{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:14:48Z","timestamp":1760242488346,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T00:00:00Z","timestamp":1504224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundations of China","award":["11671001","61472056"],"award-info":[{"award-number":["11671001","61472056"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, based on a partial order, we study the characterizations of directional derivatives and the subdifferential of fuzzy function. 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