{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T21:06:18Z","timestamp":1761599178474,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,20]],"date-time":"2018-12-20T00:00:00Z","timestamp":1545264000000},"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>With trending competition in decision-making process, linguistic decision-making is gaining attractive attention. Previous studies on linguistic decision-making have neglected the occurring probability (relative importance) of each linguistic term which causes unreasonable ranking of objects. Further, decision-makers\u2019 (DMs) often face difficulties in providing apt preference information for evaluation. Motivated by these challenges, in this paper, we set our proposal on probabilistic linguistic preference relation (PLPR)-based decision framework. The framework consists of two phases viz., (a) missing value entry phase and (b) ranking phase. In phase (a), the missing values of PLPR are filled using a newly proposed automatic procedure and consistency of PLPR is ensured using a consistency check and repair mechanism. Following this, in phase (b), objects are ranked using newly proposed analytic hierarchy process (AHP) method under PLPR context. The practicality of the proposal is validated by using two numerical examples viz., green supplier selection problem for healthcare and the automobile industry. Finally, the strength and weakness of the proposal are discussed by comparing with similar methods.<\/jats:p>","DOI":"10.3390\/sym11010002","type":"journal-article","created":{"date-parts":[[2018,12,20]],"date-time":"2018-12-20T12:54:36Z","timestamp":1545310476000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Probabilistic Linguistic Preference Relation-Based Decision Framework for Multi-Attribute Group Decision Making"],"prefix":"10.3390","volume":"11","author":[{"given":"R.","family":"Krishankumar","sequence":"first","affiliation":[{"name":"School of Computing, SASTRA University, Thanjavur-613401, Tamil Nadu, India"}]},{"given":"K. S.","family":"Ravichandran","sequence":"additional","affiliation":[{"name":"School of Computing, SASTRA University, Thanjavur-613401, Tamil Nadu, India"}]},{"given":"M. Ifjaz","family":"Ahmed","sequence":"additional","affiliation":[{"name":"School of Computing, SASTRA University, Thanjavur-613401, Tamil Nadu, India"}]},{"given":"Samarjit","family":"Kar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Durgapur-713209, West Bengal, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7463-0422","authenticated-orcid":false,"given":"Sanjay K.","family":"Tyagi","sequence":"additional","affiliation":[{"name":"Department of General Studies, Higher College of Technology, Fujairah-4114, UAE"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,20]]},"reference":[{"key":"ref_1","first-page":"175","article-title":"Multi-attributes decision-making: an operations research approach","volume":"15","author":"Triantaphyllou","year":"1998","journal-title":"Encycl. Electr. Electron. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0020-0255(95)00025-K","article-title":"A sequential selection process in group decision-making with a linguistic assessment approach","volume":"239","author":"Herrera","year":"1995","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0888-613X(96)00121-1","article-title":"Linguistic measures based on fuzzy coincidence for reaching consensus in group decision-making","volume":"16","author":"Herrera","year":"1997","journal-title":"Int. J. Approx. Reason."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.ins.2016.08.034","article-title":"Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets","volume":"372","author":"Gou","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of a linguistic variable and its application to approximate reasoning\u2013I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0165-0114(95)00107-7","article-title":"A model of consensus in group decision-making under linguistic assessments","volume":"78","author":"Herrera","year":"1996","journal-title":"Fuzzy Sets Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.dss.2004.08.011","article-title":"An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision-making with uncertain multiplicative linguistic preference relations","volume":"41","author":"Xu","year":"2006","journal-title":"Decis. Support. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s11071-015-2595-y","article-title":"A linguistic entropy weight method and its application in linguistic multi-attribute group decision-making","volume":"84","author":"He","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0377-2217(90)90057-I","article-title":"How to make a Decision: Analytical hierarchy process","volume":"48","author":"Saaty","year":"1990","journal-title":"Eur. J. Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/S0377-2217(98)00383-X","article-title":"Choice functions and mechanisms for linguistic preference relations","volume":"120","author":"Herrera","year":"2000","journal-title":"Eur. J. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S0165-0114(99)00024-X","article-title":"Linguistic decision analysis: steps for solving decision problems under linguistic information","volume":"115","author":"Herrera","year":"2000","journal-title":"Fuzzy Sets Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.omega.2004.04.008","article-title":"Deviation measures of linguistic preference relations in group decision-making","volume":"33","author":"Xu","year":"2005","journal-title":"Omega"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.knosys.2015.07.035","article-title":"Building and managing fuzzy ontologies with heterogeneous linguistic information","volume":"88","author":"Perez","year":"2015","journal-title":"Knowl.-Based Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.asoc.2015.09.058","article-title":"Interactive algorithms for improving incomplete linguistic preference relations based on consistency measures","volume":"32","author":"Wang","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/TFUZZ.2011.2170076","article-title":"Hesitant fuzzy linguistic term sets for decision-making","volume":"20","author":"Rodriguez","year":"2012","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_16","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra","year":"2010","journal-title":"Int. J. Intell. