{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:08Z","timestamp":1760147528504,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T00:00:00Z","timestamp":1675987200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NSFC)","award":["12171193","2021GGJS158","23B110012"],"award-info":[{"award-number":["12171193","2021GGJS158","23B110012"]}]},{"name":"the Fund of Young Backbone Teacher in Henan Province","award":["12171193","2021GGJS158","23B110012"],"award-info":[{"award-number":["12171193","2021GGJS158","23B110012"]}]},{"name":"Key project of Henan Education Department","award":["12171193","2021GGJS158","23B110012"],"award-info":[{"award-number":["12171193","2021GGJS158","23B110012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>P-sets (P stands for Packet), a set pair with dynamic and law characteristics, are made up of an internal and an outer P-set, which is obtained by introducing dynamic characteristics into the Cantor set and improving the Cantor set. The concepts of \u03b1F-sub-information, \u03b1F\u00af-sub-information, and (\u03b1F,\u03b1F\u00af)-sub-information are presented in this paper based on P-sets, and it is then suggested that the relationship between the generation of sub-information and its attribute, the process of attribute reasoning, reasoning structure, and sub-information intelligent separation-acquisition be explored. These findings were used to design a sub-information intelligent separation-identification algorithm. By using these results, the application of intelligent separation and the identification of case information are given.<\/jats:p>","DOI":"10.3390\/sym15020477","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T04:07:19Z","timestamp":1676261239000},"page":"477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Intelligent Separation and Identification of Sub-Information Based on Dynamic Mathematical Model"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiuquan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1109\/TITS.2020.3040909","article-title":"Diversified Personalized Recommendation Optimization Based on Mobile Data","volume":"22","author":"Cao","year":"2021","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/MNET.011.2000154","article-title":"Analysis of Using Blockchain to Protect the Privacy of Drone Big Data","volume":"35","author":"Lv","year":"2021","journal-title":"IEEE Netw."},{"key":"ref_3","first-page":"3500713","article-title":"Pig Face Recognition Based on Trapezoid Normalized Pixel Difference Feature and Trimmed Mean Attention Mechanism","volume":"72","author":"Xu","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_4","first-page":"209","article-title":"P-sets and its applications","volume":"9","author":"Shi","year":"2009","journal-title":"J. Adv. Syst. Sci. Appl."},{"key":"ref_5","first-page":"1","article-title":"Separated fuzzy set (A\u02dcF\u00af,A\u02dcF) and the intelligent fusion of fuzzy information","volume":"57","author":"Shi","year":"2022","journal-title":"J. Shandong Univ. Nat. Sci."},{"key":"ref_6","first-page":"1","article-title":"An algebraic model of P-sets","volume":"36","author":"Li","year":"2020","journal-title":"J. Shangqiu Norm. Univ."},{"key":"ref_7","first-page":"53","article-title":"Function p(\u03c3,\u03c4)-Set and Its Characteristics","volume":"56","author":"Yu","year":"2018","journal-title":"J. Jilin Univ. Nat. Sci."},{"key":"ref_8","first-page":"1","article-title":"Big data structure-logic characteristics and big data law","volume":"54","author":"Shi","year":"2019","journal-title":"J. Shandong Univ. Nat. Sci."},{"key":"ref_9","first-page":"113","article-title":"Big date intelligent retrieval and big date block element intelligence separation","volume":"47","author":"Hao","year":"2020","journal-title":"J. Comput. Sci."},{"key":"ref_10","first-page":"124","article-title":"P-intuitionistic fuzzy sets and its applications","volume":"36","author":"Hao","year":"2022","journal-title":"J. Fuzzy Syst. Math."},{"key":"ref_11","first-page":"337","article-title":"P-sets and the reasoning-identification of disaster information","volume":"7","author":"Fan","year":"2012","journal-title":"Int. J. Converg. Inf. Technol."