In this study, Data Envelopment Analysis (DEA) models are improved by employing spherical fuzzy sets (SFSs), which is an extension of generalized fuzzy sets. SFSs were recently introduced as a novel type of fuzzy set that allows decision-makers to express their level of uncertainty directly. As a result, SFSs provide a more preferred domain for decision-makers. Fundamental Charnes-Cooper-Rhodes (CCR) model is discussed on the context of spherical trapezoidal fuzzy numbers (STrFNs), which consider each data value’s truth, indeterminacy, and falsehood degrees, and a unique solution technique is implemented. This method converts a spherical fuzzy DEA(SF-DEA) model into three pair of crisp DEA model, which may then be solved using one of many existing approaches. The largest optimal interval is determined for each DMU such that the efficiency score lies inside that interval. Furthermore, an example demonstrates this novel method and clearly explains the DMUs’ ranking technique.
This article evaluated the agricultural performance of 31 states and union territories (UTs) in India from 2012 to 2017. The best agricultural productivity states and UTs in India were obtained using Malmquist based DEA technique and the efficiency score for each year was found using CCR model. The input parameter is taken as annual rainfall, total population, GDP, Workers, and net cultivated area, and the output parameter is taken as production of rice, wheat, coarse cereals, pulses, oil seeds, and sugarcane. The productivity of the states and UTs are compared, as well as the increase or decrease in productivity is calculated. Total productivity change was calculated using cumulative Malmquist index (CMI). As a results, Punjab, Rajasthan, Sikkim, and Uttar Pradesh are the most efficient states throughout the year, while Kerala and Goa are the least efficient. Maximum states and UTs advanced 61.25 % in 2015-16, whereas maximum states and UTs declined 62.52 % in 2012-13. The overall productivity change in Madhya Pradesh inceases perfectly while Nagaland's is almost decreasing. Other factors that may have an influence on state and UTs agriculture productivity include capital investment and fertiliser use. Additional social and environmental performance criteria, such as contribution to local community development and harmful emission measurement, can be integrated as output criteria for sustainability performance analysis.
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