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Constructing a fuzzy control chart with interval-valued fuzzy data is an important topic in the fields of medical, sociological, economics, service and management. In particular, when the data illustrates uncertainty, inconsistency and is incomplete which is often the. case of real data. Traditionally, we use variable control chart to detect the process shift with real value. However, when the real data is composed of interval-valued fuzzy, it is not feasible to use such an approach of traditional statistical process control (SPC) to monitor the fuzzy control chart. The purpose of this paper is to propose the designed standardized fuzzy control chart for interval-valued fuzzy data set.

The general statistical principles used on the standardized control chart are applied to fuzzy control chart for interval-valued fuzzy data.

When the real data is composed of interval-valued fuzzy, it is not feasible to use such an approach of traditional SPC to monitor the fuzzy control chart. This study proposes the designed standardized fuzzy control chart for interval-valued fuzzy data set of vegetable price from January 2009 to September 2010 in Taiwan obtained from Council of Agriculture, Executive Yuan. Empirical studies are used to illustrate the application for designing standardized fuzzy control chart. More related practical phenomena can be explained by this appropriate definition of fuzzy control chart.

This paper uses a simpler approach to construct the standardized interval-valued chart for fuzzy data based on traditional standardized control chart which is easy and straightforward. Moreover, the control limit of the designed standardized fuzzy control chart is an interval with (LCL, UCL), which consists of the conventional range of classical standardized control chart.

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.

The purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model and to improve some preliminary aggregation operators such as probabilistic interval-valued hesitant fuzzy averaging (PIVHFA) operator, probabilistic interval-valued hesitant fuzzy geometric (PIVHFG) operator, probabilistic interval-valued hesitant fuzzy weighted averaging (PIVHFWA) operator, probabilistic interval-valued hesitant fuzzy ordered weighted averaging (PIVHFOWA) operator, probabilistic interval-valued hesitant fuzzy weighted geometric (PIVHFWG) operator and probabilistic interval-valued hesitant fuzzy ordered weighted geometric (PIVHFOWG) operator to cope with multicriteria group decision-making (MCGDM) problems in an efficient manner.

(1) To design probabilistic interval-valued hesitant fuzzy TOPSIS model. (2) To improve some of the existing aggregation operators. (3) To propose the Hamming distance, Euclidean distance, Hausdorff distance and generalized distance between probabilistic interval-valued hesitant fuzzy sets (PIVHFSs).

The results of the proposed model are discussed in comparison with the aggregation-based method from the related literature and found the effectiveness of the proposed model and improved aggregation operators.

A case study concerning the healthcare facilities in public hospital is addressed.

The notion of the proposed distance measure is used as rational tool to extend TOPSIS model for probabilistic interval-valued hesitant fuzzy setting.

The healthcare system is regarded as one of the most critical service industries. The surgical unit is the heart of hospitals in that any failures directly affect the safety of patients, so they should be managed thoroughly. It is an intricate multi-attributes decision-making problem with uncertainty. Uncertain information in the form of fuzzy sets theory has been applied widely to describe the different aspects of system uncertainty. This study aims to present a new methodology to manage the healthcare system failures due to the multi-attributes decision-making process.

This study introduces a new risk evaluation methodology by failure mode and effect analysis (FMEA) and MULTIMOORA method. Group decision-making process in this methodology is presented under uncertain information in the form of interval-valued hesitant fuzzy linguistic sets (IVHFLSs). IVHFLSs encompass both qualitative and quantitative interpretation of experts to reflect their preferences, as well the ability and flexibility of derivation of linguistic information by several linguistic terms increase. To avoid the different ranking order of MULTIMOORA approaches, a new interval multi-approaches multi-attribute methodology, namely, technique of precise order preference (TPOP), is extended to provide precise ranking order.

The application and precision of proposed integrated IVHFL-MULTIMOORA methodology with TPOP is examined in a case study of healthcare systems. The results indicate the superiority of proposed methodology to prioritize and assess the failures as well as handling system uncertainty.

This study addresses the challenges of an organization to prioritize potential failures by implementing FMEA method. Moreover, this paper contributes to making the manager's ability in decision-making. The value of this study can be discussed in two aspects. First and foremost, this study provides a new FMEA-based methodology to rank failures precisely. The results prove that the proposed methodology is more robust to changes of different ranking order methods, applied by FMEA. On the other hand, using the capability of IVHFLSs allows collecting accurate information in an ambiguous and uncertain environment.

Exact confidence interval estimation for the new extreme value model is often impractical. This paper seeks to evaluate the accuracy of approximate confidence intervals for the two‐parameter new extreme value model.

The confidence intervals of the parameters of the new model based on likelihood ratio, Wald and Rao statistics are evaluated and compared through the simulation study. The criteria used in evaluating the confidence intervals are the attainment of the nominal error probability and the symmetry of lower and upper error probabilities.

