{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T19:06:09Z","timestamp":1770750369264,"version":"3.50.0"},"reference-count":82,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T00:00:00Z","timestamp":1624752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Aggregation operators are fundamental concept for information fusion in real-life problems. Many researchers developed aggregation operators for multi-criteria decision-making (MCDM) under uncertainty. Unfortunately, the existing operators can be utilized under strict limitations and constraints. In this manuscript, we focused on new prioritized aggregation operators which remove the strict limitations of the existing operators. The addition of reference parameters associated with membership and non-membership grades in the linear Diophantine Fuzzy sets provide a robust modeling for MCDM problems. The primary objective of this manuscript is to introduce new aggregation operators for modeling uncertainty by using linear Diophantine Fuzzy information. For this objective we develop aggregation operators (AO) namely, \"linear Diophantine Fuzzy prioritized weighted average\" (LDFPWA) operator and \"linear Diophantine Fuzzy prioritized weighted geometric\" (LDFPWG) operator. Certain essential properties of new prioritized AOs are also proposed. A secondary objective is to discuss a practical application of third party reverse logistic provider (3PRLP) optimization problem. The efficiency, superiority, and rationality of the proposed approach is analyzed by a numerical example to discuss 3PRLP. The symmetry of optimal decision and ranking of feasible alternatives is followed by a comparative analysis.<\/jats:p>","DOI":"10.3390\/sym13071152","type":"journal-article","created":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T23:57:22Z","timestamp":1624838242000},"page":"1152","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":59,"title":["Novel Approach for Third-Party Reverse Logistic Provider Selection Process under Linear Diophantine Fuzzy Prioritized Aggregation Operators"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8115-9168","authenticated-orcid":false,"given":"Muhammad","family":"Riaz","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8318-0750","authenticated-orcid":false,"given":"Hafiz Muhammad Athar","family":"Farid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6443-4962","authenticated-orcid":false,"given":"Muhammad","family":"Aslam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8522-1942","authenticated-orcid":false,"given":"Dragan","family":"Pamucar","sequence":"additional","affiliation":[{"name":"Department of Logistics, Military Academy, University of Defence in Belgarde, 11000 Belgarde, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9657-0889","authenticated-orcid":false,"given":"Darko","family":"Bozani\u0107","sequence":"additional","affiliation":[{"name":"Military Academy, University of Defence in Belgarde, 11000 Belgarde, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_3","first-page":"S27","article-title":"Geometrical interpretation of the elemets of the intuitionistic fuzzy objects","volume":"20","author":"Atanassov","year":"1986","journal-title":"Int. J. Bioautom."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1002\/int.21584","article-title":"Pythagorean membership grades, complex numbers, and decision making","volume":"28","author":"Yager","year":"2013","journal-title":"Int. J. Intell. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yager, R.R. (2013, January 24\u201328). Pythagorean fuzzy subsets. Proceedings of the IFSA World Congress and NAFIPS Annual Meeting (IFSA\/NAFIPS), Edmonton, AB, Canada.","DOI":"10.1109\/IFSA-NAFIPS.2013.6608375"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","article-title":"Pythagorean membership grades in multi criteria decision-making","volume":"22","author":"Yager","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","article-title":"Generalized orthopair fuzzy sets","volume":"25","author":"Yager","year":"2017","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"394","DOI":"10.2991\/ijcis.2017.10.1.27","article-title":"A new criterion for soft set based decision making problems under incomplete information","volume":"10","author":"Alcantud","year":"2017","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","article-title":"Intuitionistic fuzzy aggregation operators","volume":"15","author":"Xu","year":"2007","journal-title":"IEEE Transections Fuzzy Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/03081070600574353","article-title":"Some geometric aggregation operators based on intuitionistic fuzzy sets","volume":"35","author":"Xu","year":"2006","journal-title":"Int. J. Gen. