{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T16:53:36Z","timestamp":1790268816587,"version":"4.1.0"},"reference-count":16,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,7]],"date-time":"2017-07-07T00:00:00Z","timestamp":1499385600000},"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, 51272159"],"award-info":[{"award-number":["71471172, 51272159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"The Natural Science Foundation of Zhejiang province","award":["LY15A040001"],"award-info":[{"award-number":["LY15A040001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Existing intuitionistic linguistic variables can describe the linguistic information of both the truth\/membership and falsity\/non-membership degrees, but it cannot represent the indeterminate and inconsistent linguistic information. To deal with the issue, this paper originally proposes the concept of a linguistic neutrosophic number (LNN), which is characterized independently by the truth, indeterminacy, and falsity linguistic variables. Then, we define the basic operational laws of LNNs and the score and accuracy functions of LNN for comparing LNNs. Next, we develop an LNN-weighted arithmetic averaging (LNNWAA) operator and an LNN-weighted geometric averaging (LNNWGA) operator to aggregate LNN information and investigate their properties. Further, a multiple attribute group decision-making method based on the proposed LNNWAA or LNNWGA operator is established under LNN environment. Finally, an illustrative example about selecting problems of investment alternatives is presented to demonstrate the application and effectiveness of the developed approach.<\/jats:p>","DOI":"10.3390\/sym9070111","type":"journal-article","created":{"date-parts":[[2017,7,7]],"date-time":"2017-07-07T10:37:17Z","timestamp":1499423837000},"page":"111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":71,"title":["Multiple Attribute Group Decision-Making Method Based on Linguistic Neutrosophic Numbers"],"prefix":"10.3390","volume":"9","author":[{"given":"Zebo","family":"Fang","sequence":"first","affiliation":[{"name":"Department of Physics, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang, 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":"Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of a linguistic variable and its application to approximate reasoning Part I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. 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