Abstract—When Atanssov created Intuitionistic Fuzzy Sets, he
imposed the condition that the sum of membership and non-membership
values for each point in the universe of discourse
should be less than or equal to one. We challenge this constraint
and define some new types of Intuitionistic Fuzzy Sets such that,
for any point in the universe of discourse, the sum of membership
and non-membership values can be greater than one, or their
difference can be negative or positive, while one value is greater
than the other, or the sum of their squares is less than or equal
to one.