Intuitionistic Fuzzy Set and Type II Fuzzy Set - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 20

1.11 Summary
This chapter discusses on IFSs, intuitionistic fuzzy operations and IFRs. It
also discusses on interval-valued fuzzy set and Type II fuzzy set. IFS deals
with the vagueness and also the uncertainty in describing the vagueness.
The vagueness is represented in the form of a membership function, and the
uncertainty is described in the form of hesitation degree while defining the
membership function.
Type II fuzzy set considers the fuzzy membership function as fuzzy. This
uncertainty is represented as lower and upper levels of the membership
function. Sometimes, the membership degrees are not exactly defined but
a vague range is defined and so the membership function lies in an interval
range. This is the interval-valued fuzzy set.
Similar to the operations and relations on fuzzy sets, there are also oper-
ations and relations on IFSs that use t -norms and t -conorms, namely, are
union, intersection, complement and negate. IFRs such as reflexivity, sym-
metricity, transitivity and equivalence relation are also discussed along with
examples.
References
1. Atanassov, K.T., Intuitionistic fuzzy set, Fuzzy Sets and Systems , 20, 87-97, 1986.
2. Burillo, P. and Bustince, H., Intuitionistic fuzzy relations, Mathware and Soft
Computing , 3(Part I), 5-38, 1995.
3. Bustince, H., Construction of intuitionistic fuzzy relations with predetermined
properties, Fuzzy Sets and Systems , 109(3), 379-403, 2000.
4. Bustince, H. and Burillo, P., Structures of intuitionistic fuzzy relations, Fuzzy
Sets and Systems , 78, 293-303, 1996.
5. Bustince, H., Kacpryzk, J., and Mohedano, V., Intuitionistic fuzzy generators:
Application to intuitionistic fuzzy complementation, Fuzzy Sets and Systems ,
114, 485-504, 2000.
6. Bustince, H. and Burillo, P., Correlation of interval-valued intuitionistic fuzzy
sets, Fuzzy Sets and System s, 74, 237-244, 1995.
7. Chaira, T., Enhancement of medical images using Atanassov's intuitionistic
fuzzy domain using an alternative intuitionistic fuzzy generator with applica-
tion to medical image segmentation, International Journal of Intelligent and Fuzzy
Systems , 27(3), 1347-1359, 2014.
8. De, S.K., Biswas, R., and Roy, A.R., Some operations on intuitionistic fuzzy sets,
Fuzzy Sets and Systems , 114, 477-484, 2000.
9. Ensafi, P. and Tizoosh, H.R., Type II fuzzy image enhancement, in Lecture Notes
in Computer Sciences , Vol. 3656, M. Kamel and A. Campilho (Eds.), Springer,
Berlin, Germany, pp. 159-166, 2005.