Data envelopment analysis based on triangular neutrosophic numbers

Abstract

Data envelopment analysis (DEA) is one of the best mathematical techniques to compute the overall performance of units with some inputs and outputs. The original DEA methods are developed to tackle the information based on the crisp number but no ability to handle the indeterminacy, impreciseness, vagueness, inconsistent, and incompleteness information such as triangular neutrosophic numbers (TNNs). This study attempts to establish a new model of DEA, where the information on decision-making units is TNNs. Initially, the concept and features of a conventional DEA model and the comparative TNNs are discussed. Besides, some new ranking functions of TNNs are presented. Furthermore, based on the mentioned ranking functions, an algorithm for solving the new model has been established. A comparison of the new model with an existing method and other kinds of uncertainty tools has been provided. In comparison with the existing methods, the significant characteristic of the new model is that it can handle the triangular neutrosophic information simply and effectively. Finally, the implementation of this strategy for an example has been applied for various models of DEA.

Triangular Single Valued Neutrosophic Data Envelopment Analysis: Application to Hospital Performance Measurement

“…All data were expressed by using TSVNNs, and can be found in Tables 1 and 2. [40,44,46], [42,43,45], [43,44,55] [32,35,38] , [32,33,35], [34,36,45] [192,195,198] , [185,193,197], [194,196,205 [22,25,40] , [20,24,27], [23,25,29] [20,23,26] , [21,22,24], [22,25,30] [25,31,37] , [29,30,32], [30,…”

“…To overcome this lack of information, Atanassov [26] introduced an extension of FSs called intuitionistic fuzzy sets (IFSs). There are also several models of DEA with intuitionistic fuzzy data: see [27][28][29][30].…”

“…Input information of the nominee hospitals. ( [81.62, 82.07, 85.51] , [81.41, 81.94, 83.35], [81.78, 85.49, 88.16] v 1 ⊕[18,20,29] ,[19,21,23],[28,30,35] v 2 ⊕ [ 157.75, 177.57, 264.52 ], [157.75, 176.68, 250.75], [180.29, 263.98, 272.16] v 3 )− ( [139, 145, 158] , [139, 140, 147], [146, 155, 167] u 1 ⊕ [208, 214, 218] , [195, 209, 215], [210, 217, 230] u 2 ) ≤ 0, ( [19.54, 20.41, 20.59] , [20.15, 20.25, 20.32], [20.54, 20.58, 20.70] v 1 ⊕ [18, 21, 25] , [15, 19, 23], [20, 24, 30] v 2 ⊕ [32.89, 35.56, 87.74 ] , [35.25, 35.50, 35.61], [87.50, 87.94, 88.30] v 3 )− ( [86, 93, 151] , [83, 85, 87], [89, 138, 160] u 1 ⊕ [114, 116, 118] , [114, 115, 117], [116, 118, 125] u 2 ) ≤ 0, ( [23.89, 24.60, 26.09] , [23.56, 23.60, 23.68], [25.97, 26.35, 26.72] v 1 ⊕ [30, 36, 41] , [34, 35, 37], [35, 40, 57] v 2 ⊕ [63.23, 69.58, 120.73 ] , [63, 65.17, 94.93], [64.47, 118.75, 124.75 ] v 3 )− ( [84, 93, 143] , [84, 89, 120], [90, 140, 155] u 1 ⊕ [110, 117, 121] , [105, 112, 120], [113, 119, 128] u 2 ) ≤ 0, ( [21.33, 21.49, 23.31] , [20.94, 24.25, 22.68 ], [21.38, 23.14, 23.94 ] v 1 ⊕ [50, 55, 60] , [50, 53, 57], [56, 59, 70] v 2 ⊕ [72.84, 82.84, 94.18 ] , [82.15, 82.68, 84.89 ], [85.75, 93.50, 97.18 ] v 3 )− ( [101, 113, 170] , [110, 112, 115], [112, 120, 177] u 1 ⊕ [101, 107, 111] , [95, 100, 104], [108, 112, 115] u 2 ) ≤ 0, ( [145.77, 148.28, 169.01], [145.77, 147.16, 168.31], [150.69, 168.95, 175.18] v 1 ⊕…”

A Neutrosophic-Based Approach in Data Envelopment Analysis with Undesirable Outputs

“…In the DEA literature, there are also some models of DEA with IFSs, see [52][53][54][55][56][57][58][59][60]. However, in actual activities, there are some indeterminate information.…”

“…As far as we know, there are few studies concerning DEA with neutrosophic information. e utilization of neutrosophic set in DEA can be traced to Edalatpanah [61] and additional investigations have been accessible in [62][63][64][65][66][67]. However, these neutrosophic DEA methods are formulated solely for desirable outputs and cannot eliminate the influence of undesirable factors on the efficiency evaluation.…”