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s40815-019-00763-2","article-title":"m-polar Neutrosophic Topology with Applications to Multi-Criteria Decision-Making in Medical Diagnosis and Clustering Analysis","volume":"22","author":"Hashmi","year":"2020","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/TFUZZ.2012.2189405","article-title":"Intuitionistic fuzzy information aggregation using Einstein operators","volume":"20","author":"Wang","year":"2012","journal-title":"IEEE Transections Fuzzy Syst."},{"key":"ref_13","first-page":"645953","article-title":"Interval neutrosophic sets and their applications in multi-criteria decision making problems","volume":"2014","author":"Zhang","year":"2014","journal-title":"Sci. World J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/int.20386","article-title":"Generalized aggregation operators for intuitionistic fuzzy sets","volume":"25","author":"Zhao","year":"2010","journal-title":"Int. J. Intell. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1002\/int.21809","article-title":"A new generalized Pythagorean fuzzy information aggregation using Einstein operators and its applications to decision-making","volume":"31","author":"Garg","year":"2016","journal-title":"Int. J. Intell. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7041","DOI":"10.1007\/s00521-018-3521-2","article-title":"An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets","volume":"31","author":"Mahmood","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/math7020166","article-title":"Lexicographic orders of intuitionistic fuzzy values and their relationships","volume":"7","author":"Feng","year":"2019","journal-title":"Mathematics"},{"key":"ref_18","first-page":"1","article-title":"Extensions of Dombi aggregation operators for decision making under m-polar fuzzy information","volume":"6","author":"Akram","year":"2020","journal-title":"J. Math."},{"key":"ref_19","unstructured":"Akram, M., Shahzadi, G., and Peng, X. (2021, May 20). Extension of Einstein Geometric Operators to Multi-Attribute Decision Making under q-Rung Orthopair Fuzzy Information. Available online: https:\/\/link.springer.com\/article\/10.1007."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1002\/int.21738","article-title":"Some results for Pythagorean fuzzy sets","volume":"30","author":"Peng","year":"2015","journal-title":"Int. J. Intell. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1002\/int.21676","article-title":"Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets","volume":"29","author":"Zhang","year":"2014","journal-title":"Int. J. Intell. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1002\/int.22239","article-title":"Correlation coefficients of dual type-2 hesitant fuzzy sets and their applications in clustering analysis","volume":"35","author":"Karaaslan","year":"2020","journal-title":"Int. J. Intell. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sitara, M., Akram, M., and Riaz, M. (2021). Decision-making analysis based on q-rung picture fuzzy graph structures. J. Appl. Math. Comput.","DOI":"10.1007\/s12190-020-01471-z"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5417","DOI":"10.3233\/JIFS-190550","article-title":"Linear Diophantine fuzzy set and its applications towards multi-attribute decision making problems","volume":"37","author":"Riaz","year":"2019","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kamaci, H. (2021). Linear Diophantine fuzzy algebraic structures. J. Ambient. Intell. Humaniz. Comput.","DOI":"10.1007\/s12652-020-02826-x"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ayub, S., Shabir, M., Riaz, M., Aslam, M., and Chinram, R. (2021). Linear Diophantine fuzzy relations and their algebraic properties with decision making. Symmetry, 13.","DOI":"10.3390\/sym13060945"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Almagrabi, A.O., Abdullah, S., and Shams, M. (2021). A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19. J. Ambient. Intell. Humanoized Comput.","DOI":"10.1007\/s12652-021-03130-y"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"44","DOI":"10.31181\/rme200101044p","article-title":"Normalized weighted Geometric Dombi Bonferoni Mean Operator with interval grey numbers: Application in multicriteria decision making","volume":"1","author":"Pamucar","year":"2020","journal-title":"Rep. Mech. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"54","DOI":"10.31181\/oresta2003049p","article-title":"The application of the hybrid interval rough weighted Power-Heronian operator in multi-criteria decision making","volume":"3","author":"Pamucar","year":"2020","journal-title":"Oper. Res. Eng. Sci. Theory Appl."