The connectedness of \(H(\lambda)\) unit interval and \(H(\lambda)\) real line (Q1387431)

In [Fuzzy Sets Syst. 82, No. 1, 103-110 (1996; Zbl 0877.54004)] the author defined and studied \(H(\lambda)\) real line \(\widetilde R(L)\), the weak inducification of \(R(L)\). Although a series of properties of \(\widetilde{I}\) and \(\widetilde R(L)\) have been discussed [\textit{G.-J. Wang} and \textit{L.-S. Xu}, Sci. China Ser. A 35, No. 12, 1434-1443 (1992; Zbl 0783.54008); \textit{D.-X. Zhang} and \textit{Y.-M. Liu}, Acta Math. Sin. 36, No. 1, 68-73 (1993; Zbl 0783.54009); \textit{S.-G. Li}, loc. cit.], the problem of whether \(\widetilde{I}(L)\) and \(\widetilde R(L)\) are connected or not is essentially still open. This letter gives an affirmative answer to this problem.