{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T21:34:02Z","timestamp":1784237642294,"version":"3.55.0"},"reference-count":55,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,4,22]]},"abstract":"<jats:p>In today\u2019s education industry, online teaching is increasingly becoming an important teaching way, and it is necessary to evaluate the quality of online teaching so as to improve the overall level of the education industry. The online teaching quality evaluation is a typical multi-attribute group decision-making (MAGDM) problem, and its evaluation index can be expressed by linguistic term sets (LTSs) by decision makers (DMs). Especially, multi-granularity probabilistic linguistic term sets (MGPLTSs) produced from many DMs are more suitable to express complex fuzzy evaluation information, and they can not only provide different linguistic term set for different DMs the give their preferences, but also reflect the importance of each linguistic term. Based on the advantages of MGPLTSs, in this paper, we propose a transformation function of MGPLTSs based on proportional 2-tuple fuzzy linguistic representation model. On this basis, the operational laws and comparison rules of MGPLTSs are given. Then, we develop a new Choquet integral operator for MGPLTSs, which considers the relationship among attributes and does not need to consider the process of normalizing the probabilistic linguistic term sets (PLTSs), and can effectively avoid the loss of evaluation information. At the same time, the properties of the proposed operator are also proved. Furthermore, we propose a new MAGDM method based on the new operator, and analyze the effectiveness of the proposed method by online teaching quality evaluation. Finally, by comparing with some existing methods, the advantages of the proposed method are shown.<\/jats:p>","DOI":"10.3233\/jifs-202543","type":"journal-article","created":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T13:07:03Z","timestamp":1614690423000},"page":"9915-9935","source":"Crossref","is-referenced-by-count":23,"title":["Online teaching quality evaluation based on multi-granularity probabilistic linguistic term sets"],"prefix":"10.1177","volume":"40","author":[{"given":"Peide","family":"Liu","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiyu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fei","family":"Teng","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","reference":[{"issue":"2","key":"10.3233\/JIFS-202543_ref1","first-page":"101","article-title":"Online IS education for the 21st century","volume":"25","author":"He","year":"2014","journal-title":"The Journal of Information and Systems in Education"},{"issue":"2","key":"10.3233\/JIFS-202543_ref2","first-page":"1","article-title":"Teaching Graduate Economics: Online vs. Traditional Classroom Instruction","volume":"11","author":"Bennett","year":"2019","journal-title":"Journal for Economic Educators"},{"key":"10.3233\/JIFS-202543_ref3","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.iheduc.2019.04.001","article-title":"Award-winning faculty online teaching practices: Course design, assessment and evaluation, and facilitation","volume":"42","author":"Martin","year":"2019","journal-title":"Internet and Higher Education"},{"issue":"2","key":"10.3233\/JIFS-202543_ref4","first-page":"5","article-title":"Introduction to the special issue: Faculty development for online teaching","volume":"16","author":"Jones","year":"2012","journal-title":"Online Learning-formerly The Journal of Asynchronous Learning Networks"},{"key":"10.3233\/JIFS-202543_ref5","unstructured":"Schmidt S.W. , Tschida C.M. and Hodge E. , How Faculty Learn To Teach Online: What Administrators Need to Know, Online Journal of Distance Learning Administration 19(1) (2016)."},{"issue":"5","key":"10.3233\/JIFS-202543_ref6","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1007\/s11528-017-0211-3","article-title":"Designing Personalized Online Teaching Professional Development through Self-Assessment","volume":"61","author":"Rhode","year":"2017","journal-title":"Techtrends"},{"issue":"3","key":"10.3233\/JIFS-202543_ref7","first-page":"46","article-title":"Faculty Development for the 21st Century","volume":"44","author":"Diaz","year":"2009","journal-title":"Educational Review"},{"issue":"2","key":"10.3233\/JIFS-202543_ref8","doi-asserted-by":"crossref","first-page":"701","DOI":"10.3233\/IFS-141441","article-title":"An extended TODIM method for multiple attribute group decision