Abstract
The primary purpose of this article is to measure the relative efficiency and productivity change over time in rural healthcare systems in the presence of fuzzy data. First, a novel ranking function based on the lower and upper bounds of alpha-cut of the trapezoidal fuzzy numbers (TrFNs) is proposed to compare the TrFNs. The suggested ranking technique is used to construct the fuzzy data envelopment analysis (FDEA), Malmquist fuzzy DEA (Mal-FDEA), and undesirable Malmquist fuzzy DEA (UN-Mal-FDEA ) models. The proposed models evaluate the efficiency and productivity of decision-making units (DMUs) when the input and output data are given in the form of TrFNs. In addition, a case study of the rural healthcare system in a developing country has been considered to demonstrate the applicability of the developed models. The work considers number of sub-centers (SCs), the number of primary health centers (PHCs), the number of community health centers (CHCs), nursing Staff at PHCs, an auxiliary nurse and midwives (ANM) at SCs, doctors at PHCs, pharmacists at PHCs, laboratory technicians at PHCs, radiographers at CHCs, and specialists at CHCs as input parameters and average population covered by CHCs, average village covered by CHCs, number of patients, and infant mortality rates as output parameters to analyze the performance of the rural healthcare systems. We show the UN-Mal-FDEA model has a higher production value than the Mal-FDEA model. The results of our proposed models enable us to recognize inefficiencies that states may rectify without compromising healthcare quality.
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