{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:26:00Z","timestamp":1777703160542,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2017,12,1]],"date-time":"2017-12-01T00:00:00Z","timestamp":1512086400000},"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 & Fuzzy Systems"],"published-print":{"date-parts":[[2017,12]]},"abstract":"\n The concept of A-subset is introduced in lattice implication algebras. Firstly, the properties of the A-subset are discussed when A is a general set of lattice implication algebras. Next, the properties of A-subset are investigated when the A is an LI-ideal of lattice implication algebras. We obtain some properties of A-subset and prove that B(A)(the A-subset of B) is an LI-ideal in lattice implication algebras. Finally, the properties of A-subset are investigated in lattice implication product algebras. We prove that the A-subset of\n \n \n \n \u220f<\/mml:mo>\n \n i<\/mml:mi>\n =<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n n<\/mml:mi>\n <\/mml:msubsup>\n \n \n B<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n is the product of A-subset of\n B<\/jats:italic>\n \n i<\/jats:italic>\n <\/jats:sub>\n \u00a0(\n i<\/jats:italic>\n \u00a0=\u00a01, \u20022, \u22ef\u00a0, \u2002\n n<\/jats:italic>\n ) respectively\n \n \n \n (<\/mml:mo>\n \n \n (<\/mml:mo>\n \n \n \u220f<\/mml:mo>\n \n i<\/mml:mi>\n =<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n n<\/mml:mi>\n <\/mml:msubsup>\n \n \n B<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n \n (<\/mml:mo>\n \n \n \u220f<\/mml:mo>\n \n i<\/mml:mi>\n =<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n n<\/mml:mi>\n <\/mml:msubsup>\n \n \n A<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:mrow>\n \n \n =<\/mml:mo>\n \n (<\/mml:mo>\n \n \n \u220f<\/mml:mo>\n \n i<\/mml:mi>\n =<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n n<\/mml:mi>\n <\/mml:msubsup>\n \n \n B<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n \n \n \n A<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n .\n <\/jats:p>","DOI":"10.3233\/jifs-17779","type":"journal-article","created":{"date-parts":[[2017,12,1]],"date-time":"2017-12-01T12:40:21Z","timestamp":1512132021000},"page":"3939-3947","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Study on the properties of A-subset"],"prefix":"10.1177","volume":"33","author":[{"given":"Xiqing","family":"Long","sequence":"first","affiliation":[{"name":"School of Math, YiBin University, YiBin, P.R. 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