Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy and Indeterminacy Based Cross Entropy


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Double Refined Indeterminacy Neutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache (2013), which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into two, based on membership; as indeterminacy leaning towards truth membership (IT) and indeterminacy leaning towards false membership (IF). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular case of the refined neutrosophic set (where each T, I, F can be refined into T1, T2, ...; I1, I2, ...; F1, F2, ...). DRINS is better equipped at dealing indeterminate and inconsistent information, with more accuracy than SVNS, which fuzzy sets and Intuitionistic Fuzzy Sets (IFS) are incapable of. Based on the cross entropy of neutrosophic sets, the cross entropy of DRINSs, known as Double Refined Indeterminacy neutrosophic cross entropy, is proposed in this paper. This proposed cross entropy is used for a multicriteria decision-making problem, where the criteria values for alternatives are considered under a DRINS environment. Similarly, an indeterminacy based cross entropy using DRINS is also proposed. The double valued neutrosophic weighted cross entropy and indeterminacy based cross entropy between the ideal alternative and an alternative is obtained and utilized to rank the alternatives corresponding to the cross entropy values. The most desirable one(s) in decision making process is selected. An illustrative example is provided to demonstrate the application of the proposed method. A brief comparison of the proposed method with the existing methods is carried out.



Edited by:

Adrian Olaru




I. Kandasamy and F. Smarandache, "Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy and Indeterminacy Based Cross Entropy", Applied Mechanics and Materials, Vol. 859, pp. 129-143, 2017

Online since:

December 2016




* - Corresponding Author

[1] F. Smarandache, n-valued refined neutrosophic logic and its applications in physics, Progress in Physics, vol. 4, pp.143-146, (2013).

[2] L. A. Zadeh, Fuzzy sets, Information and control, vol. 8, no. 3, pp.338-353, (1965).

[3] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, vol. 20, no. 1, pp.87-96, (1986).

DOI: 10.1016/s0165-0114(86)80034-3

[4] K. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy sets and systems, vol. 31, no. 3, pp.343-349, (1989).

DOI: 10.1016/0165-0114(89)90205-4

[5] L. A. Zadeh, Probability measures of fuzzy events, Journal of mathematical analysis and applications, vol. 23, no. 2, pp.421-427, (1968).

DOI: 10.1016/0022-247x(68)90078-4

[6] C. E. Shannon, A mathematical theory of communication, ACM SIGMOBILE Mobile Computing and Communications Review, vol. 5, no. 1, pp.3-55, (2001).

[7] S. Kullback and R. A. Leibler, On information and sufficiency, The annals of mathematical statistics, vol. 22, no. 1, pp.79-86, (1951).

DOI: 10.1214/aoms/1177729694

[8] J. Lin, Divergence measures based on the shannon entropy, IEEE Transactions on Information theory, vol. 37, no. 1, pp.145-151, (1991).

DOI: 10.1109/18.61115

[9] X.G. Shang and W.S. Jiang, A note on fuzzy information measures, Pattern Recognition Letters, vol. 18, no. 5, pp.425-432, (1997).

DOI: 10.1016/s0167-8655(97)00028-7

[10] A. De Luca and S. Termini, A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory, Information and control, vol. 20, no. 4, pp.301-312, (1972).

DOI: 10.1016/s0019-9958(72)90199-4

[11] I. K. Vlachos and G. D. Sergiadis, Intuitionistic fuzzy information-applications to pattern recognition, Pattern Recognition Letters, vol. 28, no. 2, pp.197-206, (2007).

DOI: 10.1016/j.patrec.2006.07.004

[12] Q.S. Zhang and S.Y. Jiang, A note on information entropy measures for vague sets and its applications, Information Sciences, vol. 178, no. 21, pp.4184-4191, (2008).

DOI: 10.1016/j.ins.2008.07.003

[13] J. Ye, Fault diagnosis of turbine based on fuzzy cross entropy of vague sets, Expert Systems with Applications, vol. 36, no. 4, pp.8103-8106, (2009).

DOI: 10.1016/j.eswa.2008.10.017

[14] J. Ye, Multicriteria fuzzy decision-making method based on the intuitionistic fuzzy crossentropy, " in Intelligent Human-Machine Systems and Cybernetics, 2009. IHMSC, 09. International Conference on, vol. 1. IEEE, 2009, pp.59-61.

DOI: 10.1109/ihmsc.2009.23

[15] J. Ye, Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decisionmaking method based on the weights of alternatives, Expert Systems with Applications, vol. 38, no. 5, pp.6179-6183, (2011).

DOI: 10.1016/j.eswa.2010.11.052

[16] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Probability, and Statistics. American Research Press, Rehoboth, (2000).

[17] H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, Single valued neutrosophic sets, Review, p.10, (2010).

[18] J. Ye, Multicriteria decision-making method using the correlation coefficient under singlevalued neutrosophic environment, International Journal of General Systems, vol. 42, no. 4, pp.386-394, (2013).

DOI: 10.1080/03081079.2012.761609

[19] J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, Journal of Intelligent & Fuzzy Systems, vol. 26, no. 5, pp.2459-2466, (2014).

[20] J. Ye, Single valued neutrosophic cross-entropy for multicriteria decision making problems, Applied Mathematical Modelling, vol. 38, no. 3, pp.1170-1175, (2014).

DOI: 10.1016/j.apm.2013.07.020

[21] J. Ye, Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making, Journal of Intelligent & Fuzzy Systems, vol. 26, no. 1, pp.165-172, (2014).

[22] A. Salama, A. Haitham, A. Manie, and M. Lotfy, Utilizing neutrosophic set in social network analysis e-learning systems, International Journal of Information Science and Intelligent System, vol. 3, no. 2, (2014).

[23] H.D. Cheng and Y. Guo, A new neutrosophic approach to image thresholding, New Mathematics and Natural Computation, vol. 4, no. 03, pp.291-308, (2008).

DOI: 10.1142/s1793005708001082

[24] A. Sengur and Y. Guo, Color texture image segmentation based on neutrosophic set and wavelet transformation, Computer Vision and Image Understanding, vol. 115, no. 8, pp.1134-1144, (2011).

DOI: 10.1016/j.cviu.2011.04.001

[25] M. Zhang, L. Zhang, and H. Cheng, A neutrosophic approach to image segmentation based on watershed method, Signal Processing, vol. 90, no. 5, pp.1510-1517, (2010).

DOI: 10.1016/j.sigpro.2009.10.021

[26] W. Vasantha and F. Smarandache, Fuzzy cognitive maps and neutrosophic cognitive maps. Infinite Study, (2003).

[27] W. Vasantha and F. Smarandache, Analysis of social aspects of migrant labourers living with hiv/aids using fuzzy theory and neutrosophic cognitive maps: With special reference to rural tamil nadu in india, arXiv preprint math/0406304, (2004).

[28] I. Kandasamy, Double Valued neutrosophic sets and its applications to clustering, 2016, manuscript submitted for publication.

[29] H. Wang, Y. -Q. Zhang, and R. Sunderraman, Soft semantic web services agent, " in Fuzzy Information, 2004. Processing NAFIPS, 04. IEEE Annual Meeting of the, vol. 1. IEEE, 2004, pp.126-129.

DOI: 10.1109/nafips.2004.1336263

[30] C. Tan and X. Chen, Intuitionistic fuzzy choquet integral operator for multi-criteria decision making, Expert Systems with Applications, vol. 37, no. 1, pp.149-157, (2010).

DOI: 10.1016/j.eswa.2009.05.005

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