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A Cosine Similarity Measure Based on the Choquet Integral for Intuitionistic Fuzzy Sets and Its Applications to Pattern Recognition
Volume 32, Issue 4 (2021), pp. 849–864
Murat Olgun ORCID icon link to view author Murat Olgun details   Ezgi Türkarslan ORCID icon link to view author Ezgi Türkarslan details   Mehmet Ünver ORCID icon link to view author Mehmet Ünver details   Jun Ye ORCID icon link to view author Jun Ye details  

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https://doi.org/10.15388/21-INFOR460
Pub. online: 10 September 2021      Type: Research Article      Open accessOpen Access

Received
1 August 2020
Accepted
1 August 2021
Published
10 September 2021

Abstract

There exist various types of similarity measures for intuitionistic fuzzy sets in the literature. However, in many studies the interactions among the elements are ignored in the construction of the similarity measure. This paper presents a cosine similarity measure for intuitionistic fuzzy sets by using a Choquet integral model in which the interactions between elements are considered. The proposed similarity measure is applied to some pattern recognition problems and the results are compared with some existing results to demonstrate the effectiveness of this new similarity measure.

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Biographies

Olgun Murat
https://orcid.org/0000-0002-8660-5435
olgun@ankara.edu.tr

M. Olgun was born in 1979 in Aksaray (Turkey). He graduated from Ankara University (Turkey), Faculty of Science, Department of Mathematics, in 2001 with a bachelor’s degree. He obtained his master’s degree, in 2004 and his doctorate, in 2010, at Ankara University, respectively. He started as an assistant professor at Ankara University in 2011. He received the title of associate professor in 2016. He is currently working as an associate professor at Ankara University. His research interests are fuzzy measure and set theory, fixed point theory, spectral theory, difference and functional equations, general topology, operator theory, and ordinary differential equations. He is married and has two children.

Türkarslan Ezgi
https://orcid.org/0000-0001-5736-839X
ezgi.turkarslan@tedu.edu.tr

E. Türkarslan was born in Ankara in 1991. She graduated from Ankara University, Faculty of Science, Department of Mathematics, in 2013. In 2014, she completed pedagogical formation education at Hacettepe University Faculty of Education. In 2017, she completed master graduate education with the master thesis titled Some Approaches That Relief Calculation Complexity of Identification of Fuzzy Measure. Since September 2017, she continues doctoral studies at Ankara University, Department of Mathematics, and her doctoral studies are supported by the Scientific and Technological Research Council of Turkey (TUBITAK). Ezgi Türkarslan has been working as a research assistant at TED University since February 2019.

Ünver Mehmet
https://orcid.org/0000-0002-0857-1006
munver@ankara.edu.tr

M. Ünver graduated from the Department of Mathematics, Ankara University (Turkey), in 2007. He finished his master education in Ankara University, in 2009. He studied summability theory and Korovkin type approximation theory during his master’s. He got his PhD degree in mathematics from Ankara University in 2013. He studied summability theory, Korovkin type approximation theory. He worked as an Assistant Professor at Ankara University for about 2 years and he has been working as an associate professor at Ankara University since 2017. His current research interests are fuzzy measure and set theory, multicriteria decision-making, Korovkin type approximation theory, and summability theory.

Ye Jun
https://orcid.org/0000-0003-2841-6529
yejun1@nbu.edu.cn

J. Ye received his MS degree in automation and robotics from the Technical University of Koszalin, Poland, in 1997. In 2012, he was a visiting scholar in the School of Engineering of Southern Polytechnic State University in USA. Now, he is a professor at Ningbo University, China. He has more than 30 years of experience in teaching and research. His research interests include neutrosophic theory and applications, soft computing, decision making theory and method, intelligent control, robotics, pattern recognitions, rock mechanics, and fault diagnosis. He has published more than 270 papers in journals. He was selected as one of “Elsevier Chinese Most Cited Researchers” in 2019 and 2020.


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Choquet integral cosine similarity measure intuitionistic fuzzy set pattern recognition

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