{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T20:00:05Z","timestamp":1767211205593,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T00:00:00Z","timestamp":1646611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central University","award":["MS117"],"award-info":[{"award-number":["MS117"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Due to the complexity and uncertainty of objective things, interval-valued intuitionistic fuzzy (I-VIF) numbers are often used to describe the attribute values in multiple-attribute decision making (MADM). Sometimes, there are correlations between the attributes. In order to make the decision-making result more objective and reasonable, it is often necessary to take the correlation factors into account. Therefore, the study of MADM based on the correlations between attributes in the I-VIF environment has important theoretical and practical significance. Thus, in this paper, we propose new operators (AOs) for I-VIF information that are able to reflect the completeness of the information, attribute relevance, and the risk preference of decision makers (DMs). Firstly, we propose some new AOs for I-VIF information, including I-VIF generalized Heronian mean (I-VIFGHM), I-VIF generalized weighted Heronian mean (I-VIFGWHM), and I-VIF three-parameter generalized weighted Heronian mean (I-VIFTPGWHM). The properties of the obtained operators, including their idempotency, monotonicity, and boundedness are studied. Furthermore, an MADM method based on the I-VIFGWHM operator is provided. Finally, an example is provided to explain the rationality and feasibility of the proposed method.<\/jats:p>","DOI":"10.3390\/info13030138","type":"journal-article","created":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T10:21:16Z","timestamp":1646648476000},"page":"138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multiple-Attribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Generalized Weighted Heronian Mean"],"prefix":"10.3390","volume":"13","author":[{"given":"Ximei","family":"Hu","sequence":"first","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuxia","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya-Ru","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,7]]},"reference":[{"key":"ref_1","unstructured":"Xu, Z. 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