{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T06:41:33Z","timestamp":1770273693680,"version":"3.49.0"},"reference-count":36,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T00:00:00Z","timestamp":1557619200000},"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":[[2019,6,11]]},"abstract":"<jats:p>\n                    In this paper, we introduce the degree to which a mapping\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"fraktur\">C<\/mml:mi>\n                        <mml:mo>:<\/mml:mo>\n                        <mml:msup>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:mi>X<\/mml:mi>\n                        <\/mml:msup>\n                        <mml:mo>\u27f6<\/mml:mo>\n                        <mml:mi>M<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    is an (\n                    <jats:italic>L<\/jats:italic>\n                    ,\n                    <jats:italic>M<\/jats:italic>\n                    )-fuzzy convexity. When\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>X<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:msub>\n                          <mml:mi mathvariant=\"fraktur\">C<\/mml:mi>\n                          <mml:mi>X<\/mml:mi>\n                        <\/mml:msub>\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>Y<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:msub>\n                          <mml:mi mathvariant=\"fraktur\">C<\/mml:mi>\n                          <mml:mi>Y<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    are (\n                    <jats:italic>L<\/jats:italic>\n                    ,\n                    <jats:italic>M<\/jats:italic>\n                    )-fuzzy convex spaces to some extent, the degrees to which a mapping\n                    <jats:italic>f<\/jats:italic>\n                    :\n                    <jats:italic>X<\/jats:italic>\n                    \u27f6\n                    <jats:italic>Y<\/jats:italic>\n                    is convexity-preserving or convex-to-convex are defined. Finally, the degree to which a surjective mapping\n                    <jats:italic>f<\/jats:italic>\n                    :\n                    <jats:italic>X<\/jats:italic>\n                    \u27f6\n                    <jats:italic>Y<\/jats:italic>\n                    is a quotient mapping is also defined. We not only give their characterizations but also discuss the relationships among them.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18659","type":"journal-article","created":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T11:46:34Z","timestamp":1558093594000},"page":"6619-6629","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Degrees of (\n                    <i>L<\/i>\n                    ,\n                    <i>M<\/i>\n                    )-fuzzy convexities"],"prefix":"10.1177","volume":"36","author":[{"given":"Yu","family":"Zhong","sequence":"first","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, P.R. China"}]},{"given":"Fu-Gui","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China"}]},{"given":"Jie-Tao","family":"Zou","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, P.R. China"}]},{"given":"Chu-Yi","family":"Zou","sequence":"additional","affiliation":[{"name":"The Second Middle School of Fengcheng, Jiangxi Province, P.R. 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