Document Type : Research Paper
Authors
Department of Mathematics, Research Scholar, Nirmala College for Women, Coimbatore, India.
Abstract
In this paper, we investigate the multiple attribute decision making problems with spherical fuzzy information. The advantage of spherical fuzzy set is easily reflecting the ambiguous nature of subjective judgments because the spherical fuzzy sets are suitable for capturing imprecise, uncertain and inconsistent information in the multiple attribute decision making analysis. Thus, the cross- entropy of spherical fuzzy sets called, spherical fuzzy cross-entropy, is proposed as an extension of the cross-entropy of fuzzy sets. Then, a multiple attribute decision making method based on the proposed spherical fuzzy cross entropy is established in which attribute values for alternatives are spherical fuzzy numbers. In decision making process, we utilize the spherical fuzzy weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Keywords
- Spherical fuzzy set
- Spherical fuzzy cross entropy
- Spherical fuzzy weighted cross entropy
- Enterprise resource planning system selection
Main Subjects
- Antonov, I. (1995). On a new geometrical interpretation of the intuitionistic fuzzy sets. Notes on Intuitionistic fuzzy sets, 1(1), 29-31.
- De Luca, A., & Termini, S. (1972). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and control, 20(4), 301-312. http://dx.doi.org/10.1016/S0019-9958(72)90199-4
- Kutlu Gündoğdu, F., & Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of intelligent & fuzzy systems, 36(1), 337-352.
- Gong, Z., Xu, X., Yang, Y., Zhou, Y., & Zhang, H. (2016). The spherical distance for intuitionistic fuzzy sets and its application in decision analysis. Technological and economic development of economy, 22(3), 393-415.
- Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The annals of mathematical statistics, 22(1), 79-86. http://dx.doi.org/10.1214/aoms/1177729694
- Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE transactions on information theory, 37(1), 145-151. http://dx.doi.org/10.1109/18.61115
- Shang, X. G., & Jiang, W. S. (1997). A note on fuzzy information measures. Pattern recognition letters, 18(5), 425-432. http://dx.doi.org/10.1016/S0167-8655(97)00028-7.
- Shannon, C. E. (1948). A mathematical theory of communication. The bell system technical journal, 27(3), 379-423. http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x
- Vlachos, I. K., & Sergiadis, G. D. (2007). Intuitionistic fuzzy information–applications to pattern recognition. Pattern recognition letters, 28(2), 197-206. http://dx.doi.org/10.1016/j.patrec.2006.07.004
- Xia, M., & Xu, Z. (2012). Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Information fusion, 13(1), 31-47. http://dx.doi.org/10.1016/j.inffus.2010.12.001
- Yang, Y., & Chiclana, F. (2009). Intuitionistic fuzzy sets: spherical representation and distances. International journal of intelligent systems, 24(4), 399-420.
- Ye, J. (2009). Fault diagnosis of turbine based on fuzzy cross entropy of vague sets. Expert systems with applications, 36(4), 8103-8106. http://dx.doi.org/10.1016/j.eswa.2008.10.017
- Ye, J. (2009, August). Multicriteria fuzzy decision-making method based on the intuitionistic fuzzy cross-entropy. 2009 international conference on intelligent human-machine systems and cybernetics(Vol. 1, pp. 59-61). IEEE. http://dx.doi.org/10.1109/ihmsc.2009.23
- Ye, J. (2011). Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives. Expert systems with applications, 38(5), 6179-6183. http://dx.doi.org/10.1016/j.eswa.2010.11.052
- Zadeh, L. A. (1965). Fuzzy sets. Information control, 8, 338–353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
- Zadeh, L. A. (1968). Probability measures of fuzzy events. Journal of mathematical analysis and applications, 23, 421–427. http://dx.doi.org/10.1016/0022-247X(68)90078-4
- Zhang, Q. S., & Jiang, S. Y. (2008). A note on information entropy measures for vague sets and its applications. Information sciences, 178(21), 4184-4191. http://dx.doi.org/10.1016/j.ins.2008.07.003
- Zhang, Q., & Jiang, S. (2010). Relationships between entropy and similarity measure of interval‐valued intuitionistic fuzzy sets. International journal of intelligent systems, 25(11), 1121-1140.
)