A Parabolic Based Fuzzy Data Envelopment Analysis Model with an Application

Sahil, Mohammad Aqil; Kaushal, Meenakshi; Lohani, Q. M. Danish

doi:10.1109/fuzz48607.2020.9177742

Cited by 5 publications

(4 citation statements)

References 36 publications

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“…In the indirect approach, the undesirable outputs are transformed into desirable inputs using a monotone decreasing function [27] . On the other hand, the direct method directly incorporates undesirable outputs by assigning them negative weights without using any transformation functions [4] , [28] , [29] . In literature, hybrid studies involve shared resources and undesirable outputs.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Within the framework of DMU structures, DEA is categorized into two main approaches: black-box and network DEA. Black-box DEA utilizes initial inputs to generate final outputs without delving into internal processes, thereby overlooking inefficiencies (see [1] , [2] , [3] , [4] , [5] ). In contrast, the network’s DEA considers internal processes to identify the sources of inefficiency for each DMU individually.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

Sahil,

Lohani

2024

MethodsX

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Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

Sahil,

Lohani

2024

MethodsX

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“…Peykani et al [31] utilized possibility, necessity and credibility measures to develop an adjustable fuzzy DEA model which can consider the different optimistic-pessimistic attitudes of a decision-maker. Sahil et al [34] presented a fuzzy DEA model to evaluate efficiency in the presence of parabolic fuzzy inputs and outputs by using the α-cut approach. The other studies on fuzzy DEA can be seen in Gholizadeh and Fazlollahtabar [12], Gholizadeh et al [14], Puri and Yadav [32], and Wang and Chin [41].…”

Section: Introductionmentioning

confidence: 99%

A novel dynamic data envelopment analysis approach with parabolic fuzzy data: Case study in the Indian banking sector

Kaur

Puri

2022

RAIRO-Oper. Res.

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Data envelopment analysis (DEA) is a non-parametric approach that measures the efficiency of a decision-making unit (DMU) statically and requires crisp input-output data. However, as a performance analysis tool, DEA overlooks the inter-relationship present among periods, and in many real applications, it is challenging to define the information for variables like customer satisfaction, service quality, etc. in precise form. To fix this, the present paper develops a novel parabolic fuzzy dynamic DEA (PFDDEA) approach that not only measures the system and period fuzzy efficiencies of DMUs by considering the inter-dependence among periods in the presence of undesirable resources but also handles data as parabolic fuzzy numbers (PFNs). It evaluates fuzzy efficiencies in a dynamic environment by distinguishing the role of links as inputs/outputs. In the proposed approach, system fuzzy efficiencies are estimated by solving the proposed PFDDEA models based on the α-cut approach that guarantees the shape of the membership function of the system fuzzy efficiencies obtained at different α-levels as PFNs. Further, an algorithmic approach for measuring period fuzzy efficiencies based on the concept of α-cuts and Pareto’s efficiency is developed that leads to the estimation of the shapes of their membership functions. Finally, a relationship has been derived between upper (lower) bound system efficiency and upper (lower) bound period efficiencies at each α-level. To the best of our knowledge, this is the first attempt that dynamically evaluates fuzzy efficiencies (system and period) of DMUs when the data for the inputs/outputs/links are PFNs. To validate the applicability and robustness of the proposed approach, it is applied to eleven Indian banks for two periods 2019-2020 and 2020-2021, including loss due to non-performing assets (NPAs) as an undesirable output and unused assets as a link between periods. Here, NPAs are the bad loans that cease to generate income for the banks. The findings of the study (i) depict the system and period efficiencies as PFNs, (ii) conclude that the Federal Bank (FB) is the most efficient and Punjab National Bank (PNB) is the least efficient bank in the system and all periods, and (iii) provide implications that are highly valuable for bank experts to consider the impact of NPAs and unused assets for improving underperformed banks. These findings indicate that the proposed PFDDEA approach is highly useful for ranking/benchmarking in a dynamic manner keeping in view the presence of uncertain data variables represented as PFNs.

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“…Kao and Liu [7] formulated a pair of parametric FDEA models to derive the lower and upper bound on the membership function of efficiency score by using the α−cut approach. Based on the α−cut approach, Sahil et al derived an FDEA model to evaluate the efficiency score of DMUs in the presence of parabolic fuzzy inputs and outputs (see [8]). Peykani et al [9] developed an FDEA model with the help of possibility, necessity, and credibility measures.…”

Section: Introductionmentioning

confidence: 99%

A Novel Pythagorean Fuzzy Data Envelopment Analysis Model: An Assessment of Indian Public Sector Banks

Sahil

Kaushal

Lohani

2022

Preprint

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Fuzzy data envelopment analysis (FDEA) is an efficient modeling technique to rank decision-making units (DMUs) with imprecise inputs/outputs. It is a linear programming problem that constructs an optimal frontier line, known as an efficient frontier. The role of the efficient frontier is to distinguish between the efficient DMUs with inefficient DMUs such that all efficient DMUs lie on the frontier line. Whereas the inefficient DMUs are enveloped by the frontier line. This optimization problem aims to improve the efficiency score of each inefficient DMU, that is, to move them to the efficient frontier. In this study, we propose a novel approach called the Pythagorean approach, which is both input and output oriented. The proposed approach is implemented in the CCR model, and a new version of the BCC model is introduced, namely a novel Pythagorean BCC model. The deterministic form of the Pythagorean BCC model is extended to a fuzzy environment to deal with the vagueness of the given dataset. In the paper, a new form of a non-linear fuzzy number, namely a sine-shaped fuzzy number, has been introduced to display the higher order of uncertainty. Consequently, the Pythagorean BCC model is further extended to a novel Pythagorean fuzzy BCC model. The model's efficacy is finally tested in the Indian public sector banks.

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A Parabolic Based Fuzzy Data Envelopment Analysis Model with an Application

Cited by 5 publications

References 36 publications

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

A novel dynamic data envelopment analysis approach with parabolic fuzzy data: Case study in the Indian banking sector

A Novel Pythagorean Fuzzy Data Envelopment Analysis Model: An Assessment of Indian Public Sector Banks

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