Similarity, Distance Measures and Entropy - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 63

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Similarity, Distance Measures and Entropy
4.1 Introduction
Most of the problems in medical science, engineering and environmental
science do not always involve crisp data. And traditional methods may not
be used successfully when uncertainties are involved. Many new approaches
and theories are introduced since the introduction of fuzzy set and have
showed successful applications in various fields. These are similarity, dis-
tance or entropy measures that are the vital in image processing and are
used in many image processing applications such as image retrieval, reg-
istration and segmentation. Similarity measure indicates that the degree of
similarity between two fuzzy sets and entropy denotes the fuzziness in a
fuzzy set. But fuzzy sets consider only one uncertainty which is the degree
of belongingness or membership degree. But in reality, it may not always
be certain that the non-membership degree in a fuzzy set is just equal to
1 minus the degree of membership. Many researchers extended fuzzy
measures [1,7,10,13,24] using intuitionistic fuzzy set ( IFS ) which are char-
acterized by membership and non-membership functions. Intuitionistic
fuzzy-based models may be adequate in many situations when we face
human opinions such as 'yes' or 'no' or 'does not apply', more specifically
in voting where people can vote for or against or does not vote. Using
these sets, new approaches such as fuzzy distance/similarity/entropy mea-
sures are extended. Such a generalization of fuzzy set gives us additional
information to represent imperfect knowledge that will help in describing
many real-time problems accurately. Different types of similarity/distance/
entropy measures using IFS are discussed later.
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