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A novel method for ranking generalized fuzzy numbers with two different heights and its application in fuzzy risk analysis. (English) Zbl 1458.03033

Summary: Due to the large use of fuzzy numbers, the ranking of these numbers is very important. In this paper, we propose a new method for ranking generalized fuzzy numbers with different left and right heights. The proposed method, at first obtains the centers of gravity of fuzzy numbers and left and right side crisp numbers; then by computing left and right areas associated with them, ranks the fuzzy numbers. The proposed method can overcome the flaws and defects of some ranking methods, and the provided examples are evidence of this. Finally this method is applied to the fuzzy risk analysis problem.

MSC:

03E72 Theory of fuzzy sets, etc.
91B06 Decision theory
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[1] S. Abbasbandy, T. Hajjari,A new approach for ranking of trapezoidal fuzzy numbers, Computers and Mathematics with Applications,57(2009), 413-419. · Zbl 1165.03337
[2] S. H. Chen,Ranking fuzzy numbers with maximizing and minimizing set, Fuzzy Sets and Systems,17(1985), 113-129. · Zbl 0618.90047
[3] S. J. Chen, S. M. Chen,Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, IEEE Transactions on Fuzzy Systems,11(2003), 45-56.
[4] J. H. Chen, S. M. Chen,A new method for ranking generalized fuzzy numbers for handling fuzzy risk analysis problems, Proceedings of the 9th Joint International Conference on Information Sciences(JCIS), 2006.
[5] S. M. Chen, J. H. Chen,Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads, Expert Systems with Applications,36(3) (2009), 6833-6842.
[6] S. M. Chen, A. Munif, G. S. Chen, H. C. Liu, B. C. Kuo,Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights, Expert Systems with Applications,39(2012), 6320-6334.
[7] S. M. Chen, K. Sanguansat,Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers, Expert Systems with Applications,38(2011), 2163-2171.
[8] C. H. Cheng,A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems,95(1998), 307-317. · Zbl 0929.91009
[9] T. C. Chu, C. T. Tsao,Ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications,43(2002), 111-117. · Zbl 1113.62307
[10] D. Dubois, H. Prade,The mean value of a fuzzy number, Fuzzy Sets and Systemas,24(1978), 279-300. · Zbl 0634.94026
[11] R. Ezzati, T. Allahviranloo, S. Khezerloo, M. Khezerloo,An approach for ranking of fuzzy numbers, Expert Systems with Applications,39(2012), 690-695.
[12] T. Hajjari,Fuzzy risk analysis based on ranking of fuzzy numbers via new magnitude method, Iranian Journal of Fuzzy Systems,12(2015), 17-29. · Zbl 1336.91033
[13] R. Jain,Decision-making in the presence of fuzzy variables, IEEE Transactions on Systems, Man, and Cybernetics, 6(1976), 698-703. · Zbl 0337.90005
[14] W. Jiang,An improved method to rank generalized fuzzy numbers with different left heights and right heights, Journal of Intelligent and Fuzzy Systems,28(2015), 2343-2355. · Zbl 1414.91108
[15] B. Khorshidi,A new method for finding the center of gravity of polygons, Journal of Geometry,96(2009), 81-91. · Zbl 1201.52001
[16] T. S. Liou, M. J. Wang,Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems,50(1992), 247-255. A novel method for ranking generalized fuzzy numbers with two different heights and its application . . .91 · Zbl 1229.03043
[17] S. Murakami, S. Maeda, S. Imamura,Fuzzy decision analysis on the development of centralized regional energy control system, IFAC Symptoms on Fuzzy Inform Knowledge Representation and Decision Anal., (1983) 363-368.
[18] K. Patra, S. K Mondal,Risk analysis in diabetes prediction based on a new approach of ranking of generalized trapezoidal fuzzy numbers, Cybernetics Systems International Journal,43(8) (2012), 623-650. · Zbl 1331.62433
[19] Y. J. Wang, H. S. Lee,The revised method of ranking fuzzy numbers with an area between the centroid and original points, Computers and Mathematics with Applications,55(2008), 2033-2042. · Zbl 1137.62313
[20] Y. M. Wang, Y. Luo,Area ranking of fuzzy numbers based on positive and negative ideal points, Computers and Mathematics with Applications,59(2009), 1769-1779. · Zbl 1189.03061
[21] D. Wu, X. Liu, F. Xue, H. Zheng, Y. Shou, W. Jiang,Fuzzy risk analyses based on a new method for ranking generalized fuzzy numbers, Iranian Journal of Fuzzy Systems,15(2018), 117-139. · Zbl 1422.91210
[22] R. R. Yager,Ranking fuzzy subsets over the unit interval, In Proceeding of the 17th IEEE International Conference on Decision and Control San Diego, CA, USA, 1978. · Zbl 0429.04009
[23] J. S. Yao, K. Wu,Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems,116(2000), 275-288. · Zbl 1179.62031
[24] L. A. Zadeh,Fuzzy sets, Information Control,8(1965), 338-353. · Zbl 0139.24606
[25] D. Zhang,On generalized fuzzy numbers, Iranian Journal of Fuzzy Systems,1(2019), 61-73 · Zbl 1429.03187
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