are described, with particular emphasis on commercial diesel engines. The various lubricant contaminants include soot, water, acids and particulate metals. Lubricant life may be prolonged by suitable design of the lubricant and of the engine, but more particularly by reducing the levels of contaminant in the lubricant such that the performance of the lubricant may be maintained. At the same time, wear rates within the engine must be within acceptable levels. The various options for reducing the levels of contaminant include lubricant by‐pass filtration systems, including barrier filters, refiners and centrifugal filters.

Due to the current pandemic, the importance of logistics functions and decisions is well understood both at the level of companies and users. Logistics systems and related decisions are of vital importance in making supply chains effective, efficient and without disruption. Logistic pressure factors may emerge at different points along the logistics process, and given the role of logistics decisions as one of the important indicators of competitiveness, the determination of the logistics pressures that are likely to increase the costs of business, and their causative factors are a vital aspect of the logistics decision-making process. The study aims to provide assistance in the selection of the most ideal logistics decision by ranking the pressure factors affecting the logistics system, especially during the pandemic period for logistics enterprises operating in Ordu and Giresun provinces and which have a corporate identity.

In this study, it is aimed to make the most ideal logistics decision selection by ranking the pressure factors affecting the logistics system, especially during the pandemic period for the logistics enterprises operating in Ordu and Giresun provinces and having a corporate identity. For that purpose interval-valued Pythagorean fuzzy (IVPF)–analytic hierarchy process (AHP) based combinative distance-based assessment (CODAS) methodology was used. Additionally sensitivity and comparison analysis were discussed.

Competitive pressure was found as the most important pressure factor affecting the logistics system during the pandemic period. Change in regulatory rules was the pressure factor found to have the least effect on the logistics system. Using the weights of logistics pressure factors, “Operational Decisions” was found to be the most ideal logistics decision selection.

The findings provide support for the evaluation of logistical pressures and decision options by presenting a decision model capable of processing ambiguous information. During a pandemic or similar period, the study assists decision makers in determining a new route. The findings will also call business managers' attention to logistical pressure factors and lead them toward more realistic and feasible practices in the logistics decision-making process.

This study provided an effective and applicable solution to a decision-making problem in the logistics sector including logistics pressure factors and the selection of logistics decisions. In this context, a methodology was presented that will allow businesses to self-evaluate their own logistics pressure factors and the selection of optimal solutions.

This study aims to introduce the achievements and benefits of applying wheel/rail-force–based maintenance interval extension of the C80 series wagon in China.

Chinese wagons' existing maintenance strategy had left a certain safety margin for the characteristics of widely running range, unstable service environment and submission to transportation organization requirements. To reduce maintenance costs, China railway (CR) has attempted to extend the maintenance interval since 2020. The maintenance cycle of C80 series heavy haul wagons is extended by three months (no stable routing) or 50,000 km (regular routing). However, in the meantime, the alarming rate of the running state, a key index to reflect the severe degree of hunting stability, by the train performance detection system (TPDS) for the C80 series heavy haul wagons has increased significantly.

The present paper addresses a big data statistical way to evaluate the risk of allowing the C80 series heavy haul wagons to remain in operation longer than stipulated by the maintenance interval initial set. Through the maintenance and wayside-detector data, which is divided into three stages, the extension period (three months), the current maintenance period and the previous maintenance period, this method reveals the alarming rate of hunting was correlated with maintenance interval. The maintainability of wagons will be achieved by utilizing wagon performance degradation modeling with the state of the wheelset and the often-contact side bearing. This paper also proposes a statistical model to return to the average safety level of the previous maintenance period's baseline through correct alarming thresholds for unplanned corrective maintenance.

The paper proposes an approach to reduce safety risk due to maintenance interval extension by effective maintenance program. The results are expected to help the railway company make the optimal solution to balance safety and the economy.

The purpose of this paper lies in the combination of fuzzy set and interval grey set, namely, considering the fuzzy set theory, rough set theory and grey system theory. The paper then presents a unified form (or symbol system) which can be more useful to describe a wide variety of theories.

Considering the lower bounds and upper bounds of interval grey set are classical set, this paper draws lessons from the classical set to fuzzy set transition mode which was advanced by Professor Zadeh. The paper puts forward the concept of interval fuzzy set, and then relaxes the constraints of the lower bound of interval fuzzy set to make it more widely used in actual uncertain problems.

For the examples which have been given in the paper, interval fuzzy set and its three theorems are proved practical and flexible.

The theorems proved in the paper can be used as a useful extension to the classical fuzzy set, which can also be applied to fuzzy clustering, fuzzy classification, fuzzy pattern recognition and so on.

The paper puts forward the concept of interval fuzzy set and the three theorems of interval fuzzy set and proves their practicability and flexibility. The theorems can be used for further study on interval fuzzy set.

Remanufacturing of worn blades with various defects normally requires processes such as scanning, regenerating a geometrical reference model, additive manufacturing (AM) through laser cladding, adaptive machining and polishing and quality inspection. Unlike the manufacturing process of a new part, the most difficult problem for remanufacturing such a complex surface part is that the reference model adaptive to the worn part is no longer available or useful. The worn parts may suffer from geometrical deformation, distortion and other defects because of the effects of harsh operating conditions, thereby making their original computer aided design (CAD) models inadequate for the repair process. This paper aims to regenerate the geometric models for the worn parts, which is a key issue for implementing AM to build up the parts and adaptive machining to reform the parts. Unlike straight blades with similar cross sections, the tip geometry of the worn tip of a twist blade needs to be regenerated by a different method.

This paper proposes a surface extension algorithm for the reconstruction of a twist blade tip through the extremum parameterization of a B-spline basis function. Based on the cross sections of the scanned worn blade model, the given control points and knot vectors are firstly reconstructed into a B-spline curve D. After the extremum of each control point is calculated by extremum parameterization of a B-spline basis function, the unknown control points are calculated by substituting the extremum into the curve D. Once all control points are determined, the B-spline surface of the worn blade tip can be regenerated. Finally, the extension algorithm is implemented and validated with several examples.

The proposed algorithm was implemented and verified through the exampled blades. Through the extension algorithm, the tip geometry of the worn tip of a twist blade can be regenerated. This method solved a key problem for the repair of a twist blade tip. It provides an appropriate reference model for repairing worn blade tips through AM to build up the blade tip and adaptive machining/polishing processes to reform the blade geometry.

The extension errors for different repair models are compared and analyzed. The authors found that there are several factors affecting the accuracy of the regenerated model. When the cross-section interval and the extension length are set properly, the restoration accuracy for the blade tip can be improved, which is acceptable for the repairing.

The lack of a reference geometric model for worn blades is a significant problem when implementing blade repair through AM and adaptive machining processes. Because the geometric reference model is unavailable for the repair process, reconstruction of the geometry of a worn blade tip is the first crucial step. The authors proposed a surface extension algorithm for the reconstruction of a twist blade tip. Through the implementation of the proposed algorithm, the blade tip model can be regenerated.

Remanufacturing of worn blades with various defects is highly demeaned for the aerospace enterprises considering sustainable development. Unlike straight blades, repair of twist blades encountered a very difficult problem because the geometric reference model is unavailable for the repair processes. This paper proposed a different method to generate the reference model for the repair of a twist blade tip. With this model, repair of twist blades can be implemented through AM to build up the blade tip and adaptive machining to subtract the extra material.

The authors proposed a surface extension algorithm to reconstruct the geometric model for repair of twist blades.