Neutrosophic Küme Üzerinde Yeni Entropi Ölçüsü ve Çok Kriterli Karar Verme Uygulamaları

Bu çalışmadaki amacımız, tek-değerli neutrosophic kümeler (SVNSs) ve aralık-değerli neutrosophic kümeler (INSs) için iki yeni entropi ölçüsü oluşturmaktır. Buna ek olarak, oluşturulan entropilerin temel özelliklerini gösterdik. Son olarak, oluşturulan entropi ölçülerinin belirsizlik derecesini temsil edebilmede daha makul ve güvenilir olduklarını gösteren bir sayısal örnek verdik.

Anahtar Kelimeler:

Neutrosophic küme, Tek-değerli neutrosophic küme, Aralık-değerli neutrosophic küme, Entropi ölçüsü, Karar verme

New Entropy Measures Based on Neutrosophic Set and Their Applications to Multi-Criteria Decision Making

Our aim in this work is to obtain two new entropy measures for single valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs). Moreover, we give the essential properties of the proposed entropies. Finally, we introduce a numerical example to show that the entropy measures are more reliable and reasonable for representing the degree of uncertainty.

Keywords:

Neutrosophic set, Single-valued neutrosophic set, Interval neutrosophic set, Entropy measure, Decision making,

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[1] Smarandache, F. 1998. A unifying field in logics. neutrosophy: Neutrosophic probability, set and logic, American Research Press, Rehoboth, 157p.
[2] Smarandache, F. 2005. A generalization of the intuitionistic fuzzy set. International journal of Pure and Applied Mathematics, 24(2005), 287-297.
[3] Wang, H., Smarandache, F., Zhang Y.Q., Sunderraman, R. 2005. Single valued neutrosophic sets, in Proc. of 10th Int. Conf. on Fuzzy Theory and Technology, July 21-26, Salt Lake City, Utah.
[4] Wang, H., Smarandache, F., Zhang Y.Q., Sunderraman, R. 2005. Interval neutrosophic sets and logic: Theory and applications in computing', Hexis, Phoenix, AZ, 99p.
[5] Zadeh, L.A . 1965. Fuzzy sets. Information and Control, 8(1965), 338-356.
[6] De Luca, A., Termini, S. 1972. A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control, 20(1972), 301-312.
[7] Shannon, C.E., 1948. A mathematical theory of communication. Bell system technical journal, 27(3), 379-423.
[8] Burillo, P. Bustince, H., 1996. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy sets and systems, 78(3), 305-316.
[9] Szmidt, E. Kacprzyk, J., 2001. Entropy for intuitionistic fuzzy sets. Fuzzy sets and systems, 118(3), 467-477.
[10] Ye, J., 2010. Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Applied Mathematical Modelling, 34(12), 3864-3870.
[11] Wei, C.P., Wang, P., Zhang, Y.Z., 2011. Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Information Sciences, 181(19), 4273-4286.
[12] Majumdar, P., Samanta, S.K., 2014. On similarity and entropy of neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 26(3), pp.1245-1252.
[13] Aydoğdu, A. 2015. On Similarity and Entropy of Single Valued Neutrosophic Sets. General Mathematics Notes, 29 (1) (2015), 67-74.
[14] Aydoğdu, A. 2015. On Entropy and Similarity Measure of Interval Valued Neutrosophic Sets. Neutrosophic Sets and Systems, 9(2015), 47-49.
[15] Ye, J., Du, S., 2017. Some distances, similarity and entropy measures for interval-valued neutrosophic sets and their relationship. International Journal of Machine Learning and Cybernetics, pp.1-9.
[16] Ye J. 2013. Multicriteria decision-making method using the the correlation coefficient under single-valued neutrosophic environment. International Journal of General Systems, 42(49) (2013), 386-394.
[17] Ye, J., 2014. Single valued neutrosophic cross-entropy for multicriteria decision making problems. Applied Mathematical Modelling, 38(3), pp.1170-1175.
[18] Ye, J., 2015. Improved cross entropy measures of single valued neutrosophic sets and interval neutrosophic sets and their multicriteria decision making methods. Cybernetics and Information Technologies, 15(4), 13-26.
[19] Tian, Z.P., Zhang, H.Y., Wang, J., Wang, J.Q. and Chen, X.H., 2016. Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. International Journal of Systems Science, 47(15), 3598-3608.
[20] Şahin, R., 2017. Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Computing and Applications, 28(5), pp.1177-1187.
[21] Peng X., Dai J. 2018. A bibliometric analysis of neutrosophic set: Two decades review from 1998 to 2017, Artificial Intelligence Review, doi: 10.1007/s10462-018-9652-0.
[22] Peng X., Dai J. 2018. Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function, Neural Computing and Applications, 29 (10) (2018), 939-954.