Zapata, H.; Bustince, H.; Montes, S.; Bedregal, B.; Dimuro, G. P.; Takáč, Z.; Baczyński, M.; Fernandez, J. Interval-valued implications and interval-valued strong equality index with admissible orders. (English) Zbl 1422.03049 Int. J. Approx. Reasoning 88, 91-109 (2017). Summary: In this work we introduce the definition of interval-valued fuzzy implication function with respect to any total order between intervals. We also present different construction methods for such functions. We show that the advantage of our definitions and constructions lays on that we can adapt to the interval-valued case any inequality in the fuzzy setting, as the one of the generalized modus ponens. We also introduce a strong equality measure between interval-valued fuzzy sets, in which we take the width of the considered intervals into account, and, finally, we discuss a construction method for this measure using implication functions with respect to total orders. Cited in 17 Documents MSC: 03B52 Fuzzy logic; logic of vagueness Keywords:interval-valued fuzzy implications; admissible order; interval-valued generalized modus ponens; interval-valued strong equality index PDFBibTeX XMLCite \textit{H. Zapata} et al., Int. J. Approx. Reasoning 88, 91--109 (2017; Zbl 1422.03049) Full Text: DOI References: [1] Aczél, J., On Applications and Theory of Functional Equations (1969), Birkhäuser: Birkhäuser Basel, Stuttgart · Zbl 0176.12801 [2] Alsina, C.; Trillas, E., When \((S, N)\)-implications are \((T, T_1)\)-conditional functions?, Fuzzy Sets Syst., 134, 305-310 (2003) · Zbl 1014.03026 [3] Asiaín, M. J.; Bustince, H.; Mesiar, R.; Kolesárová, A.; Takáč, Z., Negations with respect to admissible orders in the interval-valued fuzzy set theory, IEEE Trans. Fuzzy Syst. (2017), in press [4] Baczyński, M.; Jayaram, B., Fuzzy Implications, Studies in Fuzziness and Soft Computing, vol. 231 (2008), Springer: Springer Berlin · Zbl 1147.03012 [5] Baldwin, J. 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