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Riaz, M., Salabun, W., Farid, H.M.A., Ali, N., and Watr\u00f3bski, J. (2020). A robust q-rung orthopair fuzzy information aggregation using Einstein operations with application to sustainable energy planning decision management. Energies, 13.","DOI":"10.3390\/en13092155"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Riaz, M., Pamucar, D., Farid, H.M.A., and Hashmi, M.R. (2020). q-Rung Orthopair Fuzzy Prioritized Aggregation Operators and Their Application Green Supplier Chain Management. Symmetry, 12.","DOI":"10.3390\/sym12060976"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.3233\/JIFS-192114","article-title":"Some q-rung orthopair fuzzy hybrid aggregation operators and TOPSIS method for multi-attribute decision-making","volume":"39","author":"Riaz","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Riaz, M., Farid, H.M.A., Kalsoom, H., Pamucar, D., and Chu, Y.M. (2020). A Robust q-rung orthopair fuzzy Einstein prioritized aggregation operators with application towards MCGDM. Symmetry, 12.","DOI":"10.3390\/sym12061058"},{"key":"ref_34","first-page":"771","article-title":"Multi-criteria decision making based on bipolar picture fuzzy operators and new distance measures","volume":"127","author":"Riaz","year":"2021","journal-title":"Comput. Model. Eng. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.ijar.2007.08.009","article-title":"Prioritized aggregation operators","volume":"48","author":"Yager","year":"2008","journal-title":"Int. J. Approx. Reason."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"105","DOI":"10.31181\/rme2001020105t","article-title":"Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management","volume":"2","author":"Ali","year":"2021","journal-title":"Rep. Mech. Eng."},{"key":"ref_37","first-page":"375","article-title":"A cloud TOPSIS model for green supplier selection","volume":"18","author":"Ramakrishnan","year":"2020","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_38","first-page":"455","article-title":"Comparison of three fuzzy MCDM methods for solving the supplier selection problem","volume":"17","author":"Petrovic","year":"2019","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"37","DOI":"10.31181\/dmame2003037b","article-title":"Supplier selection for steelmaking company by using combined Grey-MARCOS methods","volume":"3","author":"Badi","year":"2020","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"19","DOI":"10.31181\/dmame2104019k","article-title":"Weighting the factors affecting logistics outsourcing","volume":"4","author":"Karamasa","year":"2021","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.omega.2014.05.009","article-title":"Third-Party Logistics Selection Problem: A Literature Review on Criteria and Methods","volume":"49","author":"Aguezzoul","year":"2014","journal-title":"Omega"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.omega.2005.01.003","article-title":"Empirical research opportunities in reverse supply chains","volume":"34","author":"Prahinski","year":"2006","journal-title":"Omega"},{"key":"ref_43","first-page":"350","article-title":"Evaluation and selection of a third-party reverse logistics provider using ANP and IFG-MCDM methodology","volume":"10","author":"Zareinejad","year":"2013","journal-title":"Life Sci. J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s00170-009-2092-x","article-title":"A new model for selecting third-party reverse logistics providers in the presence of multiple dual-role factors","volume":"46","author":"Saen","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3769","DOI":"10.1016\/j.cor.2006.01.012","article-title":"Developing a decision model for business process outsourcing","volume":"34","author":"Yang","year":"2007","journal-title":"Comput. Oper. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.ijpe.2009.09.010","article-title":"A classification of logistic outsourcing levels and their impact on service performance: Evidence from the food processing industry","volume":"124","author":"Hsiao","year":"2010","journal-title":"Int. J. Prod. Econ."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.tre.2014.03.005","article-title":"Quality management, environmental management maturity, green supply chain practices and green performance of Brazilian companies with ISO 14001 certification: Direct and indirect effects","volume":"67","author":"Jabbour","year":"2014","journal-title":"Transp. Res. Logist. Transp. Rev."