{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:31:04Z","timestamp":1777509064260,"version":"3.51.4"},"reference-count":9,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T00:00:00Z","timestamp":1500508800000},"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>In nature, the mechanical properties of geological bodies are very complex, and their various mechanical parameters are vague, incomplete, imprecise, and indeterminate. However, we cannot express them by the crisp values in classical probability and statistics. In geotechnical engineering, we need to try our best to approximate exact values in indeterminate environments because determining the joint roughness coefficient (JRC) effectively is a key parameter in the shear strength between rock joint surfaces. In this original study, we first propose neutrosophic interval probability (NIP) and define the confidence degree based on the cosine measure between NIP and the ideal NIP. Then, we propose a new neutrosophic interval statistical number (NISN) by combining the neutrosophic number with the confidence degree to express indeterminate statistical information. Finally, we apply NISNs to express JRC under indeterminate (imprecise, incomplete, and uncertain, etc.) environments. By an actual case, the results demonstrate that NISNs are suitable and effective for JRC expressions and have the objective advantage.<\/jats:p>","DOI":"10.3390\/sym9070123","type":"journal-article","created":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T11:21:59Z","timestamp":1500549719000},"page":"123","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":171,"title":["Expressions of Rock Joint Roughness Coefficient Using Neutrosophic Interval Statistical Numbers"],"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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Yong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Rock Mechanics and Geohazards, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,20]]},"reference":[{"key":"ref_1","unstructured":"Smarandache, F. (1998). Neutrosophy: Neutrosophic Probability, Set, and Logic, American Research Press."},{"key":"ref_2","unstructured":"Smarandache, F. (2013). Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability, Sitech & Education Publishing."},{"key":"ref_3","unstructured":"Smarandache, F. (2014). Introduction to Neutrosophic Statistics, Sitech & Education Publishing."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1007\/s00521-015-2123-5","article-title":"Bidirectional projection method for multiple attribute group decision making with neutrosophic numbers","volume":"28","author":"Ye","year":"2015","journal-title":"Neural Comput. Appl."},{"key":"ref_5","first-page":"377","article-title":"Multiple-attribute group decision-making method under a neutrosophic number environment","volume":"25","author":"Ye","year":"2016","journal-title":"J. Intell. Syst."},{"key":"ref_6","first-page":"139","article-title":"A projection model of neutrosophic numbers for multiple attribute decision making of clay-brick selection","volume":"12","author":"Chen","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_7","first-page":"43","article-title":"Misfire fault diagnosis method of gasoline engines using the cosine similarity measure of neutrosophic numbers","volume":"8","author":"Kong","year":"2015","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1927","DOI":"10.3233\/IFS-151903","article-title":"Fault diagnoses of steam turbine using the exponential similarity measure of neutrosophic numbers","volume":"30","author":"Ye","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4825709","DOI":"10.1155\/2016\/4825709","article-title":"Neutrosophic functions of the joint roughness coefficient (JRC) and the shear strength: A case study from the pyroclastic rock mass in Shaoxing City, China","volume":"2016","author":"Ye","year":"2016","journal-title":"Math. Prob. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/7\/123\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:21Z","timestamp":1760208201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/7\/123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,20]]},"references-count":9,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["sym9070123"],"URL":"https:\/\/doi.org\/10.3390\/sym9070123","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,20]]}}}