Abstract
Data envelopment analysis (DEA) is a powerful tool for evaluating the efficiency of decision-making units for ranking and comparison purposes and to differentiate efficient and inefficient units. Classic DEA models are ill-suited for the problems where decision-making units consist of multiple stages with intermediate products and those where inputs and outputs are imprecise or nondeterministic, which is not uncommon in the real world. This paper presents a new DEA model for evaluating the efficiency of decision-making units with two-stage structures and triangular intuitionistic fuzzy data. The paper first introduces two-stage DEA models, then explains how these models can be modified with intuitionistic fuzzy coefficients, and finally describes how arithmetic operators for intuitionistic fuzzy numbers can be used for a conversion into crisp two-stage structures. In the end, the proposed method is used to solve an illustrative numerical example.
Highlights
Data envelopment analysis is a standard quantitative tool with extensive use in efficiency evaluations and performance analysis [1]
Most of the commonly used Data envelopment analysis (DEA) models are criticized for treating units as black boxes and ignoring their internal processes, the efficiency of these processes, and their relationships [5, 6]. is black box approach causes the analysis to miss a lot of valuable information about decision-making units (DMUs) and limits its scope to the fundamental inputs and the ultimate outputs [7]
Unlike the model of Kao and Hwang [36] which cannot deal with intermediate variables with dual input/ output roles, the model of Chen et al [35] can properly consider both roles of these variables. erefore, this paper presents a new model, based on the two-stage model of Chen et al, for evaluating the efficiency of two-stage DMUs with intuitionistic fuzzy numbers under variable returns to scale (VRS) conditions
Summary
Data envelopment analysis is a standard quantitative tool with extensive use in efficiency evaluations and performance analysis [1]. Arya and Yadav [34] proposed a model called SBM, which is a nonradial DEA model for evaluating the efficiency of DMUs where inputs and outputs have intuitionistic fuzzy data. E two-stage model of Kao and Hwang [36] is an opposite model to consider the relationships between subprocesses and the overall process, and this model is certainly more logical than its precedents This model cannot be extended to work under variable returns to scale (VRS) conditions, as it becomes nonlinear in these conditions. Erefore, the motivation of this present study is to develop two-stage DEA models in intuitionistic fuzzy environment with the variable returns to scale assumption based on the Chen et al [35] model. Another aim of this study is to linearize the proposed model with the expected value of intuitionistic fuzzy numbers
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