Wu, Xinxing; Zhang, Xu; Chen, Guanrong Answers to some questions about Zadeh’s extension principle on metric spaces. (English) Zbl 1452.54009 Fuzzy Sets Syst. 387, 174-180 (2020). Summary: This paper shows that there exists a contraction whose Zadeh’s extension is not a contraction under the Skorokhod metric, answering negatively Problems 5.8 and 5.12 posted in [D. Jardón et al., “Some questions about Zadeh’s extension on metric spaces”, ibid. 379, 115–124 (2020; doi:10.1016/j.fss.2018.10.019)]. Cited in 3 Documents MSC: 54A40 Fuzzy topology 54E35 Metric spaces, metrizability Keywords:contraction; fuzzy set; Skorokhod metric; Zadeh’s extension PDFBibTeX XMLCite \textit{X. Wu} et al., Fuzzy Sets Syst. 387, 174--180 (2020; Zbl 1452.54009) Full Text: DOI References: [1] Billingsley, P., Convergence of Probability Measures (1968), Wiley: Wiley New York · Zbl 0172.21201 [2] Boroński, J. P.; Kupka, J., The topology and dynamics of the hyperspaces of normal fuzzy sets and their inverse limit spaces, Fuzzy Sets Syst., 321, 90-100 (2017) · Zbl 1377.54009 [3] Font, J. J.; Sanchis, D.; Sanchis, M., Completeness, metrizability and compactness inspaces of fuzzy-number-valued functions, Fuzzy Sets Syst., 353, 124-136 (2018) · Zbl 1397.54010 [4] Jacod, J.; Shirayaev, A. N., Limit Theorems for Stochastic Processes (1987), Springer: Springer New York [5] Jardón, D.; Sánchez, I.; Sanchis, M., Some questions about Zadeh’s extension on metric spaces, Fuzzy Sets Syst. (2019) [6] Joo, S. Y.; Kim, Y. K., The Skorokhod topology on space of fuzzy numbers, Fuzzy Sets Syst., 111, 497-501 (2000) · Zbl 0961.54024 [7] Kupka, J., On approximations of Zadeh’s extension principle, Fuzzy Sets Syst., 283, 26-39 (2016) · Zbl 1376.54009 [8] Wu, X.; Chen, G., Sensitivity and transitivity of fuzzified dynamical systems, Inf. Sci., 396, 14-23 (2017) · Zbl 1431.37008 [9] Wu, X.; Ding, X.; Lu, T.; Wang, J., Topological dynamics of Zadeh’s extension on upper semicontinuous fuzzy sets, Int. J. Bifurc. Chaos, 27, Article 1750165 pp. (2017) · Zbl 1380.37024 [10] Wu, X.; Wang, L.; Liang, J., The chain properties and Li-Yorke sensitivity of Zadeh’s extension on the space of upper semi-continuous fuzzy sets, Iran. J. Fuzzy Syst., 15, 83-95 (2018) · Zbl 1417.54019 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.