HOHF

AcronymDefinition
HOHFHelping Our Heroes Foundation
HOHFHigh-Output Heart Failure
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Actually, the HOHFS is a generalization of hesitant fuzzy set (HFS) introduced by Torra [10].
In view of Definition 4, it is easily deduced that each HOHFS becomes a T2FS if all its G-Type FSs are the same and are in the form ofT2FS.
A HOHFS [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] reduces to an IVHFS, when all G-Type [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for any x [member of] X are considered as closed intervals of real numbers in [0,1].
Obviously, a [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is also an special case of HOHFS where all G-Type FSs [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for any x [member of] X are considered as IFSs.
Having introduced HOHFEs of a HOHFS [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we now turn our attention to the interpretation of HOHFS [?
which is of fundamental importance in the study of HOHFS aggregation and the higher order hesitant fuzzy soft matrix that will be introduced within the next parts of the paper.
Note that if there is no confusion, HOHFS operator, HOHFE operator, and G-Type FS operator are denoted by the same symbol.
Thus, the HOHFS operator is performed as the well-known HFS operator [29, 30].
As a corollary of Theorem 7, it can be observed that HOHFS operators inherit subsequently all operational properties of G-Type FS operators.