Document Type : Original Article
In this paper, we presented for the first time a multidimensional scaling approach to find the scaling as well as the ranking of triangular fuzzy numbers. Each fuzzy number was represented by a row in a matrix, and then found the configuration points (scale points) which represent the fuzzy numbers in . Since these points are not uniquely determined, then we presented different techniques to reconfigure the points to compare them with other methods. The results showed the ability of ranking fuzzy numbers.
- Ali E., Verdegay, J. L. and Garg, H. Signed distance ranking based approach for solving bounded interval-valued fuzzy numbers linear programming problems. International Journal of Intelligent Systems, 2019, 34(2), 2055-2076, doi: 10.1002/int.22130.
- Borg, I. and Groenen, P. J. F. Modern Multidimensional Scaling: Theory and Applications, 2005, Springer; 2nd edition.
- Asady, B. and Zendehnam, A. Ranking fuzzy numbers by distance minimization. Applied Mathematical Modelling, 2007, 31(11), 2589-2598.
- Cheng, C.-H. A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 1998, 95(3), 307– 317.
- Dubois, D. and Prade, H. The mean value of a fuzzy number, Fuzzy Sets and Systems, 1987, 24(3), 279–300.
- Lee, E. S. and Li, R.-J. Comparison of fuzzy numbers based on the probability measure of fuzzy events, Computers and Mathematics with Applications, 1988, 15(10), 887–896.
- Luengo, E. L. Fuzzy mean-variance portfolio selection problems, Advanced Modeling and optimization, 2010, 12(3), 400-410.
- Bortolan, G. and Degani, R. A review of some methods for ranking fuzzy subsets, Fuzzy Sets and Systems, 1985, 15(1), 1–19.
- Zadeh, L. A. Fuzzy sets, Information and Control, 1965, 8(3), 338–353.
- Jahantigh, M. A., Hajighasemi, S. and Allahviranloo, T. A fuzzy distance measure for generalized fuzzy numbers, Data Envelopment Analysis and Decision Science, 2014, 1-11.
- Brunelli, M. and Mezei, J. How different are ranking methods for fuzzy numbers? A numerical study, International Journal of Approximate Reasoning, 2013, 54, 627–639.
- Parandin, N. and Fariborzi, M. A. Ranking of fuzzy numbers by distance method, Journal of Applied Mathematics, 2008, 5(19), 47-55.
- PhaniBushan and RaoPeddia. Defuzzification method for ranking fuzzy numbers based on centroids and maximizing and minimizing set, Decision Science Letters, 2019, 8, 411–428.
- Phani Bushan Rao, P. and Ravi Shankar, N. Ranking fuzzy numbers with a distance method using Circumcenter of centroids and an index of modality, Advances in Fuzzy Systems, (2011).
- Jain, R. Decision making in the presence of fuzzy variables, IEEE Transactions on Systems, Man and Cybernetics, 1976, 6(10), 698–703.
- Rencher, A. C. Multivariate Statistical Inference and Applications, 2009,Wiley Series in Probability and Statistics.
- Yager, R. R. A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 1981, 24(2), 143–161.
- Chen, S.-H. Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, 1985, 17(2), 113–129.
- Allahviranloo, T. and Saneifard, R. Defuzzification method for ranking fuzzy numbers based on center of gravity, Iranian Journal of Fuzzy Systems, 2012, 9(6), 57-67.
- Chu, T.-C. and Tsao, C.-T. Ranking fuzzy numbers with an area between the centroid point and original point, Computers & Mathematics with Applications, 2002, 43, 111–117.
- Chang, W. Ranking of fuzzy utilities with triangular membership function, Proceeding of the International conference on policy analysis information system, 1981, 105, 263-272.
- Wang, Y. M. and Luo, Y. Area ranking of fuzzy numbers based on positive and negative idea points, Computers and Mathematics with Application, 2009, 58, 1769-1779.
- Bai Y., Wang D. Fundamentals of Fuzzy Logic Control — Fuzzy Sets, Fuzzy Rules and Defuzzifications, 2006, In: Bai Y., Zhuang H., Wang D. (eds) Advanced Fuzzy Logic Technologies in Industrial Applications. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-84628-469-4_2.