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At that time, it is clear that the study of R- and S-implica- tions has been essential in the development of fuzzy mathemat- ical morphology, that has been mainly applied to edge detection and image processing. As we have commented, for these appli- cations, the fuzzy mathematical morphology with the majority of the desired morphological properties is the one derived from nilpotent t-norms and their derived R-implications. However, implementations of this approach prove that the behavior of the t-norm minimum, especially in edge detection, is better than that of nilpotent t-norms in general (although with minimum many properties are missing, including the duality between morpho- logical operators). To solve this problem, uninorms and their derived R-implications have been recently introduced in this context (see [15] and [26]). This paper has proved that a fuzzy mathematical morphology can be derived from several kinds of uninorms, having the same properties as those derived from nilpotent t-norms. Moreover, its applicability to edge detection is equal to or better than that of the mathematical morphology based on the t-norm minimum (see [27]).