Issue:A new similarity measure for intuitionistic fuzzy sets and its use in supporting a medical diagnosis

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Title of paper: A new similarity measure for intuitionistic fuzzy sets and its use in supporting a medical diagnosis Author(s): Eulalia Szmidt Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland szmidt@ibspan.waw.pl Janusz Kacprzyk Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland kacprzyk@ibspan.waw.pl Mikhail Matveev CLBME-BAS, Sofia-1113, Acad. G. Bonchev Str., Bl. 105 mgm@clbme.bas.bg Presented at: 9th International Conference on Intuitionistic Fuzzy Sets, Sofia, 7-8 May 2005 Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 11 (2005), Number 4, pages 130-138 Download:  PDF (5679  Kb, File info) Abstract: We propose a new measure of similarity for intuitionistic fuzzy sets, and use it in supporting a medical diagnosis. The proposed measure takes into account two kinds of distances — one to an object to be compared, and one to its complement. We infer about the similarity of preferences on the basis of a difference between the two types of distances. We show that inferring without taking into account a distance to a complement of an object can be misleading. The proposed here the new measure of similarity is simpler from a point of view of calculations than the measure we have proposed previously. Keywords: fuzzy sets, intuitionistic fuzzy sets, similarity References: Atanassov K. (1986) Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, Vol. 20, 87-96. Atanassov K. (1999), Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag. Bouchon-Meunier B., Rifgi M., and Bothorel S. (1996). General measures of comparison of objects. Fuzzy Sets and Systems, Vol. 84, No. 2, 143-153. Chen S., Yeh M. and Hsiao P. (1995). A comparison of similarity measures of fuzzy values. Fuzzy Sets and Systems, Vol. 72, No. 1, 79-89. Cross V. and Sudkamp T. (2002) Similarity and Compatibility in Fuzzy Set Theory. Physica-Verlag. De S.K., Biswas R. and Roy A.R. (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems, Vol. 117, No.2, pp. 209 — 213. Dengfeng L. and Chuntian C. (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, Vol. 23, 221-225. Pappis C., and Karacapilidis N. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems, Vol. 56, 171-174. Szmidt E. (2000) Applications of Intuitionistic Fuzzy Sets in Decision Making. (D.Sc. dissertation) Techn. Univ., Sofia, 2000. Szmidt E. and Baldwin J. (2003) New Similarity Measure for Intuitionistic Fuzzy Set Theory and Mass Assignment Theory. Notes on IFSs, Vol. 9, No. 3, 60-76. Szmidt E. and Baldwin J. (2004) Entropy for Intuitionistic Fuzzy Set Theory and Mass Assignment Theory. Notes on IFSs, Vol. 10, No. 3, 15-28. Szmidt E. and Kacprzyk J. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 114, No. 3, 505-518. Szmidt E. and Kacprzyk J. (2000) On Measures on Consensus Under Intuitionistic Fuzzy Relations. [PMU 2000, 1454-1461. Szmidt E., Kacprzyk J. (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 118, No. 3, 467-477. Szmidt E. and Kacprzyk J. (2002) An Intuitionistic Fuzzy Set Based Approach to Intelligent Data Analysis (an application to medical diagnosis). In A. Abraham, L.Jain, J. Kacprzyk (Eds.): Recent Advances in Intelligent Paradigms and and Applications. Springer-Verlag, 57-70. Szmidt E. and Kacprzyk J. (2002) Analysis of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Preferences. Proc. 9th Int. Conf. IPMU 2002, Annecy, France, 1859-1865. Szmidt E. and Kacprzyk J. (2004) Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. Proc. 10th Int. Conf. IPMU 2004, Perugia, Italy, 1405-1412. Tversky A. (1977) Features of similarity. Psychol. Rev. Vol. 84, pp. 327-352. Wang X., De Baets B., and Kerre E. (1995). A comparative study of similarity measures. Fuzzy Sets and Systems, Vol.73, No. 2, pp. 259-268. L.A. Zadeh (1965) Fuzzy sets. Information and Control, 8, 338-353. Zadeh, L.A. (1983). A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl., Vol. 9, No. 1, 149-184. Zwick R., Carlstein E., Budescu D. (1987). Measures of similarity among fuzzy concepts: A comparative analysis. Int. J. of Approx. Reasoning, Vol. 1, 221-242. Citations: Issue:On one of the geometrical interpretations of the intuitionistic fuzzy sets ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.