Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units
The proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline&quo...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/6/1402 |
| _version_ | 1797610355572080640 |
|---|---|
| author | Awadh Pratap Singh Musrrat Ali |
| author_facet | Awadh Pratap Singh Musrrat Ali |
| author_sort | Awadh Pratap Singh |
| collection | DOAJ |
| description | The proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cuts. The model is based on fuzzy data envelopment analysis (FDEA) and considers two objectives, and a solution method and ranking system are provided. Generally, the efficiency score obtained for a DMU using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cut approach is an interval. Intervals are partially ordered sets, due to which ranking intervals is a challenging task. The proposed BOFDEA model with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cuts provides the efficiency of DMUs in the crisp form, not in the form of intervals. Due to this, ranking DMUs with the proposed method’s help becomes very easy and less computationally. The proposed model has been validated through numerical examples, and a real-world application in the education sector has been shown to demonstrate its practicality. |
| first_indexed | 2024-03-11T06:13:14Z |
| format | Article |
| id | doaj.art-493ff7883f1d41fca7795614f220b50f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:14Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-493ff7883f1d41fca7795614f220b50f2023-11-17T12:28:09ZengMDPI AGMathematics2227-73902023-03-01116140210.3390/math11061402Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making UnitsAwadh Pratap Singh0Musrrat Ali1School of Liberal Studies, University of Petroleum and Energy Studies, Prem Nagar 248007, Uttarakhand, IndiaDepartment of Basic Sciences, PYD, King Faisal University, Al Ahsa 31982, Saudi ArabiaThe proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cuts. The model is based on fuzzy data envelopment analysis (FDEA) and considers two objectives, and a solution method and ranking system are provided. Generally, the efficiency score obtained for a DMU using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cut approach is an interval. Intervals are partially ordered sets, due to which ranking intervals is a challenging task. The proposed BOFDEA model with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cuts provides the efficiency of DMUs in the crisp form, not in the form of intervals. Due to this, ranking DMUs with the proposed method’s help becomes very easy and less computationally. The proposed model has been validated through numerical examples, and a real-world application in the education sector has been shown to demonstrate its practicality.https://www.mdpi.com/2227-7390/11/6/1402data envelopment analysistriangular fuzzy numberperformance efficiencyranking approachgeometric average efficiency approach |
| spellingShingle | Awadh Pratap Singh Musrrat Ali Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units Mathematics data envelopment analysis triangular fuzzy number performance efficiency ranking approach geometric average efficiency approach |
| title | Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units |
| title_full | Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units |
| title_fullStr | Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units |
| title_full_unstemmed | Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units |
| title_short | Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units |
| title_sort | development of bi objective fuzzy data envelopment analysis model to measure the efficiencies of decision making units |
| topic | data envelopment analysis triangular fuzzy number performance efficiency ranking approach geometric average efficiency approach |
| url | https://www.mdpi.com/2227-7390/11/6/1402 |
| work_keys_str_mv | AT awadhpratapsingh developmentofbiobjectivefuzzydataenvelopmentanalysismodeltomeasuretheefficienciesofdecisionmakingunits AT musrratali developmentofbiobjectivefuzzydataenvelopmentanalysismodeltomeasuretheefficienciesofdecisionmakingunits |