Presence Of Imprecise Data Research Articles

Analysis of imprecise measurement data utilizing z-test for correlation

AbstractThe conventional Z-test for correlation, grounded in classical statistics, is typically employed in situations devoid of vague information. However, real-world data often comes with inherent uncertainty, necessitating an adaptation of the Z-test using neutrosophic statistics. This paper introduces a modified Z-test for correlation designed to explore correlations in the presence of imprecise data. We will present the simulation to check the effect of the measure of indeterminacy on the evolution of type-I error and the power of the test. The application of this modification is illustrated through an examination of heartbeat and temperature data. Upon analyzing the heartbeat and temperature data, it is determined that, in the face of indeterminacy, the correlation between heartbeat and temperature emerges as significant. This highlights the importance of accounting for imprecise data when investigating relationships between variables.

A DEA-WEI method for ranking universities in the presence of imprecise data

A DEA-WEI method for ranking universities in the presence of imprecise data

A DEA-WEI method for ranking universities in the presence of imprecise data

A DEA-WEI method for ranking universities in the presence of imprecise data

Unsupervised Hierarchical Classification Approach for Imprecise Data in the Breast Cancer Detection.

(1) Background: in recent years, a lot of the research of statistical methods focused on the classification problem in presence of imprecise data. A particular case of imprecise data is the interval-valued data. Following this research line, in this work a new hierarchical classification technique for multivariate interval-valued data is suggested for diagnosis of the breast cancer; (2) Methods: an unsupervised hierarchical classification method for imprecise multivariate data (called HC-ID) is performed for diagnosis of breast cancer (i.e., to discriminate between benign or malignant masses) and the results have been compared with the conventional (unsupervised) hierarchical classification approach (HC); (3) Results: the application on real data shows that the HC-ID procedure performs better HC procedure in terms of accuracy (HC-ID = 0.80, HC = 0.66) and sensitivity (HC-ID = 0.61, HC = 0.08). In the results obtained by the usual procedure, there is a high degree of false-negative (i.e., benign cancer diagnosis in malignant status) affected by the high degree of variability (i.e., uncertainty) characterizing the worst data.

Towards greener petrochemical production: Two-stage network data envelopment analysis in a fully fuzzy environment in the presence of undesirable outputs

Traditional Data Envelopment Analysis (DEA) models usually consider decision-making units (DMU) as black boxes that consume a set of inputs to produce a set of outputs and ignore the units’ internal structure. In literature, two-stage DEA models have been introduced and developed to deal with the inner workings of such DMUs; however, models in the extant literature can only be used to assess technologies with precise inputs and outputs. In this study we present an innovative two-stage DEA model for DMU evaluation in the presence of imprecise data, which are modeled using triangular fuzzy values in this study. We also innovate by including the treatment of undesirable outputs. We propose some alternative two-stage DEA network models with undesirable outputs in a full-fuzzy mode that are either directional or radial and are embedded within a multi-objective linear planning structure based on fuzzy triangular numbers. We also propose a method to solve fuzzy programming models in the presence of undesirable pollutant outputs from production processes such as greenhouse gas emissions, harmful effluents, among others. Our proposed model is then applied to a real case of 15 ammonia-manufacturing units in the Iranian petrochemical sector. The promising results that we obtained in our research and their implications for theory and practice are then presented and discussed.

Two-stage common weight DEA-Based approach for performance evaluation with imprecise data

A multi-criteria decision making approach based on data envelopment analysis (DEA) is presented to identify the best performing decision making unit (DMU) accounting for multiple inputs and multiple outputs with the presence of imprecise data. The developed α-cut based two-stage mathematical programming approach, which yields feasible solutions for all α-cut levels, generates common set of weights for inputs and outputs, and thus, provides more practical and realistic performance assessment of DMUs. A single rank-order is obtained through OWA operator that is employed for aggregating the efficiency scores regarding α-levels for each DMU. The robustness of the developed methodology is illustrated by examples taken from earlier research studies along with a case study that is conducted to aid an expatriate to identify the most desirable country in terms of quality of living. The proposed approach provides a ranking with improved discriminating power and enhanced weight dispersion with regard to inputs and outputs while also guaranteeing to determine a single best performing DMU.

A novel method for solving data envelopment analysis problems with weak ordinal data using robust measures

The efficiency measurement with traditional data envelopment analysis (DEA) requires precise input and output data. However, the input and output data is imprecise in many real-world problems. Various imprecise methods are developed to estimate the lower and upper bound efficiency scores in the presence of interval and weak ordinal data. We show the existing methods provide an estimation of the lower or upper bound efficiency score and cannot find their exact values in the presence of weak ordinal data. As a result, the ranking of decision making units (DMUs) may not be reliable since they are based on estimated efficiency scores. We propose a pair of DEA models to find the lower and upper bound efficiency scores. We prove the proposed models can find the exact values of the lower and upper bound efficiency scores in the presence of weak ordinal data. However, these exact values depend on a set of parameters in the presence of ordinal data. Therefore, we further propose a novel measure, fathoming the robustness of the efficiency function for the parameter space, to select the best practice DMUs in the presence of imprecise data. We present a real-world application in the space industry to demonstrate the applicability and superiority of the proposed method over the existing methods.

