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Mathematics 2018, 6(7), 121; https://doi.org/10.3390/math6070121

Some Generalized Dice Measures for Double-Valued Neutrosophic Sets and Their Applications

1
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
2
School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China
*
Author to whom correspondence should be addressed.
Received: 10 June 2018 / Revised: 7 July 2018 / Accepted: 9 July 2018 / Published: 10 July 2018
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Abstract

Neutrosophic sets (NSs) are used to illustrate uncertain, inconsistent, and indeterminate information existing in real-world problems. Double-valued neutrosophic sets (DVNSs) are an alternate form of NSs, in which the indeterminacy has two distinct parts: indeterminacy leaning toward truth membership, and indeterminacy leaning toward falsity membership. The aim of this article is to propose novel Dice measures and generalized Dice measures for DVNSs, and to specify Dice measures and asymmetric measures (projection measures) as special cases of generalized Dice measures via specific parameter values. Finally, the proposed generalized Dice measures and generalized weighted Dice measures were applied to pattern recognition and medical diagnosis to show their effectiveness. View Full-Text
Keywords: double-valued neutrosophic set; Dice similarity measure; pattern recognition; medical diagnosis double-valued neutrosophic set; Dice similarity measure; pattern recognition; medical diagnosis
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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Khan, Q.; Liu, P.; Mahmood, T. Some Generalized Dice Measures for Double-Valued Neutrosophic Sets and Their Applications. Mathematics 2018, 6, 121.

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