},{"key":"ref_12","first-page":"121","article-title":"The dual form of P-reasoning and identification of unknown attribute","volume":"6","author":"Lin","year":"2012","journal-title":"Int. J. Digit. Content Technol. Its Appl."},{"key":"ref_13","first-page":"53","article-title":"P-augmented matrix and its application in dynamic tracking recognition","volume":"46","author":"Zhang","year":"2022","journal-title":"J. Anhui Univ. Nat. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1007\/s00542-018-3867-5","article-title":"Outer P-information law reasoning and its application in intelligent fusion and separating of information law","volume":"24","author":"Tang","year":"2018","journal-title":"J. Microsyst. Technol."},{"key":"ref_15","first-page":"364","article-title":"Dynamic Boundary Characteristics of P-sets and Information Dynamic Fusion Generation","volume":"35","author":"Zhang","year":"2022","journal-title":"J. Xinyang Norm. Univ."},{"key":"ref_16","first-page":"9","article-title":"Quantitative characteristics and applications of P-information hidden mining","volume":"54","author":"Hao","year":"2019","journal-title":"J. Shandong Univ. Nat. Sci."},{"key":"ref_17","first-page":"202","article-title":"Information P-dependence and P-dependence mining-sieving","volume":"45","author":"Liu","year":"2018","journal-title":"J. Comput. Sci."},{"key":"ref_18","first-page":"98","article-title":"Inverse P-sets","volume":"47","author":"Shi","year":"2012","journal-title":"J. Shandong Univ. Nat. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, X.Q., Shen, L., and Shi, K.Q. (2022). (\u03b1F,\u03b1F\u00af)-information fusion generated by information segmentation and its intelligent retrieval. J. Math., 10.","DOI":"10.3390\/math10050713"},{"key":"ref_20","first-page":"735","article-title":"Inverse P-reasoning discovery identification of Inverse P-information","volume":"6","author":"Fan","year":"2012","journal-title":"J. Intercont Digit. Content Technol. Its Appl."},{"key":"ref_21","first-page":"471","article-title":"Embedding camouflage of inverse P-information and application","volume":"7","author":"Lin","year":"2012","journal-title":"Int. J. Converg. Inf. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2478\/amns.2020.2.00042","article-title":"Random inverse packet information and its acquisition","volume":"5","author":"Yu","year":"2020","journal-title":"J. Appl. Math. Nonlinear Sci."},{"key":"ref_23","first-page":"1","article-title":"Inverse separated fuzzy set (A\u02dc\u00afF,A\u02dc\u00afF\u00af) on of fuzzy information and secure acquisition","volume":"57","author":"Li","year":"2022","journal-title":"J. Shandong Univ. Nat. Sci."},{"key":"ref_24","first-page":"15","article-title":"The relationship between abnormal information system and inverse P-augmented matrices","volume":"54","author":"Zhang","year":"2019","journal-title":"J. Shandong Univ. Nat. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s13042-011-0032-1","article-title":"Function P-Sets","volume":"2","author":"Shi","year":"2011","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_26","first-page":"167","article-title":"Attribute Relations of Data Compound-decomposition and Data Intelligent Acquisition","volume":"35","author":"Chen","year":"2021","journal-title":"J. Fuzzy Syst. Math."},{"key":"ref_27","first-page":"73","article-title":"Function inverse P-sets and information law fusion","volume":"47","author":"Shi","year":"2012","journal-title":"J. Shandong Univ. Nat. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4415","DOI":"10.1007\/s00542-018-3894-2","article-title":"Inverse p-matrix reasoning model-based the intelligent dynamic separation and acquisition of educational information","volume":"24","author":"Zhang","year":"2018","journal-title":"Microsyst. Technol."},{"key":"ref_29","first-page":"104","article-title":"Function inverse P-sets and the dynamic separation of inverse P-information laws","volume":"48","author":"Tang","year":"2013","journal-title":"J. Shandong Univ. Nat. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/477\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:30:32Z","timestamp":1760121032000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,10]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020477"],"URL":"https:\/\/doi.org\/10.3390\/sym15020477","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,2,10]]}}}