{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T05:49:57Z","timestamp":1778737797270,"version":"3.51.4"},"reference-count":7,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2011,1,28]],"date-time":"2011-01-28T00:00:00Z","timestamp":1296172800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,1,28]]},"abstract":"Purpose<\/jats:title>The purpose of this paper is to advance new rules about operations of grey numbers based on kernels and greyness and analyze the reliability of these new operations.<\/jats:p><\/jats:sec>Design\/methodology\/approach<\/jats:title>A grey number is usually represented as a closed interval or a discrete set of numbers. Based on the definition of traditional grey number, novel rules that grey numbers can be represented as their kernels and associated degrees of greyness are proposed. In new rules, the operation between kernels of grey numbers has significance in the application of grey numbers. The reliability of operations of grey numbers using their kernels and the degrees of greyness derived from kernel operations and their corresponding interval operations are studied.<\/jats:p><\/jats:sec>Findings<\/jats:title>The results show that the novel rules about operation of grey numbers satisfy to the concept of grey system properly. It is useful to calculate the grey degree of grey numbers and the process of calculating is easier than traditional operation rules.<\/jats:p><\/jats:sec>Practical implications<\/jats:title>The method exposed in the paper can be used to calculate each two grey numbers. The grey degree and the calculating results of two grey numbers can be given out easily. The method can also be used to calculate grey numbers more than two.<\/jats:p><\/jats:sec>Originality\/value<\/jats:title>The paper succeeds in constructing novel operation rules of grey numbers. The reliability of novel operation rules is studied and it is new development of grey systems theory, undoubtedly.<\/jats:p><\/jats:sec>","DOI":"10.1108\/20439371111106731","type":"journal-article","created":{"date-parts":[[2011,1,22]],"date-time":"2011-01-22T07:25:06Z","timestamp":1295681106000},"page":"57-71","source":"Crossref","is-referenced-by-count":37,"title":["Reliability of operations of grey numbers using kernels"],"prefix":"10.1108","volume":"1","author":[{"given":"Yingjie","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Si\u2010feng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"key":"key2022030820403729000_b1","unstructured":"Alefeld, G. and Herzberger, J. 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(2006), \u201cStudy on algorithm of grey numbers and grey algebraic system\u201d, Proceedings of the 2006 IEEE International Conference on Systems, Man and Cybernetics, Taipei, pp. 2272\u20106.","DOI":"10.1109\/ICSMC.2006.385200"},{"key":"key2022030820403729000_b5","unstructured":"Liu, S.F., Dang, Y.G. and Fang, Z.G. (2004), Grey Systems Theory and Its Applications, The Science Press of China, Beijing."},{"key":"key2022030820403729000_b7","doi-asserted-by":"crossref","unstructured":"Yang, Y.J. (2007), \u201cExtended grey numbers and their operations\u201d, Proceedings of the 2007 IEEE International Conference on Systems, Man and Cybernetics, Montreal, pp. 2181\u20106.","DOI":"10.1109\/ICSMC.2007.4413838"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/20439371111106731","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/20439371111106731\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/20439371111106731\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:52:32Z","timestamp":1753401152000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/gs\/article\/1\/1\/57-71\/221272"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,28]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1,28]]}},"alternative-id":["10.1108\/20439371111106731"],"URL":"https:\/\/doi.org\/10.1108\/20439371111106731","relation":{},"ISSN":["2043-9377"],"issn-type":[{"value":"2043-9377","type":"print"}],"subject":[],"published":{"date-parts":[[2011,1,28]]}}}