Volume 5 | Number 2 | Year 2014 | Article Id. IJMTT-V5P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V5P525
As Similarity measure for fuzzy sets is one of the important research topics of fuzzy set theory, there are several methods to measure similarity between two fuzzy sets (FS), Intuitionistic fuzzy sets (IFS) and Intuitionistic fuzzy multi sets (IFMS). In this paper, the Normalized Hamming Similarity measure of Intuitionistic Fuzzy Multi sets (IFMS) is introduced. This new measure for IFMS is based on the geometrical interpretation of IFS which involves both similarity and dissimilarity. Using this measure, the application of medical diagnosis and pattern recognition are shown.
[1] Zadeh L. A., Fuzzy sets, Information and Control 8 (1965) 338-353.
[2] Atanassov K., Intuitionistic fuzzy sets, Fuzzy Sets and System 20 (1986) 87-96.
[3] Atanassov K., More on Intuitionistic fuzzy sets, Fuzzy Sets and Systems 33 (1989) 37-46.
[4] Yanhong L., Olson D., Qin Z., Similarity between Intuitionistic Fuzzy sets : Comparative Analysis, Pattern Recognition Letters, 28- 2 (2007) 278-285.
[5] Li D., Cheng C., New Similarity measures of Intuitionistic fuzzy sets and application to pattern recognition, Pattern Recognition Letters , 23 (2002) 221-225.
[6] Liang Z., Shi P., Similarity measures on Intuitionistic fuzzy sets, Pattern Recognition Letters, 24 (2003) 2687-2693.
[7] Szmidt E., Kacprzyk J., Remarks on some applications of Intuitionistic fuzzy sets in decision making, Notes on IFS, 2,(1996) 22-31.
[8] Szmidt E., Kacprzyk J., On measuring distances between Intuitionistic fuzzy sets, Notes on IFS, Vol. 3 (1997) 1- 13.
[9] Szmidt E., Kacprzyk J., Distances between Intuitionistic fuzzy sets. Fuzzy Sets System, 114 (2000) 505-518.
[10] Szmidt E., Kacprzyk J., Entropy for Intuitionistic Fuzzy sets, Fuzzy Sets and System, 118, (2001) 467-477.
[11] Szmidt E., Baldwin J., New similarity measure for Intuitionistic fuzzy set theory and mass assignment theory, Notes on IFS, 9, (2003) 60-79.
[12] Szmidt E., Kacprzyk J., A similarity measure for Intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. ICAISC 2004, Vol. LNAI 3070 (2004) 388-393.
[13] Yager R. R., On the theory of bags,(Multi sets), Int. Jou. Of General System, 13 (1986) 23-37.
[14] Blizard W. D., Multi set Theory, Notre Dame Journal of Formal Logic, Vol. 30, No. 1 (1989) 36-66.
[15] Shinoj T.K., Sunil Jacob John , Intuitionistic Fuzzy Multi sets and its Application in Medical Diagnosis, World Academy of Science, Engineering and Technology, Vol. 61 (2012).
[16] P. Rajarajeswari., N. Uma., On Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set, IOSR Journal of Mathematics (IOSR-JM) Vol. 5, Issue 4 (Jan. - Feb. 2013) 19-23.
[17] P. Rajarajeswari., N. Uma., Hausdroff Similarity measures for Intuitionistic Fuzzy Multi Sets and Its Application in Medical diagnosis, International Journal of Mathematical Archive-4(9),(2013) 106-111.
[18] P. Rajarajeswari., N. Uma., A Study of Normalized Geometric and Normalized Hamming Distance Measures in Intuitionistic Fuzzy Multi Sets, International Journal of Science and Research (IJSR), Vol. 2, Issue 11, November 2013, 76-80.
[19] P. Rajarajeswari., N. Uma., Intuitionistic Fuzzy Multi Similarity Measure Based on Cotangent Function, International Journal of Engineering Research & Technology (IJERT) Vol. 2 Issue 11, (Nov- 2013) 1323–1329.
P. Rajarajeswari , N. Uma, "Normalized Hamming Similarity Measure for Intuitionistic Fuzzy Multi Sets and Its Application in Medical Diagnosis," International Journal of Mathematics Trends and Technology (IJMTT), vol. 5, no. 2, pp. 219-225, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V5P525