How to cite this paper
Sadi-Nezhad, S & Shahnazari-Shahrezaei, P. (2013). Ranking fuzzy numbers using preference ratio: A utility function approach.Decision Science Letters , 2(3), 149-162.
Refrences
Abbasbandy, S., & Asady, B. (2006). Ranking of fuzzy numbers by sign distance. Information Science, 176(16), 2405-2416.
Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications, 57(3), 413-419.
Asady, B., & Zendehnam, M. (2007). Ranking fuzzy numbers by distance minimization. Applied Mathematical Modeling, 31(11), 2589-2598.
Asady, B. (2010). The revised method of ranking LR fuzzy number based on deviation degree. Expert Systems with Applications, 37(7), 5056-5060.
Bortolan, G., & Degani, R. (1985). A review of some methods for ranking fuzzy subsets. Fuzzy Sets and Systems, 15(1), 1-19.
Chen, S.H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems, 17(2), 113-129.
Chen, S.J., & Hwang, C.L. (1992). Fuzzy Multiple Attribute Decision Making. Springer, Berlin.
Chen, C.B., & Klein, C.M. (1997). A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Transaction on Systems Man and Cybernetics, 27(1), 26-35.
Chen, C.B., & Klein, C.M. (1997). An efficient approach to solving fuzzy MADM problems. Fuzzy Sets and Systems, 88(1), 51-67.
Chen, C.C., & Tang, H.C. (2008). Ranking nonnormal p-norm trapezoidal fuzzy numbers with integral value. Computers and Mathematics with Applications, 56(9), 2340-2346.
Chen, S.M., & Chen, J.H. (2009). Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications, 36(3), 6833-6842.
Chen, S.M., & Wang, C.H. (2009). Fuzzy risk analysis based on ranking fuzzy numbers using ?-cuts, belief features and signal/noise ratios. Expert Systems with Applications, 36(3), 5576-5581.
Choobineh, F., & Li, H. (1993). An index for ordering fuzzy numbers. Fuzzy Sets and Systems, 54(3), 287-294.
Chu, T., & Tsao, C. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers and Mathematics with Applications, 43(1), 111-117.
Delgado, M., Verdegay, J.L., & Villa, M.A. (1988). A procedure for ranking fuzzy numbers using fuzzy relations. Fuzzy Sets and Systems, 26(1), 49-62.
Fortemps, P., & Roubens, M. (1996). Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems, 82(3), 319-330.
Huijun, S., & Jianjun, W. (2006). A new approach for ranking fuzzy numbers based on fuzzy simulation analysis method. Applied Mathematics and Computation, 174(1), 755-767.
Kim, K., & Park, K.S. (1990). Ranking fuzzy numbers with index of optimism. Fuzzy Sets and Systems, 35(2), 143-150.
Lee, E.S., & Li, R.J. (1988). Comparison of fuzzy numbers based on the probability measure of fuzzy events. Computers and Mathematics with Applications, 15(10), 887-896.
Lee, L.W., & Chen, S.M. (2008). Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations. Expert Systems with Applications, 34(4), 2763-2771.
Liou, T.S., & Wang, M.J. (1992). Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems, 50(3), 247-255.
Liu, H.K., Wu, B., & Liu, M.L. (2008). Investors’ preference order of fuzzy numbers. Computers and Mathematics with Applications, 55(11), 2623-2630.
Ma, L.C., & Li, H.L. (2008). A fuzzy ranking method with range reduction techniques. European Journal of Operational Research, 184(3), 1032-1043.
Mabuchi, G. (1988). An approach to the comparison of fuzzy subsets with an ?-cut dependent index. IEEE Transactions on Systems Man and Cybernetics, 18(2), 264-272.
Modarres, M., & Sadi-Nezhad, S. (2001). Ranking fuzzy numbers by preference ratio. Fuzzy Sets and Systems, 118(3), 429-436.
Modarres, M., & Sadi-Nezhad, S. (2005). Fuzzy simple additive weighting method by preference ratio. Intelligent Automation and Soft Computing, 11(4), 235-244.
Sadi-Nezhad, S., & Ghaleh Assadi, R. (2008). Preference ratio-based maximum operator approximation and its application in fuzzy flow shop scheduling. Applied soft computing, 8(1), 759-766.
Sadi-Nezhad, S., & Khalili Damghani, K. (2010). Application of a fuzzy TOPSIS method base on modified preference ratio and fuzzy distance measurement in assessment of traffic police centers performance. Applied soft computing, 10(4), 1028-1039.
Shieh, B.S. (2007). An approach to centroids of fuzzy numbers. International Journal of Fuzzy Systems, 9(1), 51-54.
Tseng, T.Y., & Klein, C.M. (1989). New algorithm for the ranking procedure in fuzzy decision making. IEEE Transactions on System Man and Cybernetics, 19(5), 1289-1296.
Wang, Y.M., Yang, J.B., Xu, D.L., & Chin, K.S. (2006). On the centroids of fuzzy numbers. Fuzzy Sets and Systems, 157(7), 919-926.
Wang, Y.J., & Lee, S.H. (2008). The revised method of ranking fuzzy numbers with an area between the centroid and original points. Computers and Mathematics with Applications, 55(9), 2033-2042.
Wang, Y.M. (2009). Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets. Computers & Industrial Engineering, 57(1), 228-236.
Wang, Y.M., & Luo, Y. (2009). Area ranking of fuzzy numbers based on positive and negative ideal points. Computers and Mathematics with Applications, 58(9), 1769-1779.
