Solvability of \(L\)-fuzzy relation equations in generalized one-sided residuated groupoids (Q851515)

A generalized concept of the left (right) residuated complete lattice-ordered groupoid has been introduced by authors recently (in press). Here, the solvability of \(L\)-fuzzy relation equations in such groupoids is characterized. As an application, the solvability of \(L\)-fuzzy relation equations with infinitely \(\vee\)-distributive strong pseudo-t-norms is studied. It is shown that the main results of [\textit{F. M. Dai} and \textit{Z. D. Wang}, J. Yangzhou Univ., Nat. Sci. Ed. 5, No. 2, 8-10 (2002; Zbl 1012.03516)] are wrong and are corrected accordingly.