{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T23:24:22Z","timestamp":1781306662289,"version":"3.54.1"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,8,11]],"date-time":"2017-08-11T00:00:00Z","timestamp":1502409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71471172"],"award-info":[{"award-number":["71471172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A refined single-valued\/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees. However, existing refined single-valued\/interval neutrosophic similarity measures and their decision-making methods are scarcely studied in existing literature and cannot deal with this decision-making problem with the weights of both attributes and sub-attributes in a refined interval and\/or single-valued neutrosophic setting. To solve the issue, this paper firstly introduces a refined simplified neutrosophic set (RSNS), which contains the refined single-valued neutrosophic set (RSVNS) and refined interval neutrosophic set (RINS), and then proposes vector similarity measures of RSNSs based on the Jaccard, Dice, and cosine measures of simplified neutrosophic sets in vector space, and the weighted Jaccard, Dice, and cosine measures of RSNSs by considering weights of both basic elements and sub-elements in RSNS. Further, a decision-making method with the weights of both attributes and sub-attributes is developed based on the weighted Jaccard, Dice, and cosine measures of RSNSs under RSNS (RINS and\/or RSVNS) environments. The ranking order of all the alternatives and the best one can be determined by one of weighted vector similarity measures between each alternative and the ideal solution (ideal alternative). Finally, an actual example on the selecting problem of construction projects illustrates the application and effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/sym9080153","type":"journal-article","created":{"date-parts":[[2017,8,11]],"date-time":"2017-08-11T10:07:40Z","timestamp":1502446060000},"page":"153","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Vector Similarity Measures between Refined Simplified Neutrosophic Sets and Their Multiple Attribute Decision-Making Method"],"prefix":"10.3390","volume":"9","author":[{"given":"Jiqian","family":"Chen","sequence":"first","affiliation":[{"name":"Key Laboratory of Rock Mechanics and Geohazards, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2841-6529","authenticated-orcid":false,"given":"Jun","family":"Ye","sequence":"additional","affiliation":[{"name":"Key Laboratory of Rock Mechanics and Geohazards, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China"},{"name":"Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shigui","family":"Du","sequence":"additional","affiliation":[{"name":"Key Laboratory of Rock Mechanics and Geohazards, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,11]]},"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. Control."},{"key":"ref_2","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 Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","article-title":"Interval-valued intuitionistic fuzzy sets","volume":"31","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets Syst."},{"key":"ref_4","unstructured":"Smarandache, F. (1998). Neutrosophy: Neutrosophic Probability, Set, and Logic, American Research Press."},{"key":"ref_5","unstructured":"Wang, H., Smarandache, F., Zhang, Y.Q., and Sunderraman, R. (2005). Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis."},{"key":"ref_6","first-page":"410","article-title":"Single valued neutrosophic sets","volume":"4","author":"Wang","year":"2010","journal-title":"Multispace Multistruct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2459","DOI":"10.3233\/IFS-130916","article-title":"A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets","volume":"26","author":"Ye","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_8","first-page":"204","article-title":"Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making","volume":"16","author":"Ye","year":"2014","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15923","DOI":"10.3390\/su71215792","article-title":"Sustainable assessment of alternative sites for the construction of a waste incineration plant by applying WASPAS method with single-valued neutrosophic set","volume":"7","author":"Zavadskas","year":"2015","journal-title":"Sustainability"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.asoc.2017.03.040","article-title":"Sustainable market valuation of buildings by the single-valued neutrosophic MAMVA method","volume":"57","author":"Zavadskas","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Lu, Z.K., and Ye, J. (2017). Cosine measures of neutrosophic cubic sets for multiple attribute decision-making. Symmetry, 9.","DOI":"10.3390\/sym9070121"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lu, Z.K., and Ye, J. (2017). Single-valued neutrosophic hybrid arithmetic and geometric aggregation operators and their decision-making method. Information, 8.","DOI":"10.3390\/info8030084"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Chen, J.Q., and Ye, J. (2017). Some single-valued neutrosophic Dombi weighted aggregation operators for multiple attribute decision-making. Symmetry, 9.","DOI":"10.3390\/sym9060082"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1007\/s00500-015-1818-y","article-title":"Single valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine","volume":"21","author":"Ye","year":"2017","journal-title":"Soft Comput."},{"key":"ref_15","first-page":"143","article-title":"n-Valued refined neutrosophic logic and its applications in physics","volume":"4","author":"Smarandache","year":"2013","journal-title":"Prog. Phys."},{"key":"ref_16","first-page":"49","article-title":"Dice similarity measure between single valued neutrosophic multisets and its application in medical diagnosis","volume":"6","author":"Ye","year":"2014","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_17","first-page":"42","article-title":"Neutrosophic refined similarity measure based on cosine function","volume":"6","author":"Broumi","year":"2014","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_18","first-page":"11","article-title":"Correlation measure for neutrosophic refined sets and its application in medical diagnosis","volume":"3","author":"Broumi","year":"2014","journal-title":"Palest. J. Math."},{"key":"ref_19","first-page":"486","article-title":"Neutrosophic refined similarity measure based on cotangent function and its application to multi-attribute decision making","volume":"2","author":"Mondal","year":"2015","journal-title":"Glob. J. Adv. Res."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ji, P., Zhang, H.Y., and Wang, J.Q. (2016). A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Comput. Appl.","DOI":"10.1007\/s00521-016-2436-z"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Peng, J.J., Wang, J., and Wu, X.H. (2016). An extension of the ELECTRE approach with multi-valued neutrosophic information. Neural Comput. Appl.","DOI":"10.1007\/s00521-016-2411-8"},{"key":"ref_22","first-page":"41","article-title":"Similarity measure of refined single-valued neutrosophic sets and its multicriteria decision making method","volume":"12","author":"Ye","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Fan, C.X., and Ye, J. (2017). The cosine measure of refined-single valued neutrosophic sets and refined-interval neutrosophic sets for multiple attribute decision-making. J. Intell. Fuzzy Syst., accepted (in press).","DOI":"10.3233\/JIFS-17270"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/8\/153\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:42:10Z","timestamp":1760208130000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/8\/153"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,11]]},"references-count":23,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2017,8]]}},"alternative-id":["sym9080153"],"URL":"https:\/\/doi.org\/10.3390\/sym9080153","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,11]]}}}