Wang, Z.X., Liu, Y.J., Fan, Z.P., & Feng, B. (2009). Ranking LR fuzzy number based on deviation degree. Information Sciences, 179(13), 2070-2077.
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.
Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications, 57(3), 413-419.
Asady, B., & Zendehnam, M. (2007). Ranking fuzzy numbers by distance minimization. Applied Mathematical Modeling, 31(11), 2589-2598.
Asady, B. (2010). The revised method of ranking LR fuzzy number based on deviation degree. Expert Systems with Applications, 37(7), 5056-5060.
Bortolan, G., & Degani, R. (1985). A review of some methods for ranking fuzzy subsets. Fuzzy Sets and Systems, 15(1), 1-19.
Chen, S.H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems, 17(2), 113-129.
Chen, S.J., & Hwang, C.L. (1992). Fuzzy Multiple Attribute Decision Making. Springer, Berlin.
Chen, C.B., & Klein, C.M. (1997). A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Transaction on Systems Man and Cybernetics, 27(1), 26-35.
Chen, C.B., & Klein, C.M. (1997). An efficient approach to solving fuzzy MADM problems. Fuzzy Sets and Systems, 88(1), 51-67.
Chen, C.C., & Tang, H.C. (2008). Ranking nonnormal p-norm trapezoidal fuzzy numbers with integral value. Computers and Mathematics with Applications, 56(9), 2340-2346.
Chen, S.M., & Chen, J.H. (2009). Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications, 36(3), 6833-6842.
Chen, S.M., & Wang, C.H. (2009). Fuzzy risk analysis based on ranking fuzzy numbers using ?-cuts, belief features and signal/noise ratios. Expert Systems with Applications, 36(3), 5576-5581.
Choobineh, F., & Li, H. (1993). An index for ordering fuzzy numbers. Fuzzy Sets and Systems, 54(3), 287-294.
Chu, T., & Tsao, C. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers and Mathematics with Applications, 43(1), 111-117.
Delgado, M., Verdegay, J.L., & Villa, M.A. (1988). A procedure for ranking fuzzy numbers using fuzzy relations. Fuzzy Sets and Systems, 26(1), 49-62.
Fortemps, P., & Roubens, M. (1996). Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems, 82(3), 319-330.
Huijun, S., & Jianjun, W. (2006). A new approach for ranking fuzzy numbers based on fuzzy simulation analysis method. Applied Mathematics and Computation, 174(1), 755-767.
Kim, K., & Park, K.S. (1990). Ranking fuzzy numbers with index of optimism. Fuzzy Sets and Systems, 35(2), 143-150.
Lee, E.S., & Li, R.J. (1988). Comparison of fuzzy numbers based on the probability measure of fuzzy events. Computers and Mathematics with Applications, 15(10), 887-896.
Lee, L.W., & Chen, S.M. (2008). Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations. Expert Systems with Applications, 34(4), 2763-2771.
Liou, T.S., & Wang, M.J. (1992). Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems, 50(3), 247-255.
Liu, H.K., Wu, B., & Liu, M.L. (2008). Investors’ preference order of fuzzy numbers. Computers and Mathematics with Applications, 55(11), 2623-2630.
Ma, L.C., & Li, H.L. (2008). A fuzzy ranking method with range reduction techniques. European Journal of Operational Research, 184(3), 1032-1043.
Mabuchi, G. (1988). An approach to the comparison of fuzzy subsets with an ?-cut dependent index. IEEE Transactions on Systems Man and Cybernetics, 18(2), 264-272.
Modarres, M., & Sadi-Nezhad, S. (2001). Ranking fuzzy numbers by preference ratio. Fuzzy Sets and Systems, 118(3), 429-436.
Modarres, M., & Sadi-Nezhad, S. (2005). Fuzzy simple additive weighting method by preference ratio. Intelligent Automation and Soft Computing, 11(4), 235-244.
Sadi-Nezhad, S., & Ghaleh Assadi, R. (2008). Preference ratio-based maximum operator approximation and its application in fuzzy flow shop scheduling. Applied soft computing, 8(1), 759-766.
Sadi-Nezhad, S., & Khalili Damghani, K. (2010). Application of a fuzzy TOPSIS method base on modified preference ratio and fuzzy distance measurement in assessment of traffic police centers performance. Applied soft computing, 10(4), 1028-1039.
Shieh, B.S. (2007). An approach to centroids of fuzzy numbers. International Journal of Fuzzy Systems, 9(1), 51-54.
Tseng, T.Y., & Klein, C.M. (1989). New algorithm for the ranking procedure in fuzzy decision making. IEEE Transactions on System Man and Cybernetics, 19(5), 1289-1296.
Wang, Y.M., Yang, J.B., Xu, D.L., & Chin, K.S. (2006). On the centroids of fuzzy numbers. Fuzzy Sets and Systems, 157(7), 919-926.
Wang, Y.J., & Lee, S.H. (2008). The revised method of ranking fuzzy numbers with an area between the centroid and original points. Computers and Mathematics with Applications, 55(9), 2033-2042.
Wang, Y.M. (2009). Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets. Computers & Industrial Engineering, 57(1), 228-236.
Wang, Y.M., & Luo, Y. (2009). Area ranking of fuzzy numbers based on positive and negative ideal points. Computers and Mathematics with Applications, 58(9), 1769-1779.
Wang, Z.X., Liu, Y.J., Fan, Z.P., & Feng, B. (2009). Ranking LR fuzzy number based on deviation degree. Information Sciences, 179(13), 2070-2077.
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.