×

On similarity measures between intuitionistic fuzzy sets. (English) Zbl 1136.03327

Summary: We first review several popular similarity measures between fuzzy sets and then extend those similarity measures to intuitionistic fuzzy sets. We also propose two new similarity measures between intuitionistic fuzzy sets. These similarity measures have been found to satisfy some similarity measure axioms. Several numerical experiments are performed to assess the performance of these measures. Numerical results clearly indicate these new measures to be superior in performance to the others. Finally, we apply the new measures to evaluate students’ answerscripts. The experimental results show the superiority of the proposed measures for students’ evaluation.

MSC:

03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Finding groups in data. New York: Wiley; 1990. · Zbl 1345.62009 · doi:10.1002/9780470316801
[2] Zadeh, Inform Control 8 pp 338– (1965)
[3] Zwick, Int J Approximate Reason 1 pp 221– (1987)
[4] Pappis, Fuzzy Sets Syst 56 pp 171– (1993)
[5] Wang, Fuzzy Sets Syst 85 pp 305– (1997)
[6] Liu, Fuzzy Sets Syst 52 pp 305– (1992)
[7] Fan, Fuzzy Sets Syst 101 pp 403– (1999)
[8] Turksen, IEEE Trans Syst Man Cybern 18 pp 1049– (1988)
[9] Buckley, Fuzzy Sets Syst 58 pp 273– (1993)
[10] Candan, Data Knowl Eng 35 pp 259– (2000)
[11] Grzegorzewski, Fuzzy Sets Syst 148 pp 319– (2004) · Zbl 1163.03316
[12] Atanassov, Fuzzy Sets Syst 20 pp 87– (1986)
[13] Atanassov, Fuzzy Sets Syst 61 pp 137– (1994)
[14] Intuitionistic fuzzy sets: Theory and Applications. Heidelberg: Physica-Verlag; 1999. · doi:10.1007/978-3-7908-1870-3
[15] Atanassov, CR Acad Bulgare Sci 43 pp 9– (1990)
[16] Atanassov, Fuzzy Sets Syst 53 pp 121– (1993)
[17] Szmidt, Notes on IFS 2 pp 11– (1996)
[18] De, Fuzzy Sets Syst 117 pp 209– (2001)
[19] Fonctions {\(\Phi\)}-floues. Application À l’aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, University of Marseille, France, 1975.
[20] Dubois, Fuzzy Sets Syst 156 pp 485– (2005)
[21] Atanassov, Fuzzy Sets Syst 156 pp 496– (2005) · Zbl 1098.03060
[22] Grzegorzewski, Fuzzy Sets Syst 156 pp 492– (2005)
[23] Burillo, Fuzzy Sets Syst 78 pp 305– (1996)
[24] Liang, Pattern Recognit Lett 24 pp 2687– (2003)
[25] Wu, Pattern Recognit 35 pp 2267– (2002)
[26] Li, Pattern Recognit Lett 23 pp 221– (2002)
[27] Hung, Pattern Recognit Lett 25 pp 1603– (2004)
[28] De, Fuzzy Sets Syst 114 pp 477– (2000)
[29] Biswas, Fuzzy Sets Syst 74 pp 187– (1995)
[30] Pal, IEEE. Trans Syst Man Cybern 21 pp 1260– (1991)
[31] Pal, Inform Sci 66 pp 119– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.