عنوان مقاله [English]
Since much of human reasoning is based on imprecise, vague and subjective values, most of the decision-making processing, in reality, requires handling and evaluation of fuzzy numbers. Ranking fuzzy numbers are one of the very important research topics in fuzzy set theory because it is a base of decision-making in applications. Although so far, many methods for ranking of fuzzy numbers have been discussed broadly, most of them contained some shortcomings, such as the requirement of complicated calculations, inconstancy with human intuition and indiscrimination. In this paper, we introduce a new method by using the affine combination on the circumcenter. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers. The advantages of the new proposed are that it can be applied for most of the defuzzification and the calculation is far simple and easy than previous methods. The effectiveness of the proposed method and its advantages is demonstrated by numerical examples, comprehensive comparing the different ranking method with this method and also its benefits will be illustrated by the numerical example, as well as a case study on supply chain management.
Abbasbandy, S., & Asady, B. (2002). Note on A new approach for defuzzification. Fuzzy sets and systems, 128(1), 131-132.
Abbasbandy, S., & Asady, B. (2006). Ranking of fuzzy numbers by sign distance. Information sciences, 176(16), 2405-2416.
Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers & mathematics with applications, 57(3), 413-419.
Azadi, M., Jafarian, M., Saen, R. F., & Mirhedayatian, S. M. (2015). A new fuzzy DEA model for evaluation of efficiency and effectiveness of suppliers in sustainable supply chain management context. Computers & operations research, 54, 274-285.
Bowlin, W. F. (1998). Measuring performance: An introduction to data envelopment analysis (DEA). The journal of cost analysis, 15(2), 3-27.
De Campos Ibáñez, L. M., & Muñoz, A. G. (1989). A subjective approach for ranking fuzzy numbers. Fuzzy sets and systems, 29(2), 145-153.
Sarrico, C. S. (2001). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Journal of the operational research society, 52(12), 1408-1409.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2, 429–444.
Cheng, C. H. (1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy sets and systems, 95(3), 307-317.
Chen, L. H., & Lu, H. W. (2001). An approximate approach for ranking fuzzy numbers based on left and right dominance. Computers & mathematics with applications, 41(12), 1589-1602.
Chen, S. H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy sets and systems, 17(2), 113-129.
Chu, T. C., & Tsao, C. T. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers & mathematics with applications, 43(1-2), 111-117.
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the royal statistical society. Series A (General), 120(3), 253-290.
Fortemps, P., & Roubens, M. (1996). Ranking and defuzzification methods based on area compensation. Fuzzy sets and systems, 82(3), 319-330.
Hatami-Marbini, A., Ebrahimnejad, A., & Lozano, S. (2017). Fuzzy efficiency measures in data envelopment analysis using lexicographic multiobjective approach. Computers & industrial engineering, 105, 362-376.
Kao, C. (2006). Interval efficiency measures in data envelopment analysis with imprecise data. European journal of operational research, 174(2), 1087-1099.
Liou, T. S., & Wang, M. J. J. (1992). Ranking fuzzy numbers with integral value. Fuzzy sets and systems, 50(3), 247-255.
Rao, P., & Shankar, N. R. (2011). Ranking fuzzy numbers with a distance method using circumcenter of centroids and an index of modality. Advances in fuzzy systems, 2011, 3.
Saati, S. M., Memariani, A., & Jahanshahloo, G. R. (2002). Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy optimization and decision making, 1(3), 255-267.
Wang, Y. M., Luo, Y., & Liang, L. (2009a). Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert systems with applications, 36(3), 5205-5211.
Wang, Z. X., Liu, Y. J., Fan, Z. P., & Feng, B. (2009b). Ranking L–R fuzzy number based on deviation degree. Information sciences, 179(13), 2070-2077.
Yager, R. R. (1981). A procedure for ordering fuzzy subsets of the unit interval. Information sciences, 24(2), 143-161.