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.cie.2018.10.023","article-title":"Assessment of third-party logistics provider using multi-criteria decision-making approach based on interval rough numbers","volume":"127","author":"Pamucar","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6097","DOI":"10.1080\/00207543.2015.1022266","article-title":"A hybrid data analytic methodology for 3PL transportation provider evaluation using fuzzy multi-criteria decision making","volume":"53","author":"Yayla","year":"2015","journal-title":"Int. J. Prod. Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"121","DOI":"10.31181\/dmame1801121r","article-title":"A rough strength relational DEMATEL model for analysing the key success factors of hospital service quality","volume":"1","author":"Roy","year":"2018","journal-title":"Decis. Making Appl. Manag. Eng."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.asoc.2018.01.023","article-title":"Sustainable thirdparty reverse logistics provider evaluation and selection using fuzzy SWARA and developed fuzzy COPRAS in the presence of risk criteria","volume":"65","author":"Zarbakhshnia","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1016\/j.jclepro.2019.04.257","article-title":"The selection of 3PRLs on self-service mobile recycling machine: Interval-valued Pythagorean hesitant fuzzy best-worst multi-criteria group decision-making","volume":"230","author":"Liu","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.cor.2018.06.005","article-title":"Integrating and extending data and decision tools for sustainable third-party reverse logistics provider selection","volume":"110","author":"Bai","year":"2019","journal-title":"Oper. Res. Comput."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"118461","DOI":"10.1016\/j.jclepro.2019.118461","article-title":"A novel hybrid multiple attribute decision-making approach for outsourcing sustainable reverse logistics","volume":"242","author":"Zarbakhshnia","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_55","first-page":"6102036","article-title":"The dominance degree-based heterogeneous linguistic decision-making technique for sustainable S3PRLP selection","volume":"2020","author":"Zhang","year":"2020","journal-title":"Complexity"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.cie.2007.07.009","article-title":"A Holistic Approach for Selecting a Third-Party Reverse Logistics Provider in the Presence of Vagueness","volume":"54","author":"Efendigil","year":"2008","journal-title":"Comput. Ind. Eng."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/j.indmarman.2009.10.004","article-title":"Outsourcing Reverse Logistics of High-Tech Manufacturing Firms by using a Systematic Decision-Making Approach: TFT-LCD Sector in Taiwan","volume":"39","author":"Cheng","year":"2010","journal-title":"Ind. Mark. Manag."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"10841","DOI":"10.1016\/j.eswa.2012.03.009","article-title":"Emrouznejad, A. Strategic Logistics Outsourcing: An Integrated QFD and Fuzzy AHP Approach","volume":"39","author":"Ho","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"3872","DOI":"10.1016\/j.eswa.2012.12.040","article-title":"Application of Decision-Making Techniques in Supplier Selection: A Systematic Review of Literature","volume":"40","author":"Chai","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.resconrec.2009.06.004","article-title":"A hybrid approach using ISM and fuzzy TOPSIS for the selection of reverse logistics provider","volume":"54","author":"Govindan","year":"2009","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_61","first-page":"73","article-title":"Managing third party logistics relationships: What does it take","volume":"20","author":"Boyson","year":"1999","journal-title":"J. Bus. Logist."},{"key":"ref_62","unstructured":"Langley, C.J., Allen, O.R., and Tyndall, O.R. (2002). Third-Party Logistics Study Results and Finding of the 2002 Seventh Annual Study, Georgia Institute of Technology. Unpublished Report."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1108\/13598540210447728","article-title":"A conceptual model for selecting and evaluating third-party reverse logistics providers","volume":"7","author":"Meade","year":"2002","journal-title":"Supply Chain."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.ijpe.2003.08.003","article-title":"A framework for supply chain performance measurement","volume":"87","author":"Gunasekaran","year":"2004","journal-title":"Int. J. Prod. Econ."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1108\/01443579810192772","article-title":"Logistics strategy and structure a conceptual framework","volume":"18","author":"Stock","year":"1998","journal-title":"Int. J. Oper. Prod. Manag."