{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T16:32:48Z","timestamp":1781195568699,"version":"3.54.1"},"reference-count":47,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,1,4]]},"abstract":"<jats:p>In many cases, complex problems cannot be accurately described by precise numerical values. Fuzzy theory provides a suitable tool for solving these problems. However, if decision makers cannot reach an agreement on the method for defining linguistic variables based on fuzzy sets, TIVFNs (triangular interval-valued fuzzy numbers) can provide more accurate modeling. Therefore, solving fuzzy MCGDM (multiple criteria group decision-making) problem with an unknown expert weight and criterion weight in TIVFNs has become an important research direction. In this paper, TIVF-VIKOR (triangular interval-valued fuzzy VIKOR) method, which is suitable for the environment of TIVFNs, is proposed to solve the problem of fuzzy MCGDM. To achieve this goal, the TIVF-VIKOR method is innovatively adopted similarity and coefficient of variation are combined to calculate expert weight, and deviation maximization method based on divergence matrix is used to calculate criterion weight. VIKOR method is used to find the compromise solutions, which are converted into the form of binary connection number, and the optimal compromise solution is obtained after ranking. The proposed method is applied to the problem of machine fault detection, and the validity and feasibility of the method are illustrated. Compared with the TOPSIS\u2216ELECTRE method, the ranking results of the three methods are equivalent, and the fluctuation of the TIVF-VIKOR method is more distinct.<\/jats:p>","DOI":"10.3233\/jifs-191261","type":"journal-article","created":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T09:24:11Z","timestamp":1581672251000},"page":"221-233","source":"Crossref","is-referenced-by-count":8,"title":["A multi-criteria decision-making method based on triangular interval-valued fuzzy numbers and the VIKOR method"],"prefix":"10.1177","volume":"40","author":[{"given":"Xingang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ke","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","reference":[{"issue":"4","key":"10.3233\/JIFS-191261_ref1","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":"International Journal of Computational Intelligence Systems"},{"issue":"9\u201312","key":"10.3233\/JIFS-191261_ref2","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1007\/s00170-011-3658-y","article-title":"Thirty criteria based leanness assessment using fuzzy logic approach","volume":"60","author":"Vinodh","year":"2012","journal-title":"International Journal of Advanced Manufacturing Technology"},{"key":"10.3233\/JIFS-191261_ref4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0165-0114(87)90148-5","article-title":"A method of inference in approximate reasoning based on interval-valued fuzzy sets","volume":"21","author":"Gorzalczany","year":"1987","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-191261_ref5","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.inffus.2016.04.005","article-title":"Personalized individual semantics in computing with words for supporting linguistic group decision making, An application on consensus reaching","volume":"33","author":"Li","year":"2017","journal-title":"Information Fusion"},{"issue":"3","key":"10.3233\/JIFS-191261_ref6","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":"10.3233\/JIFS-191261_ref7","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 and Systems"},{"key":"10.3233\/JIFS-191261_ref8","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0165-0114(89)90215-7","article-title":"More on Intuitionistic Fuzzy Sets","volume":"33","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-191261_ref10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0020-0255(02)00265-7","article-title":"Some algebraic properties and a distance measure for interval-valued fuzzy numbers","volume":"148","author":"Hong","year":"2002","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-191261_ref11","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.procs.2017.12.007","article-title":"Multi-criteria decision making with triangular intuitionistic fuzzy number based on distance measure & parametric entropy approach","volume":"125","author":"Saini","year":"2018","journal-title":"Procedia Computer Science"},{"key":"10.3233\/JIFS-191261_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhydrol.2018.04.069"},{"key":"10.3233\/JIFS-191261_ref13","doi-asserted-by":"publisher","DOI":"10.1515\/math-2019-0048"},{"key":"10.3233\/JIFS-191261_ref14","doi-asserted-by":"publisher","DOI":"10.1109\/icpcsi.2017.8391853"},{"issue":"1","key":"10.3233\/JIFS-191261_ref16","doi-asserted-by":"publisher","first-page":"122","DOI":"10.3846\/20294913.2015.1070771","article-title":"An extension of the ratio system approach of MOORA method for group decision-making based on interval-valued triangular fuzzy