{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T14:53:53Z","timestamp":1767192833273,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,22]],"date-time":"2020-05-22T00:00:00Z","timestamp":1590105600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nature Science Foundation of Hebei Province","award":["No. F2014501046"],"award-info":[{"award-number":["No. F2014501046"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper proposes neutrosophic vague N-soft sets which is composed of neutrosophic vague sets and N-soft sets for the first time. The new hybrid model includes a pair of asymmetric functions: truth-membership and false-membership, and an indeterminacy-membership function. Some useful operations and propositions are given and illustrated by examples. Moreover, a method of priority relation ranking based on neutrosophic vague N-soft sets is presented. The validity of the method is verified by comparison. It is more flexible and reasonable to use this method in our daily life. Finally, a potential application of multi-attribute decision making is presented.<\/jats:p>","DOI":"10.3390\/sym12050853","type":"journal-article","created":{"date-parts":[[2020,5,22]],"date-time":"2020-05-22T10:18:18Z","timestamp":1590142698000},"page":"853","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Multi-Attribute Decision Making Method Based on Neutrosophic Vague N-Soft Sets"],"prefix":"10.3390","volume":"12","author":[{"given":"Jianbo","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziyue","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanyan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,22]]},"reference":[{"key":"ref_1","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. 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