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1016\/j.eswa.2006.12.008","article-title":"A hybrid approach to supplier selection for the maintenance of a competitive supply chain","volume":"34","author":"Ha","year":"2008","journal-title":"Expert Syst. Appl."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"6782","DOI":"10.1016\/j.eswa.2011.12.056","article-title":"An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach","volume":"39","author":"Amin","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1016\/j.ijproman.2008.10.004","article-title":"Application of graph theory and matrix methods for contractor ranking","volume":"27","author":"Darvish","year":"2009","journal-title":"Int. J. Proj. Manag."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"8639","DOI":"10.1016\/j.eswa.2008.10.012","article-title":"An integrated fuzzy model for supplier management: A case study of ISP selection and evaluation","volume":"36","author":"Amin","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1651","DOI":"10.1016\/j.ins.2010.07.026","article-title":"Structured methodology for supplier selection and evaluation in a supply chain","volume":"181","author":"Chen","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"2401","DOI":"10.1007\/s00170-016-9880-x","article-title":"Sustainable third party reverse logistic provider selection with fuzzy SWARA and fuzzy MOORA in plastic industry","volume":"91","author":"Mavi","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.jclepro.2018.05.213","article-title":"Third party reverse logistics provider selection approach based on hybrid-information MCDM and cumulative prospect theory","volume":"195","author":"Li","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1016\/j.jclepro.2010.03.020","article-title":"Integration of artificial neural network andMADA methods for green supplier selection","volume":"18","author":"Kuo","year":"2010","journal-title":"J. Clean. Prod."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1668","DOI":"10.1016\/j.asoc.2012.01.023","article-title":"Sustainable supplier selection: A ranking model based on fuzzy inference system","volume":"12","author":"Amindoust","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.resconrec.2012.09.006","article-title":"A fuzzy multi criteria approach for evaluating green supplier\u2019s performance in green supply chain with linguistic preferences","volume":"74","author":"Shen","year":"2013","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.jclepro.2012.04.014","article-title":"A fuzzy multi criteria approach for measuring sustainability performance of a supplier based on triple bottom line approach","volume":"47","author":"Govindan","year":"2013","journal-title":"J. Clean. Prod."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.jclepro.2013.02.010","article-title":"Integrated fuzzy multi criteria decision making method and multiobjective programming approach for supplier selection and order allocation in a green supply chain","volume":"47","author":"Kannan","year":"2013","journal-title":"J. Clean. Prod."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.resconrec.2014.02.004","article-title":"Mixed methodology to analyze the relationship between maturity of environmental management and the adoption of green supply chain management in Brazil","volume":"92","author":"Jabbour","year":"2014","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s10479-016-2272-7","article-title":"Integrating disassembly line balancing in the planning of a reverse logistics network from the perspective of a third party provider","volume":"253","author":"Kannan","year":"2017","journal-title":"Ann. Oper. Res."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1142\/S0219622016500474","article-title":"Decision support framework for selection of 3PL providers: Dominance-based approach in combination with grey set theory","volume":"16","author":"Sen","year":"2017","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"ref_81","first-page":"568","article-title":"Intuitionistic Fuzzy Bonferroni Means","volume":"41","author":"Xu","year":"2011","journal-title":"IEEE Trans. Syst."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.knosys.2010.04.010","article-title":"Induced generalized intuitionistic fuzzy operators","volume":"24","author":"Xu","year":"2011","journal-title":"Knowl. Based Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1152\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:25:14Z","timestamp":1760163914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1152"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,27]]},"references-count":82,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["sym13071152"],"URL":"https:\/\/doi.org\/10.3390\/sym13071152","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,27]]}}}