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TFUZZ.2013.2245136","article-title":"Consistency measures for hesitant fuzzy linguistic preference relations","volume":"22","author":"Zhu","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.ins.2014.10.047","article-title":"Some consistency measures of extended hesitant fuzzy linguistic preference relations","volume":"297","author":"Wang","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wu, Z. (2015, January 2\u20135). A consensus process for hesitant fuzzy linguistic preference relations. Proceedings of the 2015 IEEE International Conference on Fuzzy System, Istanbul, Turkey.","DOI":"10.1109\/FUZZ-IEEE.2015.7337827"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.asoc.2017.05.056","article-title":"A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms","volume":"59","author":"Song","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"T\u00fcys\u00fcz, F., and \u015eim\u015fek, B. (2017). A hesitant fuzzy linguistic term sets-based AHP approach for analyzing the performance evaluation factors: An application to cargo sector. Complex. Intell. Syst., 1\u20139.","DOI":"10.1007\/s40747-017-0044-x"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.inffus.2012.01.006","article-title":"Consistency and consensus measures for linguistic preference relations based on distribution assessments","volume":"17","author":"Zhang","year":"2014","journal-title":"Inf. Fusion"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.ins.2016.06.021","article-title":"Probabilistic linguistic term sets in multi-attribute group decision-making","volume":"369","author":"Pang","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, B., Liang, H., Gao, Y., and Zhang, G. (2018). The optimization-based aggregation and consensus with minimum-cost in group decision-making under incomplete linguistic distribution context. Knowl.-Based Syst., 1\u201336.","DOI":"10.1016\/j.knosys.2018.05.038"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.knosys.2016.12.020","article-title":"Comparisons of probabilistic linguistic term sets for multi-attributes decision-making","volume":"119","author":"Bai","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.ins.2017.06.035","article-title":"A probabilistic linguistic linear programming method in hesitant qualitative multiple attributes decision-making","volume":"416","author":"Liao","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.asoc.2018.03.027","article-title":"Some Muirhead mean operators for probabilistic linguistic term sets and their applications to multiple attribute decision-making","volume":"68","author":"Liu","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/j.asoc.2016.08.045","article-title":"Consistency-based risk assessment with probabilistic linguistic preference relation","volume":"49","author":"Zhang","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.ins.2017.06.006","article-title":"A consensus process for group decision-making with probabilistic linguistic preference relations","volume":"414","author":"Zhang","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.knosys.2018.07.016","article-title":"The consensus of probabilistic uncertain linguistic preference relations and the application on the virtual reality industry","volume":"162","author":"Xie","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.ejor.2018.07.044","article-title":"A consensus-based probabilistic linguistic gained and lost dominance score method","volume":"272","author":"Wu","year":"2019","journal-title":"Eur. J. Oper. Res."},{"key":"ref_32","first-page":"1","article-title":"Probabilistic linguistic analytic hierarchy process and its application on the performance assessment of Xiongan new area","volume":"16","author":"Xie","year":"2018","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2969","DOI":"10.3233\/IFS-141256","article-title":"Multiplicative consistency of interval-valued intuitionistic fuzzy preference relation","volume":"27","author":"Liao","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Saaty, T.L. (1980). The Analytic Hierarchy Process, Mc-Graw Hill. [1st ed.].","DOI":"10.21236\/ADA214804"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6653","DOI":"10.1080\/00207543.2017.1334976","article-title":"The state of the art development of AHP (1979\u20132017): A literature review with a social network analysis","volume":"55","author":"Emrouznejad","year":"2017","journal-title":"Int. J. Prod. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.asoc.2014.03.014","article-title":"A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection","volume":"21","author":"Osiro","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/S0895-7177(03)90083-5","article-title":"Why the magic number seven plus or minus two","volume":"28","author":"Saaty","year":"2003","journal-title":"Math. Comput. Model."},{"key":"ref_38","first-page":"1","article-title":"The 2-rank consensus reaching model in the multigranular linguistic multiple-attribute group decision-making","volume":"48","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_39","unstructured":"Li, C.C., Dong, Y., and Herrera, F. (2018). A consensus model for large-scale linguistic group decision-making with a feedback recommendation based on clustered personalized individual semantics and opposing consensus groups. IEEE Trans. Fuzzy Syst., 1\u201313."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Liu, Y., Dong, Y., Liang, H., Chiclana, F., and Herrera-Viedma, E. (2018). Multiple attribute strategic weight manipulation with minimum cost in a group decision-making context with interval attribute weights information. IEEE Trans. Syst. Man Cybern. Syst., 1\u201312.","DOI":"10.1016\/j.omega.2017.02.008"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1016\/j.omega.2017.02.008","article-title":"Strategic weight manipulation in multiple attribute decision-making","volume":"75","author":"Dong","year":"2018","journal-title":"Omega"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/1\/2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:35:10Z","timestamp":1760196910000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/1\/2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,20]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["sym11010002"],"URL":"https:\/\/doi.org\/10.3390\/sym11010002","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,12,20]]}}}