Document Type : Review Article
Authors
Abstract
Jaccard index similarity measure which applies the extension principle approach in obtaining the fuzzy maximum and fuzzy minimum has been proposed in ranking the fuzzy numbers. However, the extension principle used is only applicable to normal fuzzy numbers and, therefore, fails to rank the non-normal fuzzy numbers. Apart from that, the extension principle does not preserve the type of membership function of the fuzzy numbers and also involves laborious mathematical operations. In this paper, a simple vertex fuzzy arithmetic operation, namely function principle, is applied. This paper also proposes the degree of optimism concept in aggregating the fuzzy evidence. The method is capable to rank both normal and non-normal fuzzy numbers in a simpler manner with all types of decision makers’ perspective.
Keywords
[1] R. Jain, “Decision making in the presence of fuzzy variables”, IEEE Trans. Systems Man Cybernetics, Vol.6, pp. 698-703, (1976)
[2] M. Setnes, and V. Cross, “Compatibility based ranking of fuzzy numbers”, Proc. Fuzzy Information Processing Society, NAFIPS ’97, pp. 305-310, (1997)
[3] J. N. Sheen, “Fuzzy financial decision-making: Load management programs case study”, IEEE Transactions on Power Systems, Vol. 20(4), pp. 1808-1817, (2005)
[4] S. H. Chen, “Operations on fuzzy numbers with function principle”, Tamkang Journal of Management Science, Vol. 6 (1), pp. 13-26, (1985)
[5] C. H. Hsieh, and S. H. Chen, “A model and algorithm of fuzzy product positioning”, Information Sciences, Vol. 121, pp. 61-82, (1999)
[6] S. H. Chen, C. C. Wang, and S. M. Chang, “Fuzzy economic production quality model for items with imperfect quality”, International Journal of Innovative Computing, Information and Control, Vol. 3 (1), pp. 85-95, (2007).
[7] S. H. Chen, and C. C. Wang, “Backorder fuzzy inventory model under function principle”, Information Sciences, Vol. 95, pp. 71-79, (1996)
[8] S. H. Chen, S. T. Wang, and C. C. Chang, “Optimization of fuzzy production inventory model with repairable defective products under crisp or fuzzy production quantity”, International Journal of Operations Research, Vol. 2(2), pp. 31-37, (2005)
[9] D. Dubois, and H. Prade, “Fuzzy Sets and Systems: Theory and Applications”, New York: Academic Press, Inc., (1980)
[10] L.A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning -1”, Information Sciences, Vol. 8(3), pp. 199-249, (1975)
[11] A. Tversky, “Features of similarity”, Psychological Review, Vol. 84, pp. 327-352, (1977)
[12] J. S. Yao, and K. Wu, “Ranking fuzzy numbers based on decomposition principle and signed distance”, Fuzzy Sets and Systems, Vol. 116, pp. 275-288, (2000)
[13] L. H. Chen, and H. W. Lu, “An approximate approach for ranking fuzzy numbers based on left and right dominance”, Computers and Mathematics with Applications, Vol. 41, pp. 1589-1602, (2001)
[14] S. J. Chen, and S. M. Chen, “Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers”, Applied Intelligence, Vol. 26(1), pp. 1-11, (2007)
[15] L. H. Chen, and H. W. Lu, “The preference order of fuzzy numbers”, Computers and Mathematics with Applications, Vol. 44, pp. 1455-1465, (2002)
[16] C. H. Cheng, “A new approach for ranking fuzzy numbers by distance method”, Fuzzy Sets and Systems, Vol. 95, pp. 307-317, (1998)
[17] T. C. Chu, and C. T. Tsao, “Ranking fuzzy numbers with an area between the centroid point and original point”, Computers and Mathematics with Applications, Vol. 43, pp. 111-117, (2002)
[18] S. J. Chen, and S. M. Chen, “A new method for handling multicriteria fuzzy decision making problems using FN-IOWA operators”, Cybernetics and Systems, Vol. 34, pp. 109-137, (2003)
[19] S. Abbasbandy, and B. Asady, “Ranking of fuzzy numbers by sign distance”, Information Sciences, Vol. 176, pp. 2405-2416, (2006)
[20] B. Asady, and A. Zendehnam, “Ranking fuzzy numbers by distance minimization”, Applied Mathematical Modeling, Vol. 31, pp. 2589-2598, (2007)
[21] Y. J. Wang, and H. S. Lee, “The revised method of ranking fuzzy numbers with an area between the centroid and original points”, Computers and Mathematics with Applications, Vol. 55, pp. 2033-2042, (2008)
[22] V. V. Cross, and T. A. Sudkamp, “Similarity and Compatibility in Fuzzy Set Theory”, New York: Physica-Verlag, (2002)
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