Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

Abstract

In this paper, we reformulate the conventional DEA models as an imprecise DEA problem and propose a novel method for evaluating the DMUs when the inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose, we convert all data into interval data. In order to convert each fuzzy number into interval data, we use the nearest weighted interval approximation of fuzzy numbers by applying the weighting function, and we convert each ordinal data into interval one. In this manner, we could convert all data into interval data. The presented models determine the interval efficiencies for DMUs. To rank DMUs based on their associated interval efficiencies, we first apply the Ω-index that is developed for ranking of interval numbers. Then, by introducing an ideal DMU, we rank efficient DMUs to present a complete ranking. Finally, we use one example to illustrate the process and one real application in health care to show the usefulness of the proposed approach. For this evaluation, we consider interval, ordinal, and fuzzy data alongside the precise data to evaluate 38 hospitals selected by OIG. The results reveal the capabilities of the presented method to deal with the imprecise data.

Evaluation of Road Safety Performance Based on Self-Reported Behaviour Data Set

“…When collecting self-reported data on behaviour, the main focus is on their final presentation, since, in many cases, respondents are not able to clearly express their judgments, and it is assumed that all final values derived from such data are uncertain [21]. Recently, in an uncertain DEA framework, imprecise DEA approaches [22], fuzzy DEA methods [23], and robust DEA methods [24] have been used. In [25,26], it was shown that both imprecise DEA and fuzzy DEA models can give robust composite index scores, which implies the effectiveness and reliability of these two approaches for modelling qualitative data.…”

“…In [25,26], it was shown that both imprecise DEA and fuzzy DEA models can give robust composite index scores, which implies the effectiveness and reliability of these two approaches for modelling qualitative data. Furthermore, in [23], it is illustrated that each fuzzy number can be converted into an interval number, thus reducing the issue of the DMUs' efficiency assessment to an imprecise DEA problem. In addition to the above, rough set theory, probability theory, Shannon's entropy, and grey theory have been put forward to deal with imprecise and ambiguous data.…”

“…Fuzzy theory is the most-applied methodology for processing imprecise and inaccurate data, most notably when they are described in human language [28]. Apart from the one mentioned above (in [23]), there are two ways to implement fuzzy numbers (usually triangular or trapezoidal) for modelling linguistic variables. The first approach concerns the introduction of alternative scales-for example, the fuzzy Likert scale [29][30][31].…”

ACRMiner: An Incremental Approach for Finding Dense and Sparse Rectangular Regions from a 2D Interval Dataset

“…In data mining, transactions may be event related data in real world and are associated with intervals in both continuous and discrete domains such as intervals of distance, time, blood pressure, etc [2] [3]. An interval has start and end values associated with it [4] [5][6] [7] [8]. Interval data mining is a data mining approach that extracts hidden information, patterns, and association rules [27] from interval data sets.…”

“…Hence the support of any interval properly containing it will be less than the support of it. Let us consider a data set with two intervals I1= [4,7] andI2= [5,8] as shown in Figure 1. The overlapping (intersection) of these two intervals is the interval I3= [5,7].…”