{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T19:30:23Z","timestamp":1775071823756,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"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>The paper studies an extension TOPSIS method with the adjusted probabilistic linguistic fuzzy set in which the decision maker\u2019s behavior tendency is considered. Firstly, we propose a concept of probabilistic linguistic q-rung orthopair set (PLQROS) based on the probability linguistic fuzzy set (PLFS) and linguistic q-rung orthopair set (LQROS). The operational laws are introduced based on the transformed probabilistic linguistic q-rung orthopair sets (PLQROSs) which have the same probability. Through this adjustment method, the irrationality of the existing methods in the aggregation process is avoided. Furthermore, we propose a comparison rule of PLQROS and the aggregated operators. The distance measure of PLQROSs is also defined, which can deal with the symmetric information in multi-attribute decision making problems. Considering that the decision maker\u2019s behavior has a very important impact on decision-making results, we propose a behavioral TOPSIS decision making method for PLQROS. Finally, we apply the practical problem of investment decision to demonstrate the validity of the extension TOPSIS method, and the merits of the behavior decision method is testified by comparing with the classic TOPSIS method. The sensitivity analysis results of decision-maker\u2019s behavior are also given.<\/jats:p>","DOI":"10.3390\/sym13050891","type":"journal-article","created":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T00:06:54Z","timestamp":1621296414000},"page":"891","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Extension TOPSIS Method Based on the Decision Maker\u2019s Risk Attitude and the Adjusted Probabilistic Fuzzy Set"],"prefix":"10.3390","volume":"13","author":[{"given":"Donghai","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Applied Statistics, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"An","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanyuan","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zaiming","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"key":"ref_1","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\u2014I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0020-0255(75)90046-8","article-title":"The concept of a linguistic variable and its application to approximate reasoning\u2014II","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0020-0255(75)90017-1","article-title":"The concept of a linguistic variable and its application to approximate reasoning\u2014III","volume":"9","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1002\/int.21623","article-title":"TOPSIS for hesitant fuzzy linguistic term sets","volume":"28","author":"Beg","year":"2013","journal-title":"Int. J. Intell. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1007\/s40815-017-0432-9","article-title":"Hesitant fuzzy linguistic term set and its application in decision making: A state of the art survey","volume":"20","author":"Liao","year":"2018","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, D.H., Liu, Y.Y., and Chen, X.H. (2018). The new similarity measure and distance measure of a hesitant fuzzy linguistic term set based on a linguistic scale function. Symmetry, 10.","DOI":"10.3390\/sym10090367"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.inffus.2017.11.010","article-title":"Hesitant fuzzy linguistic term sets for linguistic decision making: Current developments, issues and challenges","volume":"43","author":"Hai","year":"2018","journal-title":"Inf. Fusion"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ins.2018.09.038","article-title":"Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS","volume":"473","author":"Wu","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s40815-018-0540-1","article-title":"New operations on generalized hesitant fuzzy linguistic term Sets for linguistic decision making","volume":"21","author":"Kong","year":"2019","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2111","DOI":"10.1007\/s40815-018-0460-0","article-title":"Distance measures for hesitant fuzzy linguistic sets and their applications in multiple criteria decision making","volume":"20","author":"Liu","year":"2018","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1080\/18756891.2015.1061394","article-title":"An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers","volume":"8","author":"Chen","year":"2015","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1234-","DOI":"10.1002\/int.21979","article-title":"Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process","volume":"33","author":"Garg","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","article-title":"Generalized orthopair fuzzy sets","volume":"25","author":"Yager","year":"2016","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_16","unstructured":"Hwang, C.L., and Yoon, K. (2012). Multiple Attribute Decision Making: Methods and Applications a State-of-the-Art Survey, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/0377-2217(94)90282-8","article-title":"TOPSIS for MODM","volume":"76","author":"Lai","year":"1994","journal-title":"Eur. J. Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0165-0114(97)00377-1","article-title":"Extensions of the TOPSIS for group decision-making under fuzzy environment","volume":"114","author":"Chen","year":"2000","journal-title":"Fuzzy Sets Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.eswa.2017.02.016","article-title":"A bibliometric-based survey on AHP and TOPSIS techniques","volume":"78","author":"Zyoud","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Liu, D.H., Chen, X.H., and Peng, D. (2018). Cosine distance measure between neutrosophic hesitant fuzzy linguistic sets and its application in multiple criteria decision making. Symmetry, 10.","DOI":"10.3390\/sym10110602"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1002\/int.22108","article-title":"Some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets","volume":"34","author":"Liu","year":"2019","journal-title":"Int. J. Intell. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TFUZZ.2018.2861719","article-title":"Improving risk evaluation in FMEA with cloud model and hierarchical TOPSIS method","volume":"27","author":"Liu","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.eswa.2017.07.045","article-title":"The behavioral TOPSIS","volume":"89","author":"Yoon","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.ins.2003.10.006","article-title":"A method based on linguistic aggregation operators for group decision making with linguistic preference relations","volume":"166","author":"Xu","year":"2004","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1002\/int.22071","article-title":"Multiple-attribute group decision-making based on power Bonferroni operators of linguistic q-rung orthopair fuzzy numbers","volume":"34","author":"Liu","year":"2019","journal-title":"Int. J. Intell. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3688","DOI":"10.1109\/TFUZZ.2018.2843330","article-title":"Probabilistic linguistic MULTIMOORA: A multi-attributes decision making method based on the probabilistic linguistic expectation function and the improved Borda rule","volume":"26","author":"Wu","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_27","first-page":"53","article-title":"Hesitant intuitionistic fuzzy linguistic term sets","volume":"20","author":"Beg","year":"2014","journal-title":"Notes Intuit. Fuzzy Sets"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00122574","article-title":"Advances in prospect theory: Cumulative representation of uncertainty","volume":"5","author":"Tversky","year":"1992","journal-title":"J. Risk Uncertain."},{"key":"ref_29","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."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/891\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:02:57Z","timestamp":1760162577000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,17]]},"references-count":29,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["sym13050891"],"URL":"https:\/\/doi.org\/10.3390\/sym13050891","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,17]]}}}