{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T18:10:00Z","timestamp":1754158200360,"version":"3.41.2"},"reference-count":42,"publisher":"Emerald","issue":"2","license":[{"start":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T00:00:00Z","timestamp":1618272000000},"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":[[2022,2,28]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a \u201cunique solution\u201d and to build the model with a trapezoidal possibility degree function.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>Using the system input and output block diagram of the model, the interval grey action quantity is restored under the condition of insufficient system influencing factors, and the trapezoidal possibility degree function is formed. Based on that, a new model able to output non-unique solutions is constructed.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>The model satisfies the non-unique solution principle of the grey theory under the condition of insufficient information. The model is compatible with the traditional model in structure and modelling results. The validity and practicability of the new model are verified by applying it in simulating the ecological environment water consumption in the Yangtze River basin.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Practical implications<\/jats:title><jats:p>In this study, the interval grey number form of grey action quantity is restored under the condition of insufficient system influencing factors, and the unique solution to the problem of the traditional model is solved. It is of great value in enriching the theoretical system of grey prediction models.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Social implications<\/jats:title><jats:p>Taking power consumption as an example, the accurate prediction of the future power consumption level is related to the utilization efficiency of the power infrastructure investment. If the prediction of the power consumption level is too low, it will lead to the insufficient construction of the power infrastructure and the frequent occurrence of \u201cpower shortage\u201d in the power industry. If the prediction is too high, it will lead to excessive investment in the power infrastructure. As a result, the overall surplus of power supply will lead to relatively low operation efficiency. Therefore, building an appropriate model for the correct interval prediction is a better way to solve such problems. The model proposed in this study is an effective one to solve such problems.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>A new grey prediction model with its interval grey action quantity based on the trapezoidal possibility degree function is proposed for the first time.<\/jats:p><\/jats:sec>","DOI":"10.1108\/gs-11-2020-0145","type":"journal-article","created":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T01:48:07Z","timestamp":1618192087000},"page":"339-356","source":"Crossref","is-referenced-by-count":3,"title":["Development of the GM(1,1,\u2297<sub><i>b<\/i><\/sub>) model with a trapezoidal possibility function and its application"],"prefix":"10.1108","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2948-9124","authenticated-orcid":false,"given":"Shuliang","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Gong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9421-8526","authenticated-orcid":false,"given":"Wenhao","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhouyi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aixing","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2021,4,13]]},"reference":[{"issue":"5","key":"key2022022406385302200_ref001","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","article-title":"The control problem of grey systems","volume":"1","year":"1982","journal-title":"Systems and Control Letters"},{"volume-title":"A Course in Grey Systems Theory","year":"1990","key":"key2022022406385302200_ref002"},{"key":"key2022022406385302200_ref003","unstructured":"Deng, J.L. 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