This study substantiates the merits of the likelihood ratio, the Wald and the Rao statistics. The results indicate that the likelihood ratio‐based intervals perform much better than the Wald and Rao intervals.

Exact interval estimates for the new model are difficult to obtain. Consequently, large sample intervals based on the asymptotic maximum likelihood estimators have gained widespread use. Intervals based on inverting likelihood ratio, Rao and Wald statistics are rarely used in commercial packages. This paper shows that the likelihood ratio intervals are superior to intervals based on the Wald and the Rao statistics.

By using small reference samples, the calculation method of confidence value and prediction method of confidence interval for multi-input system are investigated. The purpose of this paper is to offer effective assessing methods of confidence value and confidence interval for the simulation models used in establishing guidance and control systems.

In this paper, first, an improved cluster estimation method is proposed to guide the selection of the small reference samples. Then, based on analytic hierarchy process method, the new calculation method of the weight of each reference sample is derived. By using the grey relation analysis method, new calculation methods of the correlation coefficient and confidence value are presented. Moreover, the confidence interval of the sample awaiting assessment is defined. A new prediction method is derived to obtain the confidence interval of the sample awaiting assessment which has no reference sample. Subsequently, by using the prediction method and original small reference samples, Bootstrap resampling method is used to obtain more correlation coefficients for the sample to reduce the probability of abandoning the true.

The grey relational analysis is used in assessing the confidence value and interval prediction. The numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Based on the selected small reference samples, new calculation methods of the correlation coefficient and confidence value are presented to assess the confidence value of model awaiting assessment. The calculation methods of maximum confidence interval, expected confidence interval and other required confidence intervals are presented, which can be used in assessing the validities of controller and guidance system obtained from the model awaiting assessment.

Modelling and forecasting interval-valued time series (ITS) have received increasing attention in statistics and econometrics. An interval-valued observation contains more information than a point-valued observation in the same time period. The previous literature has mainly considered modelling and forecasting a univariate ITS. However, few works attempt to model a vector process of ITS. In this paper, we propose an interval-valued vector autoregressive moving average (IVARMA) model to capture the cross-dependence dynamics within an ITS vector system. A minimum-distance estimation method is developed to estimate the parameters of an IVARMA model, and consistency, asymptotic normality and asymptotic efficiency of the proposed estimator are established. A two-stage minimum-distance estimator is shown to be asymptotically most efficient among the class of minimum-distance estimators. Simulation studies show that the two-stage estimator indeed outperforms other minimum-distance estimators for various data-generating processes considered.

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.

We investigate the impact of the creation of a new incentive structure for CEOs resulting from firms introducing equity-based compensation (EBC) as a means of paying top executives on policy decisions. Contrasting a firm’s stock and operating performance in the period the CEO is compensated with EBC (EBC period) and the period when EBC is not a component of the same executive’s pay (No EBC period) leads us to conclude that awarding stock options and restricted shares to executives is not associated with improved firm performance. However, firms initiate EBC after superior performance suggesting that CEOs are awarded compensation in this form as a reward for past performance. Firms have higher unsystematic and total risk levels in the EBC period suggesting EBC influences CEOs’ risk-taking behavior and reduces agency costs arising from managerial risk aversion. While there is no change in R&D expenses and cash ratios there is a decrease in capital expenditures in the EBC period, which is consistent with reduced overinvestment agency costs. Finally, leverage and payout ratios are similar in both periods implying that firms’ financing policy is not influenced by changes in CEOs’ compensation structure.

The traditional data envelopment analysis (DEA) model as a non-parametric technique can measure the relative efficiencies of a decision-making units (DMUs) set with exact values of inputs and outputs, but it cannot handle the imprecise data. The purpose of this paper is to establish a super efficiency interval data envelopment analysis (IDEA) model, an IDEA model based on cross-evaluation and a cross evaluation-based measure of super efficiency IDEA model. And the authors apply the proposed approach to data on the 29 public secondary schools in Greece, and further demonstrate the feasibility of the proposed approach.

In this paper, based on the IDEA model, the authors propose an improved version of establishing a super efficiency IDEA model, an IDEA model based on cross-evaluation, and then present a cross evaluation-based measure of super efficiency IDEA model by combining the super efficiency method with cross-evaluation. The proposed model cannot only discriminate the performance of efficient DMUs from inefficient ones, but also can distinguish between the efficient DMUs. By using the proposed approach, the overall performance of all DMUs with interval data can be fully ranked.

A numerical example is presented to illustrate the application of the proposed methodology. The result shows that the proposed approach is an effective and practical method to measure the efficiency of the DMUs with imprecise data.

The proposed model can avoid the fact that the original DEA model can only distinguish the performance of efficient DMUs from inefficient ones, but cannot discriminate between the efficient DMUs.

This paper introduces the effective method to obtain the complete rank of all DMUs with interval data.