making based on intuitionistic uncertain linguistic variables","volume":"29","author":"Liu","year":"2015","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"01","key":"10.3233\/JIFS-202543_ref9","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1142\/S0219622018500013","article-title":"Multiple attribute decision-making methods with unbalanced linguistic variables based on maclaurin symmetric mean operators","volume":"18","author":"Teng","year":"2019","journal-title":"International Journal of Information Technology& Decision Making"},{"issue":"3","key":"10.3233\/JIFS-202543_ref10","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.3233\/JIFS-16345","article-title":"Multiple attribute group decision making methods based on some normal neutrosophic number Heronian Mean operators","volume":"32","author":"Liu","year":"2017","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"3","key":"10.3233\/JIFS-202543_ref11","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":"Information Sciences"},{"issue":"1","key":"10.3233\/JIFS-202543_ref12","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 and Systems"},{"issue":"1","key":"10.3233\/JIFS-202543_ref13","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0165-0114(98)00093-1","article-title":"A fusion approach for managing multi-granularity linguistic term sets in decision making","volume":"114","author":"Herrera","year":"2000","journal-title":"Fuzzy Sets and Systems"},{"issue":"6","key":"10.3233\/JIFS-202543_ref14","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1109\/91.890332","article-title":"A 2-tuple fuzzy linguistic representation model for computing with words","volume":"8","author":"Herrera","year":"2000","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"3","key":"10.3233\/JIFS-202543_ref15","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1109\/TFUZZ.2006.876337","article-title":"A new version of 2-tuple fuzzy linguistic representation model for computing with words","volume":"14","author":"Wang","year":"2006","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"1","key":"10.3233\/JIFS-202543_ref16","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 Transactions on Fuzzy Systems"},{"key":"10.3233\/JIFS-202543_ref17","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1080\/18756891.2015.1046329","article-title":"A hesitant fuzzy linguistic TODIM method based on a score function","volume":"8","author":"Wei","year":"2015","journal-title":"International Journal of Computational Intelligence Systems"},{"key":"10.3233\/JIFS-202543_ref18","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.ins.2013.07.027","article-title":"A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making","volume":"258","author":"Liu","year":"2014","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-202543_ref19","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.ins.2014.02.125","article-title":"Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making","volume":"271","author":"Liao","year":"2014","journal-title":"Information Sciences"},{"issue":"12","key":"10.3233\/JIFS-202543_ref20","doi-asserted-by":"crossref","first-page":"5328","DOI":"10.1016\/j.eswa.2015.02.017","article-title":"Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making","volume":"42","author":"Liao","year":"2015","journal-title":"Expert Systems with Applications"},{"key":"10.3233\/JIFS-202543_ref21","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.knosys.2014.12.009","article-title":"Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets","volume":"76","author":"Liao","year":"2015","journal-title":"Knowledge Based Systems"},{"issue":"1","key":"10.3233\/JIFS-202543_ref22","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 Transactions on Fuzzy Systems"},{"key":"10.3233\/JIFS-202543_ref23","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":"Information Sciences"},{"key":"10.3233\/JIFS-202543_ref24","first-page":"1","article-title":"TODIM-based multi-criteria decision-making method with hesitant fuzzy linguistic term sets","volume":"4","author":"Lin","year":"2019","journal-title":"Artificial Intelligence Review"},{"issue":"6","key":"10.3233\/JIFS-202543_ref25","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1007\/s13042-015-0433-7","article-title":"Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making","volume":"7","author":"Wei","year":"2016","journal-title":"International Journal of Machine Learning and