{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:26:14Z","timestamp":1773815174461,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T00:00:00Z","timestamp":1773619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Program on Key Basic Research Project","award":["2020-JCJQ-ZD-089-11"],"award-info":[{"award-number":["2020-JCJQ-ZD-089-11"]}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["JCZRYB202501320"],"award-info":[{"award-number":["JCZRYB202501320"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]},{"name":"PhD. Foundation of Guangdong University of Science and Technology","award":["KY-2022BSQD-35"],"award-info":[{"award-number":["KY-2022BSQD-35"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>To address the grey target group decision-making method (GDMM) concerning the aggregation of decision-maker information and the approach to ranking alternatives via bidirectional projection (BP), this paper develops a novel methodological framework that optimizes both information integration and alternative evaluation, where a new transformation mechanism between the three-parameter interval grey number (TPIGN) and dual connection number (CN) is established by integrating an induced TPIGN weighted average (ITPIGN-WA) operator with an improved bidirectional projection method (IBPM). The results confirm that the new framework leads to more reliable and effective group decision making (GDM). The new TPIGN conversion mechanism and the set pair potential (SPP)-based ITPIGN-WA better captures decision-maker preferences than previous operators, and the introduction of the IBPM further refines alternative ranking. This dual innovation enriches the theoretical system of grey target decision making and provides significant applied value for enhancing the quality and effectiveness of GDM processes in uncertain environments.<\/jats:p>","DOI":"10.3390\/a19030225","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T15:21:16Z","timestamp":1773674476000},"page":"225","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Grey Target Group Decision Making Based on Three-Parameter Interval Grey Numbers and Bidirectional Projection Method"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9469-1655","authenticated-orcid":false,"given":"Huabin","family":"Cheng","sequence":"first","affiliation":[{"name":"Department of Basic Science, Wuchang Shouyi University, Wuhan 430064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingchun","family":"Chen","sequence":"additional","affiliation":[{"name":"Science & Technology on Underwater Antagonizing Laboratory, Zhanjiang 524022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8118-7262","authenticated-orcid":false,"given":"Yu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Xiong","sequence":"additional","affiliation":[{"name":"College of General Education, Guangdong University of Science and Technology, Dongguan 523083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1108\/GS-11-2024-0133","article-title":"Evaluating underlying barriers and development pathways for photovoltaic solar energy in China using the grey analytic hierarchy process","volume":"15","author":"Kamdar","year":"2025","journal-title":"Grey Syst. Theory Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1108\/GS-12-2024-0147","article-title":"Evaluation of barriers to artificial intelligence adoption: Grey multi-criteria decision-making","volume":"15","author":"Nawaz","year":"2025","journal-title":"Grey Syst. Theory Appl."},{"key":"ref_3","unstructured":"Liu, S.F., and Lin, Y. (2010). Grey Systems Theory and Applications, Springer."},{"key":"ref_4","first-page":"1822","article-title":"New decision model of grey target with both the positive clout and the negative clout","volume":"30","author":"Song","year":"2010","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_5","first-page":"776","article-title":"Study on the expansion of bidirectional projection grey target decision-making model based on general grey number","volume":"39","author":"Liu","year":"2019","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1108\/GS-04-2025-0049","article-title":"A seasonal grey model with three parameter-interval grey numbers for forecasting natural gas production","volume":"16","author":"Huang","year":"2026","journal-title":"Grey Syst. Theory Appl."},{"key":"ref_7","first-page":"43","article-title":"Grey fuzzy comprehensive evaluation method based on interval numbers of three parameters","volume":"23","author":"Bu","year":"2001","journal-title":"Syst. Eng. Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/S1874-8651(10)60033-6","article-title":"Decision-making methods with three-parameter interval grey number","volume":"29","author":"Luo","year":"2009","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_9","first-page":"105","article-title":"A group grey target decision making method with three parameter interval grey number based on prospect theory","volume":"30","author":"Yan","year":"2015","journal-title":"Control Decis."