{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:41:22Z","timestamp":1777704082124,"version":"3.51.4"},"reference-count":33,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T00:00:00Z","timestamp":1532563200000},"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":[[2018,8,26]]},"abstract":"<jats:p>\n                    In this paper, we further study the theory of A-subsets in lattice implication algebras. To begin with, we introduce the propositions of homomorphism image and original image of A-subsets in lattice implication algebras. In addition, the notion of A*-subsets is introduced and some properties of A*-subsets are also investigated in lattice implication algebras. Finally, we introduce the notion of involutory LI-ideals with respect to an LI-ideal A and denote the set of all of them by\n                    <jats:italic>S<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                    <\/jats:sub>\n                    (\n                    <jats:italic>L<\/jats:italic>\n                    ). Then\n                    <jats:italic>S<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                    <\/jats:sub>\n                    (\n                    <jats:italic>L<\/jats:italic>\n                    ) can be made into a complete Boolean lattice and a lattice implication algebra with respect to the suit operations, respectively.\n                  <\/jats:p>","DOI":"10.3233\/jifs-172169","type":"journal-article","created":{"date-parts":[[2018,7,27]],"date-time":"2018-07-27T19:31:40Z","timestamp":1532719900000},"page":"2189-2198","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On A-subsets in lattice implication algebras"],"prefix":"10.1177","volume":"35","author":[{"given":"Xiqing","family":"Long","sequence":"first","affiliation":[{"name":"School of Mathematics, YiBin University, YiBin, P.R. China"}]},{"given":"Yi","family":"Liu","sequence":"additional","affiliation":[{"name":"Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, P.R. China"}]},{"given":"Yang","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Southwest Jiaotong University, Chengdu, P.R. 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