{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:49:27Z","timestamp":1777704567922,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,4,22]]},"abstract":"<jats:p>In indeterminate and inconsistent setting, existing simplified neutrosophic indeterminate set (SNIS) can be depicted by the neutrosophic number (NN) functions of the truth, falsity and indeterminacy. Then, the three NN functions in SNIS lack their refined expressions and then the simplified neutrosophic indeterminate decision making (DM) method cannot carry out the multicriteria DM problems with both criteria and sub-criteria in the setting of SNISs. To overcome the flaws, this study first proposes a new notion of a refined simplified neutrosophic indeterminate set (RSNIS), which is described by the refined truth, falsity and indeterminate NN information regarding both elements and sub-elements in a universe set, as the extension of SNIS. Next, we propose the arccosine and arctangent similarity measures of RSNISs and their multicriteria DM method with various indeterminate risk ranges so as to carry out multicriteria DM problems with weight values of both criteria and sub-criteria in RSNIS setting. Lastly, the proposed DM method is applied to a multicriteria DM example of slope design schemes for an open pit mine to illustrate its application in the indeterminate DM problem with RSNISs. The decision results and comparative analysis indicate the rationality and efficiency of the proposed DM method with different indeterminate risk ranges.<\/jats:p>","DOI":"10.3233\/jifs-201571","type":"journal-article","created":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T18:26:32Z","timestamp":1612895192000},"page":"9159-9171","source":"Crossref","is-referenced-by-count":8,"title":["Arccosine and arctangent similarity measures of refined simplified neutrosophic indeterminate sets and their multicriteria decision-making method"],"prefix":"10.1177","volume":"40","author":[{"given":"Jun","family":"Ye","sequence":"first","affiliation":[{"name":"School of Civil and Environmental Engineering, Ningbo University, Ningbo, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shigui","family":"Du","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering, Ningbo University, Ningbo, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Yong","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering, Ningbo University, Ningbo, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering, Ningbo University, Ningbo, P. R. 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Multiple attribute decision making based on immediate probabilities aggregation operators for single-valued and interval neutrosophic sets","volume":"63","author":"Garg","year":"2020","journal-title":"Journal of Applied Mathematics and Computing"},{"issue":"3","key":"10.3233\/JIFS-201571_ref18","doi-asserted-by":"crossref","first-page":"2671","DOI":"10.3934\/math.2020173","article-title":"and Nancy, Algorithms for single-valued neutrosophic decision making based on TOPSIS and Clustering methods with new distance measure","volume":"5","author":"Garg","year":"2020","journal-title":"AIMS Mathematics"},{"key":"10.3233\/JIFS-201571_ref19","first-page":"143","volume":"4","author":"Smarandache","year":"2013","journal-title":"Progress in Physics"},{"key":"10.3233\/JIFS-201571_ref20","first-page":"42","article-title":"Neutrosophic refined similarity measure based on cosine function","volume":"6","author":"Broumi","year":"2014","journal-title":"Neutrosophic Sets and 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