Cybernetics"},{"issue":"16","key":"10.3233\/JIFS-202543_ref26","doi-asserted-by":"crossref","first-page":"5513","DOI":"10.1007\/s00500-018-3169-y","article-title":"Multiple-attribute decision-making method based on hesitant fuzzy linguistic Muirhead mean aggregation operators","volume":"22","author":"Liu","year":"2018","journal-title":"Soft Computing"},{"issue":"6","key":"10.3233\/JIFS-202543_ref27","doi-asserted-by":"crossref","first-page":"189","DOI":"10.3390\/sym10060189","article-title":"Hesitant Fuzzy Linguistic Aggregation Operators Based on the Hamacher t-norm and t-conorm","volume":"10","author":"Zhu","year":"2018","journal-title":"Symmetry"},{"key":"10.3233\/JIFS-202543_ref28","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":"Information Sciences"},{"key":"10.3233\/JIFS-202543_ref29","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-criteria decision making","volume":"119","author":"Bai","year":"2017","journal-title":"Knowledge-Based Systems"},{"issue":"4","key":"10.3233\/JIFS-202543_ref30","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s41066-017-0047-4","article-title":"Probabilistic linguistic TODIM approach for multiple attribute decision-making","volume":"2","author":"Liu","year":"2017","journal-title":"Granular Computing"},{"key":"10.3233\/JIFS-202543_ref31","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.ins.2019.02.022","article-title":"Probabilistic linguistic TODIM method for selecting products through online product reviews","volume":"485","author":"Liu","year":"2019","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-202543_ref32","doi-asserted-by":"crossref","unstructured":"Wang J.X. , Liu Y.Z. and Chen X.M. , A MAGDM model with multi-granular probabilistic linguistic power, International Conference on Information Science and Control Engineering (2018), 1030\u20131035.","DOI":"10.1109\/ICISCE.2018.00212"},{"issue":"2","key":"10.3233\/JIFS-202543_ref33","doi-asserted-by":"crossref","first-page":"127","DOI":"10.3390\/sym11020127","article-title":"A MAGDM algorithm with multi-granular probabilistic linguistic information","volume":"11","author":"Wang","year":"2019","journal-title":"Symmetry"},{"issue":"5","key":"10.3233\/JIFS-202543_ref34","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1080\/01605682.2018.1458017","article-title":"A large-scale group decision-making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection","volume":"70","author":"Song","year":"2019","journal-title":"Journal of the Operational Research Society"},{"key":"10.3233\/JIFS-202543_ref35","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":"2019","journal-title":"Information Sciences"},{"issue":"2","key":"10.3233\/JIFS-202543_ref36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/exsy.12352","article-title":"Distance-based multicriteria group decision-making approach with probabilistic linguistic term sets","volume":"36","author":"Wang","year":"2019","journal-title":"Expert Systems"},{"key":"10.3233\/JIFS-202543_ref37","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1016\/j.cie.2019.07.052","article-title":"An extended MULTIMOORA method for probabilistic linguistic multi-criteria group decision-making based on prospect theory","volume":"136","author":"Liu","year":"2019","journal-title":"Computers and Industrial Engineering"},{"issue":"12","key":"10.3233\/JIFS-202543_ref38","doi-asserted-by":"crossref","first-page":"320","DOI":"10.3390\/sym9120320","article-title":"Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making","volume":"9","author":"Kobina","year":"2017","journal-title":"Symmetry"},{"issue":"2","key":"10.3233\/JIFS-202543_ref40","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0165-0114(89)90194-2","article-title":"An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure","volume":"29","author":"Murofushi","year":"1989","journal-title":"Fuzzy Sets and Systems"},{"issue":"2","key":"10.3233\/JIFS-202543_ref41","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s40314-019-0839-z","article-title":"Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator","volume":"38","author":"Chen","year":"2019","journal-title":"Computational and Applied Mathematics"},{"issue":"10","key":"10.3233\/JIFS-202543_ref43","doi-asserted-by":"crossref","first-page":"953","DOI":"10.3390\/e21100953","article-title":"TOPSIS Method for Probabilistic Linguistic MAGDM withWeight and Its Application to Supplier Selection of New Agricultural Machinery