Intuitionistic Fuzzy Set and Type II Fuzzy Set - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 1

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Intuitionisti c Fuzzy Set and Type II Fuzzy Set
1.1 Introduction
Fuzzy set theory, proposed by Zadeh in 1965, takes into account member-
ship degree and non-membership degree. Non-membership degree is the
complement of membership degree. However, in real life, this linguistic
negation does not satisfy the logical negation. The selection of member-
ship degree depends on the user's choice, which may be Gaussian, tri-
angular, exponential or any other. There is an uncertainty involved in
defining the membership function. This is the reason different results are
obtained with different membership functions. Subsequently, Atanassov
suggested an advanced fuzzy set, which is an intuitionistic fuzzy set (IFS).
In this set, non-membership degree is not equal to the complement of the
membership degree; rather, it is less than or equal to the complement of
the membership degree, due to the uncertainty in defining the member-
ship degree.
Again, the membership function defined in this fuzzy set is not precise.
Zadeh, in 1975, introduced another advanced fuzzy set called Type II fuzzy
set that represents the uncertainty in a better way by considering the Type I
(ordinary) fuzzy set 'fuzzy'.
Both IFS and Type II fuzzy set have been found useful in many real-time
image applications such as medical images and remotely sensed images.
These images are mostly poorly illuminated, where the regions/boundar-
ies are vague or hardly visible, creating uncertainty. As IFS considers more
than one (two) uncertainties - membership and non-membership degrees -
and Type II fuzzy set considers the uncertainty in the membership function,
these sets may be useful in processing such images.
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