A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector

Assessing productive efficiency of banks using integrated Fuzzy-DEA and bootstrapping: A case of Mozambican banks

“…Third, owing to the input and output data being fuzzy numbers, the efficiency scores are also fuzzy numbers (Puri and Yadav, 2013). Moreover, as long as the efficiency values considered here are the upper and lower "crisp" bounds computed for various α levels, the membership functions for the true fuzzy efficiency cannot be reconstructed, which has a number of implications on how fuzzy efficiencies should be ranked (Chen et al, 2013;Puri and Yadav, 2013;Hsiao et al, 2011).…”

“…Moreover, as long as the efficiency values considered here are the upper and lower "crisp" bounds computed for various α levels, the membership functions for the true fuzzy efficiency cannot be reconstructed, which has a number of implications on how fuzzy efficiencies should be ranked (Chen et al, 2013;Puri and Yadav, 2013;Hsiao et al, 2011). These bounds, however, can be treated as crisp values and incorporated into statistical modelling as efficiency scores subjected to certain fixed effects or treatments in order to properly assess the impact of different contextual variables.…”

“…This being the case, several researchers (Cooper et al, 1999;Despotis and Smirlis, 2002;Guo and Tanaka, 2001;Jahanshahloo et al, 2004;Kao and Liu, 2000b) started structuring FDEA models, allowing for the measurement of outputs and inputs as fuzzy numbers. Particularly with respect to FDEA applications on banking, studies to assess efficiency in the financial sector still remain scarce, and their major focus tends to relate to ranking of DMUs based on computed fuzzy efficiencies rather than predicting or explaining efficiency levels in terms of contextual variables (Chen et al, 2013;Puri & Yadav, 2014;Puri & Yadav, 2013;Wang et al, 2014;Hsiao et al, 2011;Wu et al, 2006). According to Hatami-Marbini et al (2011a), the huge dissemination of different models within a large scope of applications in terms of efficiency measurement demonstrates that FDEA models represent an effective path for handling uncertainty and vagueness when inputs/outputs are imprecise (Kao & Liu, 2000b).…”

“…Thus far, applications of FDEA to measure bank efficiency have been scarce and focused on ranking DMUs rather than predicting their efficiency levels based on a set of contextual variables (Chen et al, 2013;Puri & Yadav, 2014;Puri & Yadav, 2013;Wang, Lu & Liu, 2014;Hsiao et al, 2011;Wu, Yang, & Liang, 2006). This paper innovates first by focusing on Mozambican banks and second by simultaneously adopting three major FDEA models based on the α-level approach in combination with the conditional bootstrapped truncated regression, proposed…”

Assessing the Efficiency of commercial Tunisian Banks using Fuzzy Data Envelopment Analysis

“…Every respondent describes his judgment about the innovation degree in his bank by the following linguistic terms; very low, low, high and very high. These linguistic expressions were converted into fuzzy numbers as (5, 6, 7), (8, 10, 11), (12,13,14) and (15,16,17), respectively. In order to establish the imprecise value of the innovation level for each bank, we used the following aggregation function.…”