numbers","volume":"22","author":"Stanujkic","year":"2015","journal-title":"Technological and Economic Development of Economy"},{"key":"10.3233\/JIFS-191261_ref17","first-page":"69","article-title":"A novel triangular interval type-2 type-2 intuitionistic fuzzy sets and their aggregation operators","volume":"2018","author":"Garg","journal-title":"Iranian Jouurnal Of Fuzzy Systems"},{"issue":"2","key":"10.3233\/JIFS-191261_ref18","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1016\/j.ejor.2016.08.075","article-title":"Measuring systems sustainability with multi-criteria methods: A critical review","volume":"258","author":"Diaz-Balteiro","year":"2017","journal-title":"European Journal of Operational Research"},{"issue":"8","key":"10.3233\/JIFS-191261_ref19","doi-asserted-by":"publisher","first-page":"4126","DOI":"10.1016\/j.eswa.2015.01.003","article-title":"Fuzzy multiple criteria decision-making techniques and applications \u2013Two decades review from 1994 to 2014","volume":"42","author":"Mardani","year":"2015","journal-title":"Expert Systems with Applications"},{"key":"10.3233\/JIFS-191261_ref20","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1016\/j.wasman.2014.09.010","article-title":"Multiple stakeholders in multi-criteria decision-making in the context of Municipal Solid Waste Management: A review","volume":"35","author":"Soltani","year":"2015","journal-title":"Waste Management"},{"key":"10.3233\/JIFS-191261_ref21","first-page":"31","article-title":"ELECTRE: Une m\u00e9thode pour guider le choix en pr\u00e9sence de points de vue multiples","volume":"3","author":"Benayoun","year":"1966","journal-title":"Rev.franaise Informat.recherche Op\u00e9rationnelle"},{"key":"10.3233\/JIFS-191261_ref22","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/j.cie.2019.06.011","article-title":"A combined interval-valued ELECTRE TRI and TOPSIS approach for solving the storage location assignment problem","volume":"135","author":"Micale","year":"2019","journal-title":"Computers & Industrial Engineering"},{"key":"10.3233\/JIFS-191261_ref23","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/j.asoc.2017.11.049","article-title":"Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets","volume":"6","author":"Liao","year":"2018","journal-title":"Applied Soft Computing"},{"issue":"2","key":"10.3233\/JIFS-191261_ref24","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/j.asoc.2008.05.005","article-title":"Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets","volume":"9","author":"Ashtiani","year":"2009","journal-title":"Applied Soft Computing"},{"issue":"7","key":"10.3233\/JIFS-191261_ref25","doi-asserted-by":"crossref","first-page":"4938","DOI":"10.1016\/j.apm.2012.10.002","article-title":"Extension of VIKOR method for decision making problem based on hesitant fuzzy set","volume":"37","author":"Zhang","year":"2013","journal-title":"Applied Mathematical Modelling"},{"key":"10.3233\/JIFS-191261_ref26","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.cie.2016.05.013","article-title":"An extended VIKOR method using stochastic data and subjective judgments","volume":"97","author":"Tavana","year":"2016","journal-title":"Computers and Industrial Engineering"},{"key":"10.3233\/JIFS-191261_ref27","first-page":"5","article-title":"Multicriteria optimization of civil engineering systems","volume":"2","author":"Opricovic","year":"1998","journal-title":"Faculty of Civil Engineering"},{"issue":"10","key":"10.3233\/JIFS-191261_ref28","doi-asserted-by":"publisher","first-page":"497","DOI":"10.3390\/sym10100497","article-title":"An extended VIKOR method for multiple criteria group decision making with triangular fuzzy neutrosophic numbers","volume":"10","author":"Wang","year":"2018","journal-title":"Symmetry"},{"key":"10.3233\/JIFS-191261_ref29","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1016\/j.ins.2019.06.049","article-title":"An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods","volume":"502","author":"Wu","year":"2019","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-191261_ref31","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.knosys.2013.06.019","article-title":"The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers","volume":"52","author":"Wan","year":"2013","journal-title":"Knowledge-Based Systems"},{"key":"10.3233\/JIFS-191261_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.03.018"},{"key":"10.3233\/JIFS-191261_ref33","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/j.asoc.2011.08.020","article-title":"A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers","volume":"12","author":"Kuo","year":"2012","journal-title":"Applied Soft Computing"},{"key":"10.3233\/JIFS-191261_ref34","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/S0165-0114(02)00383-4","article-title":"Deriving priorities from fuzzy pairwise comparison judgements","volume":"134","author":"Mikhailov","year":"2003","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-191261_ref35","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0898-1221(01)00277-2","article-title":"Ranking