{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:38:20Z","timestamp":1777703900267,"version":"3.51.4"},"reference-count":24,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2017,3,27]],"date-time":"2017-03-27T00:00:00Z","timestamp":1490572800000},"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":[[2017,7]]},"abstract":"<jats:p>\n                    We introduce an MV-topology on the set of all valuations of MV-algebra and then establish Lukasiewicz semantic MV-topological space. We study the topological properties of Lukasiewicz semantic MV-topology, and prove that the Lukasiewicz semantic MV-topological space is a compact zero dimension Hausdorff MV-topological space and a N-compact space. We also establish a classical topology\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                      <mml:mi mathvariant=\"script\">D<\/mml:mi>\n                    <\/mml:math>\n                    on the valuations set of MV-algebra, and prove that topology\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                      <mml:mi mathvariant=\"script\">D<\/mml:mi>\n                    <\/mml:math>\n                    is finer than the cut topology\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                      <mml:mi mathvariant=\"script\">C<\/mml:mi>\n                    <\/mml:math>\n                    generated by Lukasiewicz semantic MV-topology. We prove that a\n                    <jats:italic>\u03c3<\/jats:italic>\n                    -complete lattice is an MV-algebra if and only if it is isomorphic to an MV-clopen lattice of a Stone MV-space. As an application, we use the compactness of topology\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                      <mml:mi mathvariant=\"script\">D<\/mml:mi>\n                    <\/mml:math>\n                    to prove the compactness of Lukasiewicz semantic and Lukasiewicz propositional logic system.\n                  <\/jats:p>","DOI":"10.3233\/jifs-161714","type":"journal-article","created":{"date-parts":[[2017,3,28]],"date-time":"2017-03-28T11:44:16Z","timestamp":1490701456000},"page":"377-387","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Lukasiewicz semantic MV-topology for\u00a0MV-algebra and its application to\u00a0Lukasiewicz propositional logic"],"prefix":"10.1177","volume":"33","author":[{"given":"Li","family":"Zhou","sequence":"first","affiliation":[{"name":"College of Science, Hunan Agricultural University, Changsha, 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