Wang, Ying-Ming; Yang, Jian-Bo; Xu, Dong-Ling; Chin, Kwai-Sang On the centroids of fuzzy numbers. (English) Zbl 1099.91035 Fuzzy Sets Syst. 157, No. 7, 919-926 (2006). Summary: In a paper by C.-H. Cheng [“A new approach for ranking fuzzy numbers by distance method”, Fuzzy Sets Syst. 95, 307–317 (1998; Zbl 0929.91009)], a centroid-based distance method was suggested for ranking fuzzy numbers, both normal and non-normal, where the fuzzy numbers are compared and ranked in terms of their Euclidean distances from their centroid points to the origin. It is found that the centroid formulae provided by the above paper are incorrect and have led to some misapplications. We present the correct centroid formulae for fuzzy numbers and justify them from the viewpoint of analytical geometry. A numerical example demonstrates that Cheng’s formulae can significantly alter the result of the ranking procedure. Cited in 1 ReviewCited in 50 Documents MSC: 91B06 Decision theory 03E72 Theory of fuzzy sets, etc. Keywords:normal fuzzy numbers; non-normal fuzzy numbers; centroid; ranking Citations:Zbl 0929.91009 PDFBibTeX XMLCite \textit{Y.-M. Wang} et al., Fuzzy Sets Syst. 157, No. 7, 919--926 (2006; Zbl 1099.91035) Full Text: DOI References: [1] S. Abbasbandy, B. Asady, Ranking of fuzzy numbers by sign distance, Inform. Sci., in press.; S. Abbasbandy, B. Asady, Ranking of fuzzy numbers by sign distance, Inform. Sci., in press. · Zbl 1293.62008 [2] Cheng, C. H., A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 95, 307-317 (1998) · Zbl 0929.91009 [3] Chu, T. C.; Tsao, C. T., Ranking fuzzy numbers with an area between the centroid point and original point, Comput. Math. Appl., 43, 111-117 (2002) · Zbl 1113.62307 [4] Dubois, D.; Prade, H., Operations on fuzzy numbers, Internat. J. Syst. Sci., 9, 613-626 (1978) · Zbl 0383.94045 [5] S. Murakami, H. Maeda, S. Lmamura, Fuzzy decision analysis on the development of centralized regional energy control system, Preprints IFAC Conf. on Fuzzy Information, Knowledge Representation and Decision Analysis, 1983, pp. 353-358.; S. Murakami, H. Maeda, S. Lmamura, Fuzzy decision analysis on the development of centralized regional energy control system, Preprints IFAC Conf. on Fuzzy Information, Knowledge Representation and Decision Analysis, 1983, pp. 353-358. [6] H. Pan, C.H. Yeh, Fuzzy project scheduling, Proc. 12th IEEE Internat. Conf. on Fuzzy Systems, 2003, pp. 755-760.; H. Pan, C.H. Yeh, Fuzzy project scheduling, Proc. 12th IEEE Internat. Conf. on Fuzzy Systems, 2003, pp. 755-760. [7] Pan, H.; Yeh, C. H., A metaheuristic approach to fuzzy project scheduling, (Palade, V.; Howlett, R. J.; Jain, L. C., Knowledge-based Intelligent Information and Engineering Systems (2003), Springer: Springer Berlin, Heidelberg), 1081-1087 [8] R.R. Yager, Ranking fuzzy subsets over the unit interval, Proc. 17th IEEE Conf. on Cybernetics and Society, 1978, pp. 921-925.; R.R. Yager, Ranking fuzzy subsets over the unit interval, Proc. 17th IEEE Conf. on Cybernetics and Society, 1978, pp. 921-925. [9] Yager, R. R., A procedure for ordering fuzzy subsets of the unit interval, Inform. Sci., 24, 143-161 (1981) · Zbl 0459.04004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.