Abstract
To investigate implicative filters of hoops furthermore, we apply n-fold theory to (α, β)-hesitant fuzzy implicative filters and introduce the notion of n-fold (α,β)-hesitant fuzzy implicative filters, and obtain some conditions for a (α,β)-hesitant fuzzy filter to be a n-fold (α,β)-hesitant fuzzy implicative filter. We also study the preimage and image of n-fold (α, β)-hesitant fuzzy implicative filters.
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