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The uncertainty of the interval variable is represented by interval factor, and the interval variable is described as its mean value multiplied by its interval factor. Based on interval arithmetic rules, an analytical method of interval finite element for uncertain structures but not probabilistic structure or fuzzy structure is presented by combining the interval analysis with finite element method. The static analysis of truss with interval parameters under interval load is studied and the expressions of structural interval displacement response and stress response are deduced. The influences of uncertainty of one of structural parameters or load on the displacement and stress of the structure are examined through examples and some significant conclusions are obtained.

To introduce an interval arithmetic (IA)‐based approach to tolerance analysis and design and to yield evaluation. The technique distinguishes itself by its reliability in the detection of even non convex and/or non simply connected regions of acceptability.

Range methods, and IA among them, inherently allow the evaluation of an overestimation of the true range spanned by a performance function of a given system because of variation of its parameters values. Such a feature is of great help in performing the robust design of any system, that is, in doing the placement of the design set within the region of acceptability, even in the presence of tolerances and parameters values drifts.

The IA‐based branch and bound numerical procedure proposed in the paper has shown its reliability and robustness during the tolerance analysis of systems exhibiting quite involved regions of acceptability.

Many remarks are reported in the paper to complete the research and extend it to a larger class of problems.

The procedure might be built into simulation environments in order to help the designer in dominating tolerances effects.

This paper shares in suggesting the use of a powerful tool, i.e. range methods, in the area of tolerance design and reliability.

This study aims to accurately evaluate the influence of various error intervals on the performance of the wiper.

The wiper structural system is decomposed into classical four-link planar for kinematics analysis, and it was modeled respectively by using interval method, universal grey number theory and enumeration approach depending on the nature of uncertainty.

The universal grey number theory is a viable methodology for the accurate analysis of uncertain structural system.

(1) The model of uncertain wiper structural system is established. (2) Universal grey number theory and new parameters are adopted to analyze the presence of uncertain wiper structural system. (3) Comparative analysis of response quantities is obtained by interval method, universal grey number theory and enumeration method.

Thermal protection of mineral‐oil‐filled substation distribution transformers is of critical importance in power systems. The failure of such a transformer is a matter of significant concern for electrical utilities, not only for the consequent severe economic losses, but also because the utility response to a customer during outage condition is one of the major factors in determining the overall customer attitude towards the utility. Therefore, it is essential to estimate the thermal state of transformers during load cycling and, in presence of overload conditions, to evaluate the need to reduce the load current or to install another transformer bay. A method of solving the transformer's thermal model, considering explicitly the source of uncertainty affecting its parameters, is required. In this paper, such an activity is developed by an interval‐based approach, which provides the calculation of the inner and outer solution in the hot‐spot temperature or top‐oil temperature estimation process, keeping track of correlation between uncertain quantities.

The purpose of this paper is to formulate the reliability optimization problem in stochastic and interval domain and also to solve the same under different stochastic set up.

Stochastic programming technique has been used to convert the chance constraints into deterministic form and the corresponding problem is transformed to mixed-integer constrained optimization problem with interval objective. Then the reduced problem has been converted to unconstrained optimization problem with interval objective by Big-M penalty technique. The resulting problem has been solved by advanced real coded genetic algorithm with interval fitness, tournament selection, intermediate crossover and one-neighbourhood mutation.

A new optimization technique has been developed in stochastic domain and the concept of interval valued parameters has been integrated with the stochastic setup so as to increase the applicability of the resultant solution to the interval valued nonlinear optimization problems.

The concept of probability distribution with interval valued parameters has been introduced. This concept will motivate the researchers to carry out the research in this new direction.

The application of genetic algorithm is extended to solve the reliability optimization problem in stochastic and interval domain.

For extending the common definitions and concepts of grey system theory to the optimization subject, a dual problem is proposed for the primal grey linear programming problem.

The authors discuss the solution concepts of primal and dual of grey linear programming problems without converting them to classical linear programming problems. A numerical example is provided to illustrate the theory developed.

By using arithmetic operations between interval grey numbers, the authors prove the complementary slackness theorem for grey linear programming problem and the associated dual problem.

Complementary slackness theorem for grey linear programming is first presented and proven. After that, a dual simplex method in grey environment is introduced and then some useful concepts are presented.

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.

The purpose of this study is to investigate the impacts of interval measured data, rather than traditional point data, on economic variability studies.

The study uses interval measured data to forecast the variability of future stock market changes. The variability (interval) forecasts are then compared with point data‐based confidence interval forecasts.

Using interval measured data in stock market variability forecasting can significantly increase forecasting accuracy, compared with using traditional point data.

An interval forecast for stock prices essentially consists of predicted levels and a predicted variability which can reduce perceived uncertainty or risk embedded in future investments, and therefore, may influence required returns and capital asset prices.

Today, social media is counted as an integral part of marketing strategies, which has led to a paradigm change in this field. As reported, social media marketing has been growing over the recent five years and is predicted to be exponentially growing in the future. However, despite the huge promise and intention to adopt social media marketing strategies by organisations, there remain challenges regarding the successful implementation of these new marketing programmes. Accordingly, marketing managers’ awareness of the success factors of social media marketing is essential to return investment in this area. Due to the little research been accomplished in this field, this paper aims to identify the success factors of social networks’ marketing and to rank the factors by using of interval best-worst method (BWM).

To serve the research aims, an extant literature review is accomplished and a focus group approach is conducted to identify the main success factors and sub-factors. To analyse the focus group discussions, a qualitative content analysis approach is applied. Interval BWM is used to calculate the weights of each identified factor.

In the final framework, six main success criteria, including strategy, process, technology, content, performance evaluation and people are identified, for each sub-criteria are developed. The interval BWM results suggest the content criterion as the most important success factor in developing a social media marketing strategy.

First, this research provides a comprehensive insight into the success factors and best practices of social media marketing. This is the first to draw on the critical factors affecting the success of social media marketing, considering people in the organisation such as top management, employees and customers, strategy, process and performance evaluation focussing on the change management requirements for applying social media marketing and technology as the technical factor of the adoption process, simultaneously. Identifying critical success factors of social media marketing will help marketing managers to avoid falling into the trap of developing social media strategies based on less important areas and ignoring the critical ones. Besides, owing to the limited resources of organisations in implementing social media marketing strategies, prioritising and weighing the success factors will lead to a focus on more important areas.

Whilst the related studies have mostly concentrated on the capabilities and activities required to conduct social media marketing and the few research investigated the critical success factors most concentrated on the customer and the content-related factors, the finding of this research goes beyond that and suggests technical, process and human aspects simultaneously in the implementation process in a holistic view.