{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:51Z","timestamp":1740134571267,"version":"3.37.3"},"reference-count":44,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We use relational algebra to define a refinement fuzzy order called<jats:italic>demonic fuzzy refinement<\/jats:italic>and also the associated fuzzy operators which are fuzzy demonic join<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msub><mml:mrow><mml:mo>\u2294<\/mml:mo><\/mml:mrow><mml:mrow><mml:mtext mathvariant=\"normal\">f<\/mml:mtext><mml:mtext mathvariant=\"normal\">u<\/mml:mtext><mml:mtext mathvariant=\"normal\">z<\/mml:mtext><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, fuzzy demonic meet<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msub><mml:mrow><mml:mo>\u2293<\/mml:mo><\/mml:mrow><mml:mrow><mml:mtext mathvariant=\"normal\">f<\/mml:mtext><mml:mtext mathvariant=\"normal\">u<\/mml:mtext><mml:mtext mathvariant=\"normal\">z<\/mml:mtext><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, and fuzzy demonic composition<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msub><mml:mrow><mml:mo>\u25a1<\/mml:mo><\/mml:mrow><mml:mrow><mml:mtext mathvariant=\"normal\">f<\/mml:mtext><mml:mtext mathvariant=\"normal\">u<\/mml:mtext><mml:mtext mathvariant=\"normal\">z<\/mml:mtext><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>. 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