{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:36:20Z","timestamp":1777703780765,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,7,6]],"date-time":"2018-07-06T00:00:00Z","timestamp":1530835200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,7,27]]},"abstract":"<jats:p>The present work aims at investigating maximal filter and its topological properties in lattice implication algebras (LIAs). To begin with, the maximal filters of LIAs are investigated and some equivalent characterizations of maximal filters are also given. In addition, the radical of filters in a LIA is introduced and its properties are also obtained, the structure of radical of maximal filter is investigated. Finally, by introducing some topological structures on the set of all maximal filters and by investigating the topological properties of them, we conclude that the set of all maximal filters is a compact topological space and the set of all maximal filters is also a Hausdorff topological space.<\/jats:p>","DOI":"10.3233\/jifs-171025","type":"journal-article","created":{"date-parts":[[2018,7,6]],"date-time":"2018-07-06T12:09:09Z","timestamp":1530878949000},"page":"673-681","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Maximal filter and its topology in lattice implication algebras"],"prefix":"10.1177","volume":"35","author":[{"given":"Ya","family":"Qin","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan province, P.R. China"}]},{"given":"Yi","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan province, P.R. China"},{"name":"Data Recovery Key Lab of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2018,7,6]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"CignoliR. D\u0105\u0155Ottano and I.M.L. MundiciD. Algebras of Lukasiewicz Logics second ed. Editions CLE State University of Campinas Campinas S.P. Brazil 1995."},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542725"},{"issue":"2","key":"e_1_3_2_4_2","first-page":"193","article-title":"Implicative filters of lattice implication algebras","volume":"34","author":"Jun Y.B.","year":"1997","unstructured":"JunY.B., Implicative filters of lattice implication algebras, Bull Korean Math Soc 34(2) (1997), 193\u2013198.","journal-title":"Bull Korean Math Soc"},{"issue":"1","key":"e_1_3_2_5_2","first-page":"53","article-title":"Positive implicative and associative filters of lattice implication algebras","volume":"35","author":"Jun Y.B.","year":"1998","unstructured":"JunY.B., XuY. and QinK.Y., Positive implicative and associative filters of lattice implication algebras, Bull Korean Math Soc 35(1) (1998), 53\u201361.","journal-title":"Bull Korean Math Soc"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171200003926"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00030-0"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.08.018"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2009.05.011"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2113-2"},{"issue":"2","key":"e_1_3_2_11_2","first-page":"201","article-title":"On ultra filters of lattice implication algebras","volume":"2","author":"Kim S.Y.","year":"1999","unstructured":"KimS.Y., RohE.H. and JunY.B., On ultra filters of lattice implication algebras, Scientiae Mathematicae 2(2) (1999), 201\u2013204.","journal-title":"Scientiae Mathematicae"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02882921"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130879"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151637"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1998.0631"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(00)00069-8"},{"key":"e_1_3_2_17_2","first-page":"45","article-title":"Some operations on lattice implication algebras","volume":"1","author":"Rom E.H.","year":"2001","unstructured":"RomE.H., KimS.Y., XuY. , Some operations on lattice implication algebras, Int J Math Math Sci 1 (2001), 45\u201352.","journal-title":"Int J Math Math Sci"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1966-0190893-2"},{"issue":"5","key":"e_1_3_2_19_2","first-page":"919","article-title":"Compact Hausdorff topology on the set of Lukasiewicz antics","volume":"45","author":"Wang G.J.","year":"2002","unstructured":"WangG.J., Compact Hausdorff topology on the set of Lukasiewicz antics, Acta Math Sinica 45(5) (2002), 919\u2013924.","journal-title":"Acta Math Sinica"},{"key":"e_1_3_2_20_2","first-page":"20","article-title":"Lattice implication algebras","volume":"1","author":"Xu Y.","year":"1993","unstructured":"XuY., Lattice implication algebras, J Southwest Jiaotong Univ 1 (1993), 20\u201327.","journal-title":"J Southwest Jiaotong Univ"},{"key":"e_1_3_2_21_2","first-page":"251","article-title":"On filters of lattice implication algebras","volume":"2","author":"Xu Y.","year":"1993","unstructured":"XuY. and QinK.Y., On filters of lattice implication algebras, J Fuzzy Math 2 (1993), 251\u2013260.","journal-title":"J Fuzzy Math"},{"key":"e_1_3_2_22_2","volume-title":"Lattice-Valued Logic-An Alternative Approach to Treat Fuzziness and Incomparability","author":"Xu Y.","year":"2003","unstructured":"XuY., RuanD., QinK., LiuJ., Lattice-Valued Logic-An Alternative Approach to Treat Fuzziness and Incomparability, Springer, New York, 2003."},{"issue":"2","key":"e_1_3_2_23_2","first-page":"251","article-title":"On filters of lattice implication algebras","volume":"1","author":"Xu Y.","year":"1993","unstructured":"XuY. and QinK.Y., On filters of lattice implication algebras, J Fuzzy Math 1(2) (1993), 251\u2013260.","journal-title":"J Fuzzy Math"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151842"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.11.014"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200810005"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.03.002"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151826"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.05.004"},{"issue":"4","key":"e_1_3_2_30_2","first-page":"8","article-title":"Characterization of maximal consistent theories over L and compactness theorem","volume":"22","author":"Zhou H.J.","year":"2008","unstructured":"ZhouH.J. and WangG.J., Characterization of maximal consistent theories over L and compactness theorem, Fuzzy Systems and Math 22(4) (2008), 8\u201314.","journal-title":"Fuzzy Systems and Math"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171025","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-171025","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:35Z","timestamp":1777455575000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-171025"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,6]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,7,27]]}},"alternative-id":["10.3233\/JIFS-171025"],"URL":"https:\/\/doi.org\/10.3233\/jifs-171025","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,6]]}}}