Products","volume":"21","author":"Lu","year":"2019","journal-title":"Entropy"},{"key":"10.3233\/JIFS-202543_ref44","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.asoc.2019.01.009","article-title":"A new method for probabilistic linguistic multi-attribute group decision making: Application to the selection of financial technologies","volume":"77","author":"Mao","year":"2019","journal-title":"Applied Soft Computing"},{"issue":"2","key":"10.3233\/JIFS-202543_ref45","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1109\/3477.915345","article-title":"A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making","volume":"31","author":"Herrera","year":"2001","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics Part B (Cybernetics)"},{"key":"10.3233\/JIFS-202543_ref46","doi-asserted-by":"crossref","unstructured":"Wang Z. and Klir G.J. , Fuzzy Measure Theory, Plenum Press, New York, 1992.","DOI":"10.1007\/978-1-4757-5303-5"},{"issue":"6","key":"10.3233\/JIFS-202543_ref47","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1109\/91.890347","article-title":"An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria","volume":"8","author":"Marichal","year":"2000","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"10.3233\/JIFS-202543_ref48","doi-asserted-by":"crossref","first-page":"101178","DOI":"10.1016\/j.ijdrr.2019.101178","article-title":"An emergency decision-making method based on D-S evidence theory for probabilistic linguistic term sets","volume":"37","author":"Li","year":"2019","journal-title":"International Journal of Disaster Risk Reduction"},{"issue":"1","key":"10.3233\/JIFS-202543_ref49","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.omega.2005.12.003","article-title":"Ranking irregularities when evaluating alternatives by using some ELECTRE methods","volume":"36","author":"Wang","year":"2008","journal-title":"Omega"},{"issue":"2","key":"10.3233\/JIFS-202543_ref50","first-page":"1","article-title":"Multiple attribute group decision-making approach based on multi-granular unbalanced hesitant fuzzy linguistic information","volume":"22","author":"Liu","year":"2019","journal-title":"International Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-202543_ref51","doi-asserted-by":"publisher","DOI":"10.21203\/rs.3.rs-29617\/v1"},{"issue":"11","key":"10.3233\/JIFS-202543_ref52","doi-asserted-by":"crossref","first-page":"11195","DOI":"10.1109\/JIOT.2020.2997133","article-title":"Evaluating IoT Platforms Using Integrated Probabilistic Linguistic MCDM Method","volume":"7","author":"Lin","year":"2020","journal-title":"IEEE Internet of Things Journal"},{"issue":"10","key":"10.3233\/JIFS-202543_ref53","doi-asserted-by":"crossref","first-page":"2521","DOI":"10.1002\/int.22159","article-title":"Some q-rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making","volume":"34","author":"Liu","year":"2019","journal-title":"International Journal of Intelligent Systems"},{"issue":"12","key":"10.3233\/JIFS-202543_ref54","doi-asserted-by":"crossref","first-page":"2341","DOI":"10.1002\/int.22032","article-title":"Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators","volume":"33","author":"Liu","year":"2018","journal-title":"International Journal of Intelligent Systems"},{"issue":"2","key":"10.3233\/JIFS-202543_ref55","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1057\/s41274-017-0182-y","article-title":"Multi-attribute group decision-making under probabilistic uncertain linguistic environment","volume":"69","author":"Lin","year":"2017","journal-title":"Journal of the Operational Research Society"},{"issue":"3","key":"10.3233\/JIFS-202543_ref56","doi-asserted-by":"crossref","first-page":"2125","DOI":"10.1007\/s11071-019-04910-0","article-title":"ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing","volume":"96","author":"Lin","year":"2019","journal-title":"Nonlinear Dynamics"},{"issue":"12","key":"10.3233\/JIFS-202543_ref57","doi-asserted-by":"crossref","first-page":"2402","DOI":"10.1002\/int.22040","article-title":"Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets","volume":"33","author":"Lin","year":"2018","journal-title":"International Journal of Intelligent Systems"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-202543","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:41:42Z","timestamp":1777455702000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-202543"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,22]]},"references-count":55,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.3233\/jifs-202543","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,22]]}}}