{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:35:19Z","timestamp":1777703719038,"version":"3.51.4"},"reference-count":16,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T00:00:00Z","timestamp":1571270400000},"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":[[2019,11,22]]},"abstract":"<jats:p>\n                    In this paper we define the notions of a norm and a prenorm on\n                    <jats:italic>BL<\/jats:italic>\n                    -algebras and we give some methods for constructing them. We introduce (pre)metrics on\n                    <jats:italic>BL<\/jats:italic>\n                    -algebras and find some connections between them and (pre)norms. Using prenorms, we find some conditions that a\n                    <jats:italic>BL<\/jats:italic>\n                    -algebra become a metric space. Finally, we show that if there exists a prenorm on a\n                    <jats:italic>BL<\/jats:italic>\n                    -algebra\n                    <jats:italic>A<\/jats:italic>\n                    , then for any filter\n                    <jats:italic>F<\/jats:italic>\n                    in\n                    <jats:italic>A<\/jats:italic>\n                    , there are topologies\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">U<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">V<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    on\n                    <jats:italic>A<\/jats:italic>\n                    and on\n                    <jats:italic>A<\/jats:italic>\n                    \/\n                    <jats:italic>F<\/jats:italic>\n                    respectively such that\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>A<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mi mathvariant=\"script\">U<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>A<\/mml:mi>\n                        <mml:mo>\/<\/mml:mo>\n                        <mml:mi>F<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mi mathvariant=\"script\">V<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    are (semi)topological\n                    <jats:italic>BL<\/jats:italic>\n                    -algebras.\n                  <\/jats:p>","DOI":"10.3233\/jifs-190988","type":"journal-article","created":{"date-parts":[[2019,10,18]],"date-time":"2019-10-18T11:01:00Z","timestamp":1571396460000},"page":"6959-6969","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Constructing (pre)norms in\n                    <i>BL<\/i>\n                    -algebras and its action on topological\n                    <i>BL<\/i>\n                    -algebras"],"prefix":"10.1177","volume":"37","author":[{"given":"R.A.","family":"Borzooei","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shahid Beheshti University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hee Sik","family":"Kim","sequence":"additional","affiliation":[{"name":"Research Institute for Natural Sciences, Dept. of Mathematics, Hanyang University, Seoul, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.","family":"Kouhestani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,10,17]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"crossref","unstructured":"ArhangelskiiA. and TkachenkoM. 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