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Mathematics 2019, 7(4), 340; https://doi.org/10.3390/math7040340

Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

1, 2, 2,* and 2,3
1
Institute of Technology, Sichuan Normal University, Chengdu 610101, China
2
School of Business, Sichuan Normal University, Chengdu 610101, China
3
School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China
*
Author to whom correspondence should be addressed.
Received: 23 March 2019 / Revised: 2 April 2019 / Accepted: 4 April 2019 / Published: 9 April 2019
(This article belongs to the Special Issue Optimization for Decision Making)
PDF [532 KB, uploaded 9 April 2019]

Abstract

In this article, we propose another form of ten similarity measures by considering the function of membership degree, non-membership degree, and indeterminacy membership degree between the q-ROFSs on the basis of the traditional cosine similarity measures and cotangent similarity measures. Then, we utilize our presented ten similarity measures and ten weighted similarity measures between q-ROFSs to deal with multiple attribute decision-making (MADM) problems including pattern recognition and scheme selection. Finally, two numerical examples are provided to illustrate the scientific and effective of the similarity measures for pattern recognition and scheme selection.
Keywords: multiple attribute decision-making (MADM); q-rung orthopair fuzzy sets (q-ROFSs); cosine function; cosine similarity measure; pattern recognition; scheme selection multiple attribute decision-making (MADM); q-rung orthopair fuzzy sets (q-ROFSs); cosine function; cosine similarity measure; pattern recognition; scheme selection
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wang, P.; Wang, J.; Wei, G.; Wei, C. Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications. Mathematics 2019, 7, 340.

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