{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T12:05:49Z","timestamp":1770033949417,"version":"3.49.0"},"reference-count":32,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,8,11]]},"abstract":"<jats:p>This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fr\u00e9chet and G\u00e2teaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fr\u00e9chet and G\u00e2teaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fr\u00e9chet and G\u00e2teaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fr\u00e9chet and G\u00e2teaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.<\/jats:p>","DOI":"10.3233\/jifs-210530","type":"journal-article","created":{"date-parts":[[2021,7,13]],"date-time":"2021-07-13T14:28:18Z","timestamp":1626186498000},"page":"1757-1775","source":"Crossref","is-referenced-by-count":0,"title":["On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability"],"prefix":"10.1177","volume":"41","author":[{"given":"M. Miri","family":"Karbasaki","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran"}]},{"given":"M. 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