{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:50:08Z","timestamp":1761598208150,"version":"3.41.2"},"reference-count":31,"publisher":"Emerald","issue":"4","license":[{"start":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T00:00:00Z","timestamp":1589932800000},"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":[[2020,5,20]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to propose an uncertainty representation and information measurement method for characterizing grey numbers, estimating their internal laws and solving how to generate them based on available information data in the real world.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>This paper attempts to present a new mathematical methodology in the field of grey numbers. The generalized grey number is defined at first with the concept of information elements and information samples. Then, the probability function of a grey number is proposed to describe the internal law of the grey number. By finding the feasible information elements from information samples, the probability calculation method for the true value of a grey number is presented. Finally, some numerical examples and comparisons are carried out to assess the efficiency and performance.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>The results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Practical implications<\/jats:title><jats:p>Uncertain information is widespread in practical applications. In this manuscript, the grey number is represented and its information is measured through some existing data in discrete or interval forms, which provides a grey information concept that utilizes information elements to represent uncertainty in the real world.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>The proposal presents a novel data-driven method to generate a grey number representation from available data rather than the classical whitening weight function constructed from experience, and the dynamic evolution process of a grey number is measured by the increase of information samples.<\/jats:p><\/jats:sec>","DOI":"10.1108\/gs-01-2020-0009","type":"journal-article","created":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T10:02:42Z","timestamp":1589968962000},"page":"495-512","source":"Crossref","is-referenced-by-count":14,"title":["Uncertainty representation and information measurement of grey numbers"],"prefix":"10.1108","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9416-7087","authenticated-orcid":false,"given":"Nanlei","family":"Chen","sequence":"first","affiliation":[]},{"given":"Naiming","family":"Xie","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2020101517183356700_ref001","first-page":"195","article-title":"Measurement of membership functions: theoretical and empirical work","volume-title":"Fundamentals of Fuzzy Sets","year":"2000"},{"issue":"3","key":"key2020101517183356700_ref002","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/S0165-0114(98)00067-0","article-title":"The fuzzy Delphi method via fuzzy statistics and membership function fitting and an application to the human resources","volume":"112","year":"2000","journal-title":"Fuzzy Sets and Systems"},{"issue":"1","key":"key2020101517183356700_ref003","first-page":"44","article-title":"Information elements based grey number linear algorithm and grey linear space","volume":"30","year":"2018","journal-title":"Journal of Grey System"},{"issue":"5","key":"key2020101517183356700_ref004","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","article-title":"Control problems of grey systems","volume":"1","year":"1982","journal-title":"Systems and Control Letters"},{"issue":"7","key":"key2020101517183356700_ref005","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1109\/JPROC.2002.801448","article-title":"Background and foreground modeling using nonparametric kernel density estimation for visual surveillance","volume":"90","year":"2002","journal-title":"Proceedings of the IEEE"},{"year":"2018","key":"key2020101517183356700_ref006","article-title":"Theory of Probability"},{"issue":"1","key":"key2020101517183356700_ref007","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0165-0114(95)00305-3","article-title":"Induction of fuzzy rules and membership functions from training examples","volume":"84","year":"1996","journal-title":"Fuzzy Sets and Systems"},{"issue":"7","key":"key2020101517183356700_ref008","doi-asserted-by":"crossref","first-page":"1862","DOI":"10.1016\/j.cam.2011.10.018","article-title":"Grey enterprise input\u2013output analysis","volume":"236","year":"2012","journal-title":"Journal of Computational and Applied Mathematics"},{"volume-title":"Grey Systems: Theory and Applications","year":"2010","key":"key2020101517183356700_ref009"},{"issue":"6","key":"key2020101517183356700_ref010","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"},{"issue":"2","key":"key2020101517183356700_ref011","first-page":"244","article-title":"New grey evaluation method based on reformative triangular whitenization weight function","volume":"26","year":"2011","journal-title":"Journal of Systems