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1007\/s40815-016-0241-6","article-title":"A new multi-attribute decision making method with three-parameter interval grey linguistic variable","volume":"2","author":"Li","year":"2017","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_11","unstructured":"Wang, X. (2017). Gray Multi-Attribute Decision Analysis and Application, Economic Management Press."},{"key":"ref_12","first-page":"96","article-title":"Multi-attribute Group Grey Target Decision-making Method Based on Three-parameter Interval Grey Number","volume":"32","author":"Ye","year":"2020","journal-title":"J. Grey Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1108\/GS-07-2020-0092","article-title":"On distance measure and TOPSIS model for probabilistic interval-valued hesitant fuzzy sets: Application to healthcare facilities in public hospitals","volume":"12","author":"Ali","year":"2022","journal-title":"Grey Syst. Theory Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1109\/21.87068","article-title":"On ordered weighted averaging Aggregation operators in multi-criteria decision making","volume":"18","author":"Yager","year":"1988","journal-title":"IEEE Trans. Syst. Man Cybern. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1016\/j.cie.2011.12.025","article-title":"Generalized power aggregation operators and their applications in group decision making","volume":"62","author":"Zhou","year":"2012","journal-title":"Comput. Ind. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/3477.752789","article-title":"Induced ordered weighted averaging operators","volume":"29","author":"Yager","year":"1999","journal-title":"IEEE Trans. Syst. Man Cybern. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1016\/j.fss.2005.12.001","article-title":"The continuous ordered weighted geometric operator and its applications to decision making","volume":"157","author":"Yager","year":"2006","journal-title":"Fuzzy Sets Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1002\/int.20097","article-title":"An overview of methods for determining OWA weights","volume":"20","author":"Xu","year":"2005","journal-title":"Int. J. Intell. Syst."},{"key":"ref_19","first-page":"1468","article-title":"Information aggregation operators over a continuous three parameters interval argument and their application to decision making","volume":"30","author":"Wang","year":"2008","journal-title":"Syst. Eng. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"e70014","DOI":"10.1111\/1752-1688.70014","article-title":"Evaluation and Diagnosis of Water Resources Spatial Equilibrium Under the High-Quality Development of Water Conservancy","volume":"61","author":"Dong","year":"2025","journal-title":"JAWRA J. Am. Water Resour. Assoc."},{"key":"ref_21","first-page":"121","article-title":"Application of set pair analysis in the uncertainty intelligent decision making","volume":"15","author":"Liu","year":"2020","journal-title":"CAAI Trans. Intell. Syst."},{"key":"ref_22","first-page":"2052","article-title":"Probabilistic linguistic multi-attribute group decision-making based on bidirectional projection method","volume":"42","author":"Hu","year":"2020","journal-title":"Syst. Eng. Electron."},{"key":"ref_23","first-page":"59","article-title":"Consistency bidirectional projection decision method within interval hesitation fuzzy information","volume":"35","author":"Wang","year":"2019","journal-title":"Stat. Decis."},{"key":"ref_24","first-page":"179","article-title":"Induced continuous ordered weighted averaging operators and their applications in interval group decision making","volume":"25","author":"Zhou","year":"2010","journal-title":"Control Decis."},{"key":"ref_25","first-page":"88","article-title":"Interval-valued Pythagorean Fuzzy Decision-making Based on the Entropy and Bidirectional Projection","volume":"22","author":"Ding","year":"2025","journal-title":"Complex Syst. Complex. Sci."},{"key":"ref_26","first-page":"1562","article-title":"Modified Bidirectional Projection Technique for Spherical Fuzzy MAGDM and Applications to Demand Evaluation for Public Sports Services for the Elderly in Rural Areas","volume":"8","author":"Wang","year":"2025","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_27","first-page":"716","article-title":"Summary and Prospect of Comprehensive Evaluation Methods of Power Quality","volume":"45","author":"Xiao","year":"2024","journal-title":"Power Gener. Technol."},{"key":"ref_28","first-page":"1751","article-title":"Comprehensive Evaluation of Power Quality on Long-time Scale Based on Fuzzy DEA","volume":"47","author":"Lin","year":"2021","journal-title":"High Volt. Eng."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/3\/225\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T05:33:42Z","timestamp":1773812022000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/3\/225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,16]]},"references-count":28,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["a19030225"],"URL":"https:\/\/doi.org\/10.3390\/a19030225","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,16]]}}}