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Ranking generalized exponential trapezoidal fuzzy numbers based on variance. (English) Zbl 1412.03021

Summary: In this paper, we calculate ranking of exponential trapezoidal fuzzy numbers based on variance. In this method, values are calculated by finding expected values using the probability density function corresponding to the membership functions of the given fuzzy number and provides the correct ordering of exponential trapezoidal fuzzy numbers and also this approach is very simple and easy to apply in the real life problems. For the validation, the results of the approach are compared with different existing approaches.

MSC:

03E72 Theory of fuzzy sets, etc.
91B06 Decision theory
Full Text: DOI

References:

[1] Abbasbandy, S.; Hajjari, T., A new approach for ranking of trapezoidal fuzzy numbers, Comput. Math. Appl, 57, 413-419, (2009) · Zbl 1165.03337
[2] Bortolan, G.; Degani, R., A review of some methods for ranking fuzzy subsets, Fuzzy Sets Syst., 15, 1, 119, (1985) · Zbl 0567.90056
[3] S.K. Barik, M.P. Biswal. Probabilistic Quadratic Programming Problems with Some Fuzzy Parameters, Hindawi Publishing Corporation, Advances in Operations Research, vol. 2012, Article ID 635282, 13 pp. · Zbl 1233.90230
[4] Chen, S.-H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets Syst., 17, 2, 113-129, (1985) · Zbl 0618.90047
[5] Chen, S.j.; Chen, S. M., Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Appl. Intell., 26, 1-11, (2007)
[6] Chen, S.-H.; Li, G.-C., Representation, ranking, ang distance of fuzzy number with exponential membership function using graded mean integration method, Tamsui Oxford J. Math. Sci, 16, 123-131, (2000) · Zbl 1022.26020
[7] Chen, S. M.; Chen, J. H., Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads, Expert Syst. Appl., 36, 6833-6842, (2009)
[8] Cheng, C., A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets Syst., 95, 3, 307-317, (1998) · Zbl 0929.91009
[9] Chu, T.; Tsao, C., Ranking fuzzy numbers with an area between the centroid point and original point, Comput. Math. Appl., 43, 1-2, 111-117, (2002) · Zbl 1113.62307
[10] Dubois, D.; Prade, H., The mean value of a fuzzy number, Fuzzy Sets Syst., 24, 3, 279-300, (1987) · Zbl 0634.94026
[11] Jain, R., Decision making in the presence of fuzzy variables, IEEE Trans. Syst. Man Cybernet., 6, 10, 698-703, (1976) · Zbl 0337.90005
[12] C. Liang, J. Wu, J. Zhang. Ranking indices and rules for fuzzy numbers based on gravity center point, Paper presented at the 6th world Congress on Intelligent Control and Automation, Dalian, China, 2006, pp. 21-23.
[13] Kumar, A.; Singh, P.; Kaur, A.; Kaur, P., Rm approach for ranking of generalized trapezoidal fuzzy numbers, Fuzzy Inf. Eng., 2, 1, 37-47, (2010) · Zbl 1255.91073
[14] Rezvani, S., Graded mean representation method with triangular fuzzy number, World Appl. Sci. J., 11, 7, 871-876, (2010)
[15] Rezvani, S., Multiplication operation on trapezoidal fuzzy numbers, J. Phys.Sci., 15, 17-26, (2011) · Zbl 1266.03064
[16] Rezvani, S., A new method for ranking in perimeters of two generalized trapezoidal fuzzy numbers, Int. J Appl. Oper. Res., 2, 3, 83-90, (2012)
[17] Rezvani, S., A new approach ranking of exponential trapezoidal fuzzy numbers, J. Phys. Sci., 16, 45-57, (2012)
[18] Rezvani, S., Ranking method of trapezoidal intuitionistic fuzzy numbers, Ann. Fuzzy Math. Inf., 5, 3, 515-523, (May 2013) · Zbl 1302.03070
[19] Rezvani, S., Ranking generalized trapezoidal fuzzy numbers with Euclidean distance by the incentre of centroids, Math. Aeterna., 3, 2, 103-114, (2013) · Zbl 1311.03076
[20] Rezvani, S., Representation of trapezoidal fuzzy numbers with shape function, Ann. Fuzzy Math. Inform., 8, 1, 89-112, (2014) · Zbl 1319.03057
[21] Rezvani, S., A new method for ranking fuzzy numbers with using trd distance based on mean and standard deviation, Int. J. Mech. Electr. Comput. Technol., 4, 12, 840-856, (2014)
[22] Rezvani, S., Representation of generalized triangular fuzzy sets, Int. J. Phys. Math. Sci., 5, 1, 41-52, (2015)
[23] Rezvani, S., A new similarity measure of generalized fuzzy numbers based on left and right apex angles (i), Palestine J. Math., 4, 1, 117-126, (2015) · Zbl 1389.03016
[24] Saneifard, R.; Saneifard, R., A modified method for defuzzification by probability density function, J. Appl. Sci. Res., 7, 2, 102-110, (2011) · Zbl 1235.93148
[25] Singh, Pushpinder, Ranking of generalized trapezoidal fuzzy numbers based on rank, mode, divergence and spread, Turkish J. Fuzzy Syst. (eISSN: 1309û1190), 1, 2, 141-152, (2010)
[26] Wang, Y. J.; Lee, H. S., The revised method of ranking fuzzy numbers with an area between the centroid and original points, Comput. Math. Appl., 55, 2033-2042, (2008) · Zbl 1137.62313
[27] Zadeh, L. A., Fuzzy set, Inf. Control, 8, 3, 338-353, (1965) · Zbl 0139.24606
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