fuzzy numbers with an area between the centroid point and the original point","volume":"43","author":"Chu","year":"2002","journal-title":"Computers and Mathematics with Applications"},{"issue":"5","key":"10.3233\/JIFS-191261_ref36","doi-asserted-by":"crossref","first-page":"3112","DOI":"10.1016\/j.apm.2012.07.035","article-title":"Extension of VIKOR method for multi-criteria group decision making problem with linguistic information","volume":"37","author":"Yanbing","year":"2013","journal-title":"Applied Mathematical Modelling"},{"key":"10.3233\/JIFS-191261_ref37","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1109\/TFUZZ.2015.2453020","article-title":"Pre-aggregation functions: Construction and an application","volume":"24","author":"Lucca","year":"2016","journal-title":"IEEE Trans. Fuzzy Syst"},{"issue":"2","key":"10.3233\/JIFS-191261_ref38","first-page":"123","article-title":"Ranking triangular interval-valued fuzzy numbers based on the relative preference relation","volume":"16","author":"Wang","year":"2019","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-191261_ref39","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-181066"},{"issue":"10","key":"10.3233\/JIFS-191261_ref40","doi-asserted-by":"publisher","first-page":"12983","DOI":"10.1016\/j.eswa.2011.04.097","article-title":"Fuzzy VIKOR with an application to water resources planning","volume":"38","author":"Opricovic","year":"2011","journal-title":"Expert Systems with Applications"},{"issue":"6","key":"10.3233\/JIFS-191261_ref41","doi-asserted-by":"publisher","first-page":"e0217786","DOI":"10.1371\/journal.pone.0217786","article-title":"Evaluating mobile services using integrated weighting approach and fuzzy VIKOR","volume":"14","author":"Suh","year":"2019","journal-title":"PLoS ONE"},{"key":"10.3233\/JIFS-191261_ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2019.01.086"},{"key":"10.3233\/JIFS-191261_ref43","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.engappai.2016.10.018","article-title":"Interval target-based VIKOR method supported on interval distance and preference degree for machine selection","volume":"57","author":"Hafezalkotob","year":"2017","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"10.3233\/JIFS-191261_ref44","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1007\/s10726-018-9593-7","article-title":"Interval-valued intuitionistic fuzzy waspas method: Application in reservoir flood control management policy","volume":"27","author":"Mishra","year":"2018","journal-title":"Group Decis Negot"},{"issue":"2","key":"10.3233\/JIFS-191261_ref45","first-page":"184","article-title":"A new principal component analysis method for interval data","volume":"29","author":"Zipan","year":"2016","journal-title":"Basic Sciences Journal of Textile Universities\/Fangzhi Gaoxiao Jichu Kexue Xuebao"},{"issue":"3\u20134","key":"10.3233\/JIFS-191261_ref46","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1007\/s00209-012-0979-y","article-title":"Dirichlet series associated with square of class numbers of binary quadratic forms","volume":"272","author":"Mizuno","year":"2012","journal-title":"Mathematische Zeitschrift"},{"issue":"1","key":"10.3233\/JIFS-191261_ref47","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0378-3812(83)80003-x","article-title":"On the thermodynamics of associated solutions. III. Vapor-liquid equilibria of binary and ternary systems with any number of associating components","volume":"10","author":"Nath","year":"1983","journal-title":"Fluid Phase Equilibria"},{"issue":"1","key":"10.3233\/JIFS-191261_ref48","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.disc.2015.08.014","article-title":"The number of elements belonging to triads in 3-connected binary matroids","volume":"339","author":"Gomes","year":"2016","journal-title":"Discrete Mathematics"},{"key":"10.3233\/JIFS-191261_ref49","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.elecom.2017.02.016","article-title":"Binary-number-based digital electrochemical detection using a single working electrode with multiple sensors","volume":"77","author":"Ino","year":"2017","journal-title":"Electrochemistry Communications"},{"key":"10.3233\/JIFS-191261_ref50","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.procs.2015.12.079","article-title":"The locating-chromatic number of binary trees","volume":"74","author":"Syofyan","year":"2015","journal-title":"Procedia Computer Science"},{"key":"10.3233\/JIFS-191261_ref52","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-04398-1"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-191261","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:42:01Z","timestamp":1777455721000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-191261"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,4]]},"references-count":47,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.3233\/jifs-191261","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,4]]}}}