Engineering"},{"issue":"3","key":"key2020101517183356700_ref012","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":"1","key":"key2020101517183356700_ref013","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1108\/GS-09-2015-0054","article-title":"New progress of grey system theory in the new millennium","volume":"6","year":"2016","journal-title":"Grey Systems: Theory and Application"},{"volume-title":"Grey Data Analysis","year":"2017","key":"key2020101517183356700_ref014"},{"key":"key2020101517183356700_ref015","first-page":"397","article-title":"Axiom on grey degree","volume":"8","year":"1996","journal-title":"The Journal of Grey System"},{"key":"key2020101517183356700_ref016","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.cam.2018.07.044","article-title":"Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China","volume":"347","year":"2019","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"1\u20132","key":"key2020101517183356700_ref017","first-page":"475","article-title":"Integrated grey relational analysis and multi objective grey linear programming for sustainable electricity generation planning","volume":"269","year":"2018","journal-title":"Annals of Operations Research"},{"issue":"1","key":"key2020101517183356700_ref018","article-title":"Standard triangular whitenization weight function and its application in grey clustering evaluation","volume":"24","year":"2012","journal-title":"Journal of Grey System"},{"issue":"1","key":"key2020101517183356700_ref019","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/S0377-2217(99)00319-7","article-title":"On comparing interval numbers","volume":"127","year":"2000","journal-title":"European Journal of Operational Research"},{"volume-title":"Density Estimation for Statistics and Data Analysis","year":"2018","key":"key2020101517183356700_ref020"},{"issue":"3","key":"key2020101517183356700_ref021","article-title":"Study on construction of whitenization weight function with interval grey number and its solving algorithm","volume":"26","year":"2014","journal-title":"Journal of Grey System"},{"issue":"3","key":"key2020101517183356700_ref022","first-page":"00","article-title":"A hybrid method for the segmentation of a ferrograph image using marker-controlled watershed and grey clustering","volume":"59","year":"2016","journal-title":"Tribology Transactions"},{"issue":"12","key":"key2020101517183356700_ref023","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1057\/jors.1995.209","article-title":"What are PERT Estimates?","volume":"46","year":"1995","journal-title":"Journal of the Operational Research Society"},{"key":"key2020101517183356700_ref024","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.energy.2018.05.147","article-title":"Using a novel multi-variable grey model to forecast the electricity consumption of Shandong Province in China","volume":"157","year":"2018","journal-title":"Energy"},{"issue":"2","key":"key2020101517183356700_ref025","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1108\/GS-11-2012-0044","article-title":"On computational algorithms of grey numbers based on information background","volume":"3","year":"2013","journal-title":"Grey Systems: Theory and Application"},{"issue":"1","key":"key2020101517183356700_ref026","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.ins.2011.09.029","article-title":"Grey sets and greyness","volume":"185","year":"2012","journal-title":"Information Sciences"},{"key":"key2020101517183356700_ref027","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.knosys.2013.10.014","article-title":"Encoding words into Cloud models from interval-valued data via fuzzy statistics and membership function fitting","volume":"55","year":"2014","journal-title":"Knowledge-Based Systems"},{"issue":"9","key":"key2020101517183356700_ref028","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1109\/TCYB.2013.2288731","article-title":"Uncertainty representation of grey numbers and grey sets","volume":"44","year":"2014","journal-title":"IEEE Transactions On Cybernetics"},{"issue":"1","key":"key2020101517183356700_ref031","first-page":"89","article-title":"Calculation method's extension of grey degree based on the area approach","volume":"24","year":"2012","journal-title":"Journal of Grey System"},{"key":"key2020101517183356700_ref029","first-page":"31832","article-title":"Calculation method's extension of the characteristic of grey number","volume":"7","year":"2018","journal-title":"IEEE Access"},{"issue":"3","key":"key2020101517183356700_ref030","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","year":"1965","journal-title":"Information and Control"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-01-2020-0009\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-01-2020-0009\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:45:28Z","timestamp":1753404328000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/gs\/article\/10\/4\/495-512\/97783"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,20]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,5,20]]}},"alternative-id":["10.1108\/GS-01-2020-0009"],"URL":"https:\/\/doi.org\/10.1108\/gs-01-2020-0009","relation":{},"ISSN":["2043-9377"],"issn-type":[{"type":"print","value":"2043-9377"}],"subject":[],"published":{"date-parts":[[2020,5,20]]}}}