{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:31:22Z","timestamp":1760146282582,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T00:00:00Z","timestamp":1729468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Fujian Provincial Science and Technology Department","award":["2023H6034","2021H6037","2021C008R","2"],"award-info":[{"award-number":["2023H6034","2021H6037","2021C008R","2"]}]},{"name":"Key Project of Quanzhou Science and Technology Plan","award":["2023H6034","2021H6037","2021C008R","2"],"award-info":[{"award-number":["2023H6034","2021H6037","2021C008R","2"]}]},{"name":"Sixth batch of Quanzhou City\u2019s introduction of high-level talent team projects","award":["2023H6034","2021H6037","2021C008R","2"],"award-info":[{"award-number":["2023H6034","2021H6037","2021C008R","2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>For a given incomplete context, object-induced approximate concepts have been defined, and this type of approximate concept can induce a type of decision rule. Based on the duality principle, another set of approximate concepts can be defined from the perspective of attributes, i.e., attribute-induced approximate concepts. Although object induced approximate concepts and attribute induced approximate concepts are symmetrical by duality principle, their induced decision rules exhibit different properties and the connections between attribute induced decision rules and object induced decision rules in incomplete formal contexts are not clear. To this end, a type of attribute-induced approximate concept and a method of extracting attribute-induced decision rules are presented. More importantly, it is revealed that given a type of decision rules, there must be corresponding decision rules of the other type, and both of them can provide some useful information, but they are not equivalent to each other. In other words, each type of decision rule can provide some unique and irreplaceable information.<\/jats:p>","DOI":"10.3390\/sym16101403","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T08:53:11Z","timestamp":1729500791000},"page":"1403","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Connections Between Attribute-Induced and Object-Induced Decision Rules in Incomplete Formal Contexts"],"prefix":"10.3390","volume":"16","author":[{"given":"Hongwei","family":"Wang","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China"},{"name":"Fujian Provincial Key Laboratory of Data-Intensive Computing, Quanzhou 362000, China"},{"name":"Fujian University Laboratory of Intelligent Computing and Information Processing, Quanzhou 362000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huilai","family":"Zhi","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China"},{"name":"Fujian Provincial Key Laboratory of Data-Intensive Computing, Quanzhou 362000, China"},{"name":"Fujian University Laboratory of Intelligent Computing and Information Processing, Quanzhou 362000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinan","family":"Li","sequence":"additional","affiliation":[{"name":"Big Data Institute, Central South University, Changsha 410075, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daxin","family":"Zhu","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China"},{"name":"Fujian Provincial Key Laboratory of Data-Intensive Computing, Quanzhou 362000, China"},{"name":"Fujian University Laboratory of Intelligent Computing and Information Processing, Quanzhou 362000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9715-4502","authenticated-orcid":false,"given":"Jianbing","family":"Xiahou","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China"},{"name":"Fujian Provincial Key Laboratory of Data-Intensive Computing, Quanzhou 362000, China"},{"name":"Fujian University Laboratory of Intelligent Computing and Information Processing, Quanzhou 362000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,21]]},"reference":[{"key":"ref_1","first-page":"385","article-title":"On the treatment of incomplete knowledge in formal concept analysis","volume":"Volume 1867","author":"Ganter","year":"2000","journal-title":"Conceptual Structures: Logical, Linguistic, and Computational Issues"},{"key":"ref_2","first-page":"195","article-title":"A possibility-theoretic view of formal concept analysis","volume":"75","author":"Dubois","year":"2007","journal-title":"Fundam. 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