Development of a Bounded Two-Stage Data Envelopment Analysis Model in the Intuitionistic Fuzzy Environment

Abstract

Data Envelopment Analysis is a powerful tool for evaluating the efficiency of decision-making units for the purpose of ranking, comparing, and differentiating efficient and inefficient units. Classical Data Envelopment Analysis methods operate by measuring the efficiency of each DMU compared to similar units without considering their internal workings and structures, which make them unsuitable for cases where DMUs are multistaged processes with intermediate products or when inputs and outputs are ambiguous or nonconfigurable. In problems that involve uncertainty, intuitionistic fuzzy sets can offer a better representation and interpretation of information than classic sets. In this paper, the noncooperative network data envelopment analysis model of Liang et al. (2008), which is based on Stackelberg game theory and efficiency decomposition, is expanded using the concepts of best and worst relative returns Data Envelopment Analysis model of Azizi et al. (2013) into an interval efficiency estimation model with α-β cuts for two-stage DMUs with trapezoidal intuitionistic fuzzy data. Furthermore, the method of Yue (2011) is used to rank these DMUs in terms of their intuitionistic fuzzy interval efficiency. A numerical example is also provided to illustrate the application of the proposed bounded two-stage intuitionistic Data Envelopment Analysis model.

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

“…In the realm of literature, numerous innovative approaches have emerged to address uncertainty through the two-stage network DEA model. However, these methods face a notable deficiency in effectively integrating shared resources, external inputs/outputs, and undesirable outputs (see [32] , [35] , [36] ).…”

“…Mohanta and Sharanappa [31] presented a new method to solve an intuitionistic fuzzy DEA model, which was applied to the agricultural sector in India. Mohammadi Ardakani et al [32] developed the best and worst relative returns two-stage DEA models within IF inputs/outputs based on cut and cut approaches. Shariatmadari Serkani et al [33] proposed a hybrid intuitionistic fuzzy analytic and network DEA model to measure the relative efficiency of the Faculty of Basic Sciences of Islamic Azad University.…”

Enhanced Performance Evaluation Through Neutrosophic Data Envelopment Analysis Leveraging Pentagonal Neutrosophic Numbers

“…By encapsulating both the degree of membership and non-membership https://doi.org/10.56578/josa010204 of an element in a set, IFSs afford a greater depth of understanding for decision-makers. Different methodologies, including weighted entropy approach [13], ranking approach [14], expected value approach [15,16], parametric approach [17], (α, β)-cut approach [18,19], and MCDM approach, have been developed to solve Intuitionistic Fuzzy DEA models [20,21].…”