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Some New Operations Over Fermatean Fuzzy Numbers and Application of Fermatean Fuzzy WPM in Multiple Criteria Decision Making
Volume 30, Issue 2 (2019), pp. 391–412
Tapan Senapati   Ronald R. Yager  

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https://doi.org/10.15388/Informatica.2019.211
Pub. online: 1 January 2019      Type: Research Article      Open accessOpen Access

Received
1 February 2018
Accepted
1 October 2018
Published
1 January 2019

Abstract

Fermatean fuzzy sets (FFSs), proposed by Senapati and Yager (2019a), can handle uncertain information more easily in the process of decision making. They defined basic operations over the Fermatean fuzzy sets. Here we shall introduce three new operations: subtraction, division, and Fermatean arithmetic mean operations over Fermatean fuzzy sets. We discuss their properties in details. Later, we develop a Fermatean fuzzy weighted product model to solve the multi-criteria decision-making problem. Finally, an illustrative example of selecting a suitable bridge construction method is given to verify the approach developed by us and to demonstrate its practicability and effectiveness.

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Biographies

Senapati Tapan
math.tapan@gmail.com

T. Senapati received the BSc, MSc and PhD degrees in mathematics all from the Vidyasagar University, India, in 2006, 2008 and 2013, respectively. He has published more than 50 articles in international journals. His research interests include aggregation operators, fuzzy logic, fuzzy algebraic structures, fuzzy decision making, and their applications.

Yager Ronald R.
yager@panix.com

R.R. Yager received the BE degree from the City College of New York, USA, in 1963, and the PhD degree in systems science from the Polytechnic University of New York, USA, in 1968. He is currently the director of the Machine Intelligence Institute and a professor of Information Systems at Iona College. He is the chief editor of the International Journal of Intelligent Systems. He has published over 900 papers and edited over 30 books in areas related to fuzzy sets, human behavioural modelling, decision-making under uncertainty and the fusion of information. He was the recipient of the IEEE Computational Intelligence Society Pioneer award in Fuzzy Systems. He received the special honorary medal of the 50-th Anniversary of the Polish Academy of Sciences. He received the lifetime outstanding achievement award from International Fuzzy Systems Association. Dr. Yager is a fellow of the IEEE, the New York Academy of Sciences and the Fuzzy Systems Association. He has served at the National Science Foundation as program director in the Information Sciences program. He was a NASA/Stanford visiting fellow and a research associate at the University of California, Berkeley. He has been a lecturer at NATO Advanced Study Institutes. He is a visiting distinguished scientist at King Saud University, Riyadh, Saudi Arabia. He is a distinguished honorary professor at the Aalborg University, Denmark.


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Keywords
Fermatean fuzzy set subtraction operation division operation Fermatean arithmetic mean operation multiple criteria decision making (MCDM) weighted product model (WPM)

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