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Ranking Fuzzy Numbers Based On Epsilon-Deviation Degree

Authors: Vincent F. Yu, Ha Thi Xuan Chi


Nejad and Mashinchi (2011) proposed a revision for ranking fuzzy numbers based on the areas of the left and the right sides of a fuzzy number. However, this method still has some shortcomings such as lack of discriminative power to rank similar fuzzy numbers and no guarantee the consistency between the ranking of fuzzy numbers and the ranking of their images. To overcome these drawbacks, we propose an epsilon-deviation degree method based on the left area and the right area of a fuzzy number, and the concept of the centroid point. The main advantage of the new approach is the development of an innovative index value which can be used to consistently evaluate and rank fuzzy numbers. Numerical examples are presented to illustrate the efficiency and superiority of the proposed method.

Keywords: Ranking fuzzy numbers, Centroid, Deviation degree.

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[1] R. Jain, Decisionmaking in the Presence of Fuzzy Variables, IEEE Transactions on Systems, Man and Cybernetics, 6 (1976) 689-703.
[2] S. Abbasbandy, B. Asady, Ranking of fuzzy numbers in sign distance, Information Sciences, 176 (2006) 2405-2416.
[3] S. Abbasbandy, T. Hajjari, A new approach for ranking of trapezoidal fuzzy numbers, Computers & amp; Mathematics with Applications, 57 (2009) 413-419.
[4] B. Asady, A. Zendehnam, Ranking fuzzy numbers by distance minimization, Applied Mathematical Modelling, 31 (2007) 2589-2598.
[5] S. M. Baas, H. Kwakernaak, Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, 13, (1977) 47-58.
[6] J. F. Baldwin, N. C. F. Guild, Comparison of fuzzy sets on the same decision space, Fuzzy Sets and Systems, 2 (1979) 213-231.
[7] D. Dubois, H. Prade, Operations on fuzzy numbers, International Journal of Systems Science, 9, (1978) 613-626.
[8] E. Kerre, E., The use of fuzzy set theory in electrocardiological diagnostics, in: MM. Gupta and E. Sanchez, Eds, Approximate Reasoning in Decision Analysis (North-Holland, Amsterdam, 1982), (1982), 277-282.
[9] A. Kumar, P. Singh, A. Kaur, Ranking of generalized Exponential Fuzzy Numbers using Integral Value Approach, International Journal of Advances in Soft Computing and Its Applications, 2 (2010) 209-220.
[10] H. Xiaowei, D. Hepu, An Area-based Approach to Ranking Fuzzy Numbers in Fuzzy Decision Making, Journal of Computational Information Systems, 7 (2011) 3333-3342.
[11] R. R. Yager, Ranking fuzzy subsets over the unit interval, in: Decision and Control including the 17th Symposium on Adaptive Processes, 1978 IEEE Conference on, 1978, pp. 1435-1437. 12] S.-Y. Chou, L. Q. Dat, V. F. Yu, A revised method for ranking fuzzy numbers using maximization set and minimization set, Computers & Industrial engineering, 61 (2011) 1342-1348.
[13] C. H. Cheng, A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 95 (1998) 307-317.
[14] T. C. Chu, C. T. Tsao, Ranking fuzzy numbers with an area between the centroid point and original point, Computers & Mathematics with Applications, 43 (2002) 111-117.
[15] E. S. Lee, R. J. L,, Comparison of fuzzy numbers based on the probability measure of fuzzy events, Computers & Mathematics with Applications, 15 (1988) 887-896.
[16] S. Mabuchi, An approach to the comparison of fuzzy subsets with an & alpha;-cut dependent index, Systems, Man, and Cybernetics, IEEE Transactions on, 18 (1988) 264-272.
[17] N. Ramli, D. Mohamad, A comparative analysis of centroid methods in ranking fuzzy numbers, European Journal of Scientific Research, 28 (2009) 492-501.
[18] Z. X. Wang, Y. J. Liu, Z. P. Fan, B. Feng, Ranking L-R fuzzy number based on deviation degree, Information Sciences, 179 (2009) 2070-2077.
[19] A. M. Nejad, M. Mashinchi, Ranking fuzzy number based on the areas on the left and on the right sides of the fuzzy number, Computers & Mathematics with Applications, 61 (2011) 431-442.
[20] B. Asady, The revised method of ranking LR fuzzy number based on deviation degree, Expert Systems with Applications, 37 (2010) 5056-5060.
[21] T. Hajjari, S. Abbasbandy, a note on "The revised method of ranking LR fuzzy number based on deviation degree, Expert Systems with Applications, 38 (2011) 13491-13492.
[22] T. Hajjari, On Deviation Degree Methods for Ranking Fuzzy Numbers, Australian Journal of Basic and Applied Sciences, 5 (2011) 750-758.
[23] S.-H. Chen, Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, 17 (1985) 113-129.
[24] D. Dubois, H. Parade, Ranking fuzzy numbers in the setting of possibility theory, Information Sciences, 30 (1983) 183-224.
[25] B. Matarazzo, G. Munda, New approaches for the comparison of L-P fuzzy numbers: a theoretical and operational analysis, Fuzzy Sets and Systems, 118 (2001) 407-418.
[26] C.-H . Cheng, D.-L. Mon, Fuzzy system reliability analysis by interval of confidence, Fuzzy Sets and Systems, 56 (1993) 29-35.
[27] A. Kaufmann, M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications 2nd ed. ed., Van Nostrand Reinhold, New York, 1991.
[28] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338-353.
[29] H. B. Mitchell, P. A. Schaefer, On ordering fuzzy numbers, International Journal of Intelligent Systems, 15 (2000) 981-993.
[30] Z.-X. Wang, Y.-J. Liu, Z.-P. Fan, B. Feng, Ranking L-R fuzzy number based on deviation degree, Information Sciences, 179 (2009) 2070-2077.
[31] B. Asady, Revision of distance minimization method for ranking of fuzzy numbers, Applied Mathematical Modelling, 35 (2011) 1306-1313.