{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:39:17Z","timestamp":1760146757698,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,7]],"date-time":"2024-12-07T00:00:00Z","timestamp":1733529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University","award":["RGP 2\/190\/45"],"award-info":[{"award-number":["RGP 2\/190\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Dempster\u2013Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions focusing on belief and plausibility intuitionistic fuzzy distance (BP-distance) and similarity (BP-similarity) until now. In this work, we propose a novel framework for the belief and plausibility of intuitionistic fuzzy sets (BP-IFSs) and their BP-distance and BP-similarity measures. We modified steps 4 and 5 of the classical TOPSIS method, utilizing both distance and similarity measures to rank the alternatives that satisfy all necessary axioms of distance and similarity. We present numerical examples involving pattern recognition, linguistic variables, and clustering to illustrate the efficiency of these measures, and we develop belief and plausibility TOPSIS (BP-TOPSIS) using the proposed criteria and apply it to complex multicriteria decision-making (MCDM) challenges. The results demonstrate the practicality and effectiveness of our approach.<\/jats:p>","DOI":"10.3390\/axioms13120858","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T11:16:48Z","timestamp":1733743008000},"page":"858","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making"],"prefix":"10.3390","volume":"13","author":[{"given":"Shahid","family":"Hussain","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]},{"given":"Zahid","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Karakoram International University, Gilgit 15100, Pakistan"}]},{"given":"Rashid","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Karakoram International University, Gilgit 15100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5454-380X","authenticated-orcid":false,"given":"Ahmad","family":"Bakhet","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]},{"given":"Hussain","family":"Arafat","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4312-8330","authenticated-orcid":false,"given":"Mohammed","family":"Zakarya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"}]},{"given":"Amirah Ayidh I","family":"Al-Thaqfan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Saudi Arabia"}]},{"given":"Maha","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and Lower Probabilities Induced by a Multivalued Mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann. Math. 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