Intuitionistic Fuzzy Multisets And Its Application in Medical Diagnosis

In this paper a new concept named Intuitionistic Fuzzy Multiset is introduced. The basic operations on Intuitionistic Fuzzy Multisets such as union, intersection, addition, multiplication etc. are discussed. An application of Intuitionistic Fuzzy Multiset in Medical diagnosis problem using a distance function is discussed in detail.

Authors:

• Shinoj T. K
• Sunil Jacob John

Keywords:

• Intuitionistic Fuzzy set
• Multiset
• Intuitionistic Fuzzy Multiset

References:

[1] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 338-353, 1965.
[2] K. T. Atanassov, Intuitionistic Fuzzy sets, VII ITKRs Session, Sofia
(deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84) (in Bulgarian), 1983.
[3] K. T. Atanassov, Intuitionistic Fuzzy sets, Fuzzy sets and Systems, 20,
87-96, 1986.
[4] G .Takeuti and S. Titani, Intuitionistic fuzzy Logic and intuitionistic Fuzzy set theory, J. Symbolic Logic, 49, 851-866, 1984.
[5] Glad Deschrijver and Etienne E. Kerre, On the position of intuitionistic
Fuzzy set theory in the framework of theories modelling imprecision,
Information Sciences, 177, 1860-1866, 2007.
[6] W .D. Blizard, Dedekind multisets and function shells, Theoretical Computer Science, 110, 79-98, 1993.
[7] W. D. Blizard, Multiset Theory, Notre Dame Journal of Formal Logic, Vol.30, No.1, 36-66, 1989.
[8] R. R. Yager, On the theory of bags, Int. J. of General Systems, 13,
23-37, 1986.
[9] Cristian S. Calude, Gheorghe Paun, Grzegorz Rozenberg and Arto
Salomaa, Multiset Processing, Springer-Verlag, Germany, 2001.
[10] De S. K., Biswas R and Roy A. R., An Application of Intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, Vol. 117, No.
2, pp. 209-213, 2001.