{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T13:16:26Z","timestamp":1780578986148,"version":"3.54.1"},"reference-count":16,"publisher":"Emerald","issue":"2","license":[{"start":{"date-parts":[[2017,8,7]],"date-time":"2017-08-07T00:00:00Z","timestamp":1502064000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["GS"],"published-print":{"date-parts":[[2017,8,7]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>The purpose of this paper is to establish the algorithm rules of the interval grey numbers and propose a new ranking method of the interval grey numbers.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>The definitions of \u201ckernels\u201d based on lower measure, upper measure or moderate measure are given according to the properties of the interval grey number problems. By means of the measurement error, the concept of the absolute degree of greyness and the relative degree of greyness corresponding to different \u201ckernel\u201d are given, and different simplified forms of the interval grey numbers are put forward.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>The definitions of \u201ckernel\u201d and the degree of greyness in this paper not only take the upper limit, lower limit and the coverage of the interval grey numbers into account, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Research limitations\/implications<\/jats:title>\n<jats:p>Though the method proposed in this paper has some deficiencies, such as the definition of relative degree of greyness is meaningless when the kernel of the interval grey number is 0, it provides a new idea for calculating and sorting the interval grey numbers and is conducive to the further development of the grey system theory.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>The method proposed in this paper can not only distinguish interval grey numbers in different situations, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse. In this basis, the interval grey number algorithm is established and a new ranking method of interval grey numbers is given.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/gs-10-2015-0073","type":"journal-article","created":{"date-parts":[[2017,6,27]],"date-time":"2017-06-27T07:32:43Z","timestamp":1498548763000},"page":"168-178","source":"Crossref","is-referenced-by-count":14,"title":["Algorithm rules of interval grey numbers based on different \u201ckernel\u201d and the degree of greyness of grey numbers"],"prefix":"10.1108","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4176-9399","authenticated-orcid":false,"given":"San-dang","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sifeng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhigeng","family":"Fang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"140","reference":[{"issue":"5","key":"key2020120602251817900_ref001","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","article-title":"Control problem of grey system","volume":"1","year":"1982","journal-title":"Systems and Control Letters"},{"key":"key2020120602251817900_ref002","volume-title":"Grey Control System","year":"1999","edition":"2nd ed."},{"issue":"zl","key":"key2020120602251817900_ref003","first-page":"130","article-title":"Study on GM(1,1) model based on interval grey number (GMBIGN(1,1))","volume":"12","year":"2004","journal-title":"Chinese Journal of Management Science"},{"issue":"2","key":"key2020120602251817900_ref004","first-page":"57","article-title":"Study on Improvement of token and arithmetic of interval grey numbers and its GM(1,1) Model","volume":"7","year":"2005","journal-title":"Engineering Science"},{"issue":"4","key":"key2020120602251817900_ref201","first-page":"502","article-title":"Proof on Perron-Frobenius theorem about the grey nonnegative matrix","volume":"21","year":"1987","journal-title":"Journal of Henan Agricultural University"},{"key":"key2020120602251817900_ref005","first-page":"70","volume":"5","year":"2009","journal-title":"Grey System Theory and Application"},{"key":"key2020120602251817900_ref010","unstructured":"Liu, S.F. and Lin, Y. (2004), \u201cAn axiomatic definition of degree of greyness of grey number\u201d, Engineering Science, Vol. 6 No. 8, pp. 91-94."},{"key":"key2020120602251817900_ref011","volume-title":"Grey Information: Theory and Practical Applications","year":"2005"},{"issue":"6","key":"key2020120602251817900_ref012","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1108\/03684920610662692","article-title":"On measures of information content of grey numbers","volume":"35","year":"2006","journal-title":"Kybernetes: The International Journal of Systems & Cybernetics"},{"key":"key2020120602251817900_ref006","volume-title":"Grey System and Application","year":"2010"},{"issue":"2","key":"key2020120602251817900_ref008","first-page":"313","article-title":"Algorithm rules of interval grey numbers based on the \u2018kernel\u2019 and the degree of greyness of grey numbers systems","volume":"32","year":"2010","journal-title":"Engineering and Electronics"},{"issue":"3","key":"key2020120602251817900_ref009","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1108\/20439371211273230","article-title":"General grey numbers and their operations","volume":"2","year":"2012","journal-title":"Grey Systems: Theory and Application"},{"issue":"4","key":"key2020120602251817900_ref013","first-page":"169","article-title":"On comparing grey numbers with their probability distribution","volume":"29","year":"2009","journal-title":"Systems Engineering \u2013 Theory & Practice"},{"issue":"2","key":"key2020120602251817900_ref014","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.inffus.2006.10.008","article-title":"Dependent uncertain ordered weighted aggregation operators","volume":"9","year":"2008","journal-title":"Information Fusion"},{"issue":"2","key":"key2020120602251817900_ref015","first-page":"315","article-title":"The ranking method of grey numbers based on relative kernel and degree of accuracy","volume":"29","year":"2014","journal-title":"Control and Decision"},{"key":"key2020120602251817900_ref016","first-page":"13","volume-title":"An Introduction to Grey System: Foundations, Methodology and Applications","year":"1998"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-10-2015-0073\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-10-2015-0073\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:46:16Z","timestamp":1753404376000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/gs\/article\/7\/2\/168-178\/86539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,7]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,8,7]]}},"alternative-id":["10.1108\/GS-10-2015-0073"],"URL":"https:\/\/doi.org\/10.1108\/gs-10-2015-0073","relation":{},"ISSN":["2043-9377"],"issn-type":[{"value":"2043-9377","type":"print"}],"subject":[],"published":{"date-parts":[[2017,8,7]]}}}