  In this paper we prove that Neutrosophic Set (NS) is an extension of
Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued
neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of
components is 1 (as in IFS), after applying the neutrosophic aggregation
operators one gets a different result from that of applying the intuitionistic
fuzzy operators, since the intuitionistic fuzzy operators ignore the
indeterminacy, while the neutrosophic aggregation operators take into
consideration the indeterminacy at the same level as truth-membership and
falsehood-nonmembership are taken. NS is also more flexible and effective
because it handles, besides independent components, also partially independent
and partially dependent components, while IFS cannot deal with these. Since
there are many types of indeterminacies in our world, we can construct
different approaches to various neutrosophic concepts. Also, Regret Theory,
Grey System Theory, and Three-Ways Decision are particular cases of
Neutrosophication and of Neutrosophic Probability. We extended for the first
time the Three-Ways Decision to n-Ways Decision, and the Spherical Fuzzy Set to
n-HyperSpherical Fuzzy Set and to n-HyperSpherical Neutrosophic Set.
