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Open AccessArticle

Distance and Similarity Measures for Spherical Fuzzy Sets and Their Applications in Selecting Mega Projects

by Muhammad Jabir Khan 1,†, Poom Kumam 1,2,3,*,†, Wejdan Deebani 4,†, Wiyada Kumam 5,*,† and Zahir Shah 2,†
1
KMUTT Fixed Point Research Laboratory, SCL 802 Fixed Point Laboratory and Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
2
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Deparments of Mathematics, College of Science and Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia
5
Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 519; https://doi.org/10.3390/math8040519
Received: 4 March 2020 / Revised: 24 March 2020 / Accepted: 25 March 2020 / Published: 3 April 2020
A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets ( SFS ) . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries. View Full-Text
Keywords: spherical fuzzy set; distance measure; similarity measures; pattern recognition; mega projects spherical fuzzy set; distance measure; similarity measures; pattern recognition; mega projects
MDPI and ACS Style

Khan, M.J.; Kumam, P.; Deebani, W.; Kumam, W.; Shah, Z. Distance and Similarity Measures for Spherical Fuzzy Sets and Their Applications in Selecting Mega Projects. Mathematics 2020, 8, 519.

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