Abstract
Recently, Wang and Liu investigated the modularity condition for overlap and grouping functions [Fuzzy Sets Syst. 372 (2019) 97-110]. They characterized the modularity equation between overlap (grouping) functions and proper uninorms, which belong to the most studied classes. In this paper, as a supplement of the above paper, we explore some new results on the modularity condition for overlap (grouping) functions and uninorms.
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