Satisfaction and Tourism Expenditure Behaviour

In the literature, the quantification of the effect of satisfaction on tourists’ expenditure behaviour has not been extensively studied. This research aims to fill in this gap, providing additional information about this crucial relation by analysing it from a microdata perspective. In particular, the Fuzzy Double-Hurdle model, a new model which combines the well-known Double-Hurdle model and the fuzzy set theory, is suggested and presented, both technically and by means of a real case study. The proposed model gathers the advantages of the Double-Hurdle model and the fuzzy set theory together producing a suitable model for the analysis of censored observations in presence of imprecise data. Specifically, the Double-Hurdle model allows to efficiently estimate the average values of a non-negative, non-normally distributed variable characterised by high frequency of zero values, as tourists’ expenditure can be, considering the two-stages nature of the decision process. On the other end, the inclusion of the fuzzy set theory in the regression model allows to cope with the imprecision of both collected information (i.e. levels of satisfaction) and kind of measurement used (i.e. Liker-type scale). The results will help tourism managers to more accurately evaluate the efficacy of their policies and marketing strategies in enhancing tourists’ satisfaction and, consequently, in increasing the level of spending at the destination.

Efficiency bounds and efficiency classifications in imprecise DEA: An extension

Park proposed a pair of mathematical data envelopment analysis (DEA) models to estimate the lower and upper bound of efficiency scores in the presence of imprecise data. This article illustrates that his approach suffers from some drawbacks: (i) it may convert weak ordinal data into an incorrect set of precise data; (ii) it utilizes various production frontiers to obtain an interval efficiency score for each decision making unit (DMU); (iii) in the absence of exact output data (pure ordinal output data), the approach leads to a meaningless model; (iv) the built model is infeasible with pure ordinal input data; (v) it may include free or unlimited production output which results in unreliable and suspicious results. Moreover, the utilized models by Park involve a positive lower bound (non-Archimedean epsilon) for the weights to deter them from being zero. However, the author ignored the requirement of determining a suitable value for the epsilon. This study constructs two new DEA models with a fixed and unified production frontier (the same constraint set) to compute the upper and lower bounds of efficiency. It is demonstrated that the suggested models can successfully capture the aforementioned shortcomings. Although these models are also epsilon-based, a new model is developed to obtain a suitable epsilon value for the proposed models. It is proved that the suggested approach effectively eliminates all the weaknesses. Additionally, a case study of Iranian Space Agency (ISA) industry is taken as an example to illustrate the superiority of the new approach over the previous ones.

The optimistic–pessimistic revenue distribution in the presence of imprecise data

In many situations, a common revenue or benefit must be distributed amongst a set of beneficiary decision making units (DMUs) with imprecise data represented by fuzzy or stochastic data. A fair revenue distribution can certainly increase the motivation of DMUs for improving their performances. The share of each DMU must be determined according to its eligibility. To access a fair distribution, we use an optimistic–pessimistic approach of data envelopment analysis which considers both weaknesses and strengths of DMUs. This method determines the share of each DMU according to a combination of its minimum and maximum possible shares which are respectively obtained under the pessimistic and optimistic approaches.

A comparative study of robust efficiency analysis and Data Envelopment Analysis with imprecise data

Data Envelopment Analysis gauges the performance of operating entities in the best scenario for input and output multipliers. Robust efficiency analysis is a conservative approach that is concerned with an assured level of performance for an entity across all possible multiplier scenarios. In this study, we extend the robust efficiency analysis procedure to the situation where precise information on some input and output data is unavailable. Perfect efficiency analysis and potential efficiency analysis methods are developed to determine, respectively, the lower and upper bounds of an entity’s robust efficiency rating. The concepts of robust efficiency are expanded to classify entities in consideration into three groups: perfectly robust efficient, potentially robust efficient and robust inefficient. Two approaches are presented to convert robust efficiency analysis models into linear programs. It is claimed that Data Envelopment Analysis and robust efficiency analysis together provide a comprehensive picture of an entity’s relative efficiency. A computational experiment is conducted to compare the traditional efficiency analysis method with robust efficiency analysis in the presence of imprecise data. The results illustrate that perfect efficiency analysis exhibits a superior power of discrimination than potential efficiency analysis and that an entity recommended by perfect efficiency analysis has a satisfactory average performance.

Developing imprecise dual-role hybrid measure of efficiency for international market selection using ternary variable

By choosing the best international market from a set of potential countries, firms plan to start new or expand existing international activities. In marketing literature, this process is known as international market selection or target market selection. In realistic situations, some of data of international markets cannot be provided accurately since they are imprecise. Some other criteria of international market analysis are dual-role, i.e., they may be classified either as an input or as an output, simultaneously. The quantity of such factors may influence relative attractiveness of international markets. Moreover, in international market selection, some factors are beyond control of decision-maker(s) and cannot be modified at discretion of management. These factors may affect final decision. As a non-parametric technique, data envelopment analysis (DEA) provides adequate ability for decision makers to select a set of international markets. In this paper, using ternary variable, a new DEA-based model is proposed for international market selection in the presence of imprecise data, dual-role factors, and non-discretionary inputs. The proposed model is able to take into account radial and non-radial measures, as well. A case study illustrates the application of the proposed model.

Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.

Selecting and full ranking suppliers with imprecise data: A new DEA method

Supplier selection, a multi-criteria decision making (MCDM) problem, is one of the most important strategic issues in supply chain management (SCM). A good solution to this problem significantly contributes to the overall supply chain performance. This paper proposes a new integrated mixed integer programming ‐ data envelopment analysis (MIP‐DEA) model for finding the most efficient suppliers in the presence of imprecise data. Using this model, a new method for full ranking of units is introduced. This method tackles some drawbacks of the previous methods and is computationally more efficient. The applicability of the proposed model is illustrated, and the results and performance are compared with the previous studies.

A note on “A decision model for ranking suppliers in the presence of cardinal and ordinal data, weight restrictions, and nondiscriminatory factors”

Farzipoor Saen (Ann. Oper. Res. 172(1):177–192, 2009) proposed a method based on Data Envelopment Analysis (DEA) for selecting the best supplier in the presence of cardinal and ordinal data, weight restrictions, and non-discriminatory factors. In the present note, we show that the DEA method proposed by Farzipoor Saen (Ann. Oper. Res. 172(1):177–192, 2009) cannot be used for selecting the best supplier in the presence of imprecise data. It is also shown that there are computational errors in calculating the amounts of the preference intensity parameter and the ratio parameter in Farzipoor Saen’s paper.

An integrated methodology for supplier selection and order allocation in the presence of imprecise data

There has been numerous number of studies related to the supplier selection and problems which adopted a variety of approaches to solve them, however, based on our knowledge none of them has been considered the major decisions related to supplier selection and order allocation in the presence of imprecise data. In an attempt to fulfil this gap, we present an integrated framework which involves two stages including supplier evaluation and order allocation. An augmented imprecise data envelopment analysis (AIDEA) is proposed for supplier evaluation as the basic IDEA model has two main drawbacks, i.e., unrealistic input-output weights and poor discriminating power among all suppliers. Then, an integer programming with fuzzy objectives and constraints is formulated to assign optimal quantity of order to allocated suppliers. The efficiency of suppliers derived from evaluation stage is an important link which integrates these two stages. Finally, the integrated methodology is implemented in a case study organisation.

Developing a worst practice DEA model for selecting suppliers in the presence of imprecise data and dual-role factor

Determining the appropriate supplier is a crucial strategic consideration in supply chain management. Worst-practice frontier data envelopment analysis (WPF-DEA) model is one of the new models in data envelopment analysis (DEA). In this paper, the concept of imprecise data envelopment analysis (IDEA) approach and dual-role factor is used to develop WPF-DEA model. Then, the proposed model is applied for supplier selection problem. A numerical example demonstrates the application of the proposed model.

Hybrid organization of functional departments and manufacturing cells in the presence of imprecise data

Hybrid organization of functional departments and manufacturing cells in the presence of imprecise data

Hybrid organization of functional departments and manufacturing cells in the presence of imprecise data

Although the benefits of forming cells are widely recognized, certain industrial decision makers do not wish an entire transformation because of possible changes that may occur, for example, in the demand, mix or routing of products. Therefore, hybrid organization of functional departments and manufacturing cells in the same shop may appear quite relevant. The problem addressed here is how to allocate machines and products so as to design such systems that take advantages of both types of layout. We suggest an approach that favours cells for the parts that are regularly manufactured over time (i.e. stable parts), and functional departments for the parts that require more flexibility. We also consider the difficulties arising in the collection of precise data in reality. Hybrid shop design problem is formulated as a constrained fuzzy multi-objective optimization problem and an evolutionary programming algorithm is devised to solve it. The approach is illustrated in test examples.

Technology selection in the presence of imprecise data, weight restrictions, and nondiscretionary factors

Technology selection is an important part of management of technology. Traditionally, technology selection models are based on cardinal data with less emphasis on ordinal data. However, with respect to technology selection complexity, emphasis has shifted to the simultaneous consideration of cardinal and ordinal data in technology selection process. The application of data envelopment analysis (DEA) for technology selection problems is based on total flexibility of the weights. However, the problem of allowing total flexibility of the weights is that the values of the weights obtained by solving the unrestricted DEA program are often in contradiction to prior views or additional available information. On the other hand, current models of technology selection problems assume complete discretion of decision-making criteria and do not assume technology selection in the conditions that some factors are nondiscretionary. To select the best technologies in the presence of cardinal data, ordinal data, nondiscretionary factors, and weight restrictions, the objective of this paper is to propose a new pair of assurance region-nondiscretionary factors-imprecise data envelopment analysis (AR-NF-IDEA) models. A numerical example demonstrates the application of the proposed method.