{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T18:22:53Z","timestamp":1789755773139,"version":"4.0.1"},"reference-count":13,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,10,1]],"date-time":"2017-10-01T00:00:00Z","timestamp":1506816000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71471172, 41427802"],"award-info":[{"award-number":["71471172, 41427802"]}],"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 rock mechanics, the study of shear strength on the structural surface is crucial to evaluating the stability of engineering rock mass. In order to determine the shear strength, a key parameter is the joint roughness coefficient (JRC). To express and analyze JRC values, Ye et al. have proposed JRC neutrosophic numbers (JRC-NNs) and fitting functions of JRC-NNs, which are obtained by the classical statistics and curve fitting in the current method. Although the JRC-NNs and JRC-NN functions contain much more information (partial determinate and partial indeterminate information) than the crisp JRC values and functions in classical methods, the JRC functions and the JRC-NN functions may also lose some useful information in the fitting process and result in the function distortion of JRC values. Sometimes, some complex fitting functions may also result in the difficulty of their expressions and analyses in actual applications. To solve these issues, we can combine the neutrosophic numbers with neutrosophic statistics to realize the neutrosophic statistical analysis of JRC-NNs for easily analyzing the characteristics (scale effect and anisotropy) of JRC values. In this study, by means of the neutrosophic average values and standard deviations of JRC-NNs, rather than fitting functions, we directly analyze the scale effect and anisotropy characteristics of JRC values based on an actual case. The analysis results of the case demonstrate the feasibility and effectiveness of the proposed neutrosophic statistical analysis of JRC-NNs and can overcome the insufficiencies of the classical statistics and fitting functions. The main advantages of this study are that the proposed neutrosophic statistical analysis method not only avoids information loss but also shows its simplicity and effectiveness in the characteristic analysis of JRC.<\/jats:p>","DOI":"10.3390\/sym9100208","type":"journal-article","created":{"date-parts":[[2017,10,2]],"date-time":"2017-10-02T13:10:05Z","timestamp":1506949805000},"page":"208","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":190,"title":["Scale Effect and Anisotropy Analyzed for Neutrosophic Numbers of Rock Joint Roughness Coefficient Based on Neutrosophic Statistics"],"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, Zhejiang Province, China, chenjiqian@yahoo.com (J.C.)"}],"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, Zhejiang Province, China, chenjiqian@yahoo.com (J.C.)"},{"name":"Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang Province, 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, Zhejiang Province, China, chenjiqian@yahoo.com (J.C.)"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0013-7952(73)90013-6","article-title":"Review of a new shear-strength criterion for rock joints","volume":"7","author":"Barton","year":"1973","journal-title":"Eng. Geol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0148-9062(79)90241-9","article-title":"Estimating joint roughness coefficients","volume":"16","author":"Tse","year":"1979","journal-title":"Int. J. Rock Mech. Min. Sci. Geomech. Abstr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.ijrmms.2014.09.009","article-title":"A new method estimating the 2D joint roughness coefficient for discontinuity surfaces in rock masses","volume":"72","author":"Zhang","year":"2014","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1007\/s00603-015-0795-x","article-title":"Characterization of anisotropy of joint surface roughness and aperture by variogram approach based on digital image processing technique","volume":"49","author":"Chen","year":"2016","journal-title":"Rock Mech. 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Introduction to Neutrosophic Statistics, Sitech & Education Publisher."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ye, J., Chen, J.Q., Yong, R., and Du, S.G. (2017). Expression and analysis of joint roughness coefficient using neutrosophic number functions. Information, 8.","DOI":"10.3390\/info8020069"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chen, J.Q., Ye, J., Du, S.G., and Yong, R. (2017). Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers. Symmetry, 9.","DOI":"10.3390\/sym9070123"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ye, J. (2017). Neutrosophic number linear programming method and its application under neutrosophic number environments. Soft Comput.","DOI":"10.1007\/s00500-017-2646-z"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1007\/s12583-009-0075-3","article-title":"Measurement of joint roughness coefficient by using profilograph and roughness ruler","volume":"20","author":"Du","year":"2009","journal-title":"J. Earth Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/10\/208\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:46:27Z","timestamp":1760208387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/10\/208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,1]]},"references-count":13,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["sym9100208"],"URL":"https:\/\/doi.org\/10.3390\/sym9100208","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,1]]}}}