{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T13:19:05Z","timestamp":1771679945909,"version":"3.50.1"},"reference-count":33,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T00:00:00Z","timestamp":1597190400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 107-2118-M-033-002-MY2"],"award-info":[{"award-number":["MOST 107-2118-M-033-002-MY2"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,8,12]]},"abstract":"<jats:p>Belief and plausibility measures in Dempster\u2013Shafer theory (DST) and fuzzy sets are known as different approaches for representing partial, uncertainty, and imprecise information. There are several generalizations of DST to fuzzy sets proposed in the literature. But, less generalization of DST to intuitionistic fuzzy sets (IFSs), that can somehow present imprecise information better than fuzzy sets, was proposed. In this paper, we first propose a simple and intuitive way to construct a generalization of DST to IFSs with degrees of belief and plausibility in terms of degrees of membership and nonmembership, respectively. We then give belief and plausibility measures on IFSs and construct belief-plausibility intervals (BPIs) of IFSs. Based on the constructed BPIs, we first use Hausdorff metric to define the distance between two BPIs and then establish similarity measures in the generalized context of DST to IFSs. By employing the techniques of ordered preference similarity to ideal solution (TOPSIS), the proposed belief and plausibility measures on IFSs in the framework of DST enable us to construct a belief-plausibility TOPSIS for solving multicriteria decision-making problems. Some examples are presented to manifest that the proposed method is reasonable, applicable, and well suited in the environment of IFSs in the framework of generalization of DST.<\/jats:p>","DOI":"10.1155\/2020\/7849686","type":"journal-article","created":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T23:46:17Z","timestamp":1597275977000},"page":"1-12","source":"Crossref","is-referenced-by-count":22,"title":["Belief and Plausibility Measures on Intuitionistic Fuzzy Sets with Construction of Belief-Plausibility TOPSIS"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4907-3548","authenticated-orcid":true,"given":"Miin-Shen","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taoyuan, Taiwan"}]},{"given":"Zahid","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karakoram International University, Gilgit-Baltistan, Pakistan"}]},{"given":"Mehboob","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taoyuan, Taiwan"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177698950"},{"key":"2","year":"1976"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1002\/int.20135"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2018.2796552"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/s0019-9958(65)90241-x"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/s0165-0114(86)80034-3"},{"key":"7","year":"1999"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1002\/int.22174"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-017-0061-6"},{"issue":"4","key":"10","doi-asserted-by":"crossref","first-page":"3923","DOI":"10.3233\/JIFS-181123","volume":"36","year":"2019","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"11","first-page":"3","volume-title":"Fuzzy sets and information granularity","year":"1979"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(82)90031-7"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1109\/21.57269"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/91.771083"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1002\/int.20246"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1002\/int.21794"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2010.04.014"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.04.026"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.11.029"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1002\/int.21990"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-017-0389-8"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-018-3248-0"},{"key":"23","year":"2006"},{"key":"24","volume-title":"Measurement uncertainty: an approach via the mathematical theory of evidence","year":"2006"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1109\/mim.2013.6417052"},{"key":"26","year":"1978"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1109\/34.232073"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/s0020-0255(71)80005-1"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(92)90090-u"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/6967390"},{"key":"31","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1109\/TPAMI.2004.1265860","volume":"26","year":"2004","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"32","year":"1985"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/2832839"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/7849686.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/7849686.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/7849686.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T23:46:27Z","timestamp":1597275987000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/7849686\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,12]]},"references-count":33,"alternative-id":["7849686","7849686"],"URL":"https:\/\/doi.org\/10.1155\/2020\/7849686","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,12]]}}}