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Open Access Article
1 - Survey of partial and directional derivatives of fuzzy multi-dimensional mappings under generalized differentiability
Mohsen Miri Karbasaki Mohammadreza Balooch Shahryari Omolbanin SedaghatfarFuzzy optimization issues have been discussed by many authors in recent articles, inspired by the concepts of generalized Hukuhara difference and generalized Hukuhara differentiability for one-dimensional functions from R to E, and have made considerable progress. In th MoreFuzzy optimization issues have been discussed by many authors in recent articles, inspired by the concepts of generalized Hukuhara difference and generalized Hukuhara differentiability for one-dimensional functions from R to E, and have made considerable progress. In this paper, the concept of total generalized differentiability is introduced by using the concept of generalized difference from R^n to E for multi-dimensional mappings. Furthermore, the total generalized differentiability of the above is also examined and then the concept of directional generalized differentiability and partial generalized differentiability for fuzzy multi-dimensional mappings is defined and discussed in detail. In addition, directional generalized differentiability and partial generalized differentiability are expressed in terms of level-wise generalized differentiability. Also, the properties and the relationship between them are discussed. Finally, the relationships between total generalized differentiability, directional generalized differentiability and partial generalized differentiability are shown to illustrate the power and ability of relationships between them by mentioning some examples. Manuscript profile
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