{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:43:55Z","timestamp":1777394635438,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T00:00:00Z","timestamp":1769385600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42405175"],"award-info":[{"award-number":["42405175"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Jiangsu Higher Education Institutions of China","award":["24KJB170008"],"award-info":[{"award-number":["24KJB170008"]}]},{"name":"Changzhou Basic Research Program","award":["CJ20240030"],"award-info":[{"award-number":["CJ20240030"]}]},{"name":"Changzhou Longcheng Talent Program-Young Scientific and Technological Talent Fostering Project","award":["CZTJ-2025-15"],"award-info":[{"award-number":["CZTJ-2025-15"]}]},{"name":"Young Scientific and Technological Talent Fostering Project of Jiangsu Province","award":["JSTJ-2025-783"],"award-info":[{"award-number":["JSTJ-2025-783"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a novel method, the Convergent Radiation Algorithm (CRA), aimed at multi-attribute group decision-making (MAGDM) in circular intuitionistic fuzzy settings. The approach is aimed at reaching geometric consensus among experts, with uncertainties and hesitancies expressed via circular intuitionistic fuzzy numbers (CIFNs). First, the qualitative judgment in professionals is converted into a geometric space where experts\u2019 assessments are represented as spatial points that reflect the differences between the opinions. All these points are gradually combined with the help of a radiation\u2013reflection\u2013convergence mechanism, which iteratively finds the Optimal Consensus Point (OCP) to minimize the overall weighted divergence over the evaluations. After that, a projection-based scoring method is used to locate good and bad optimal solutions, and the alternatives are ranked based on a comparison of their projection distance. It presents a numerical example with data supplied by the Hubei agro-ecological zone to demonstrate that the offered method helps to capture collective agreement and convergence behavior that is consistent, and makes the decision results readable and reliable.<\/jats:p>","DOI":"10.3390\/axioms15020089","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T09:21:40Z","timestamp":1769505700000},"page":"89","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergent Radiation Algorithm for Multi-Attribute Group Decision-Making with Circular Intuitionistic Fuzzy Numbers"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiqi","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junda","family":"Qiu","sequence":"additional","affiliation":[{"name":"School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China"},{"name":"School of Electrical Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1856-5988","authenticated-orcid":false,"given":"Jiali","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taiji","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongjie","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Computer Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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