{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T04:42:43Z","timestamp":1762058563663,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,17]],"date-time":"2022-07-17T00:00:00Z","timestamp":1658016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Hunan Province","award":["2021JJ40361"],"award-info":[{"award-number":["2021JJ40361"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In recent years, research on applications of three-way decision (e.g., TWD) has attracted the attention of many scholars. In this paper, we combine TWD with multi-attribute decision-making (MADM). First, we utilize the essential idea of TOPSIS in MADM theory to propose a pair of new ideal relation models based on TWD, namely, the three-way ideal superiority model and the three-way ideal inferiority model. Second, in order to reduce errors caused by the subjectivity of decision-makers, we develop two new methods to calculate the state sets for the two proposed ideal relation models. Third, we employ aggregate relative loss functions to calculate the thresholds of each object, divide all objects into three different territories and sort all objects. Then, we use a concrete example of building appearance selection to verify the rationality and feasibility of our proposed models. Furthermore, we apply comparative analysis, Spearman\u2019s rank correlation analysis and experiment analysis to illustrate the consistency and superiority of our methods.<\/jats:p>","DOI":"10.3390\/e24070986","type":"journal-article","created":{"date-parts":[[2022,7,17]],"date-time":"2022-07-17T21:00:28Z","timestamp":1658091628000},"page":"986","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Three-Way Decision Models Based on Ideal Relations in Multi-Attribute Decision-Making"],"prefix":"10.3390","volume":"24","author":[{"given":"Xiaozhi","family":"Chen","sequence":"first","affiliation":[{"name":"Hunan Provincial Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha 410081, China"},{"name":"College of Information Science and Engineering, Hunan Normal University, Changsha 410081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ligeng","family":"Zou","sequence":"additional","affiliation":[{"name":"Hunan Provincial Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha 410081, China"},{"name":"College of Information Science and Engineering, Hunan Normal University, Changsha 410081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yao, Y.Y. 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