Various types of double fuzzy continuity of fuzzy multifunctions are introduced in this paper. These types are double fuzzy upper and lower $ \alpha $-$ \eth $-continuous, almost $ \alpha $-$ \eth $-continuous, weakly $ \alpha $-$ \eth $-continuous and almost weakly $ \alpha $-$ \eth $-continuous multifunctions. Double fuzzy ideals are playing the main role in defining these types of continuous multifunctions. All implications associated with these types are ensured; also, many examples are introduced to illustrate these implications, and to explain the advantages of these new types of continuity for some previous definitions.
Citation: M. N. Abu_Shugair, A. A. Abdallah, S. E. Abbas, Ismail Ibedou. Double fuzzy $ \alpha $-$ \eth $-continuous multifunctions[J]. AIMS Mathematics, 2024, 9(6): 16623-16642. doi: 10.3934/math.2024806
Various types of double fuzzy continuity of fuzzy multifunctions are introduced in this paper. These types are double fuzzy upper and lower $ \alpha $-$ \eth $-continuous, almost $ \alpha $-$ \eth $-continuous, weakly $ \alpha $-$ \eth $-continuous and almost weakly $ \alpha $-$ \eth $-continuous multifunctions. Double fuzzy ideals are playing the main role in defining these types of continuous multifunctions. All implications associated with these types are ensured; also, many examples are introduced to illustrate these implications, and to explain the advantages of these new types of continuity for some previous definitions.
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M. N. Abu_Shugair, A. A. Abdallah, S. E. Abbas, Ismail Ibedou. Double fuzzy $ \alpha $-$ \eth $-continuous multifunctions[J]. AIMS Mathematics, 2024, 9(6): 16623-16642. doi: 10.3934/math.2024806
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