Abstract
In this paper, we mainly consider the construction and characterization of so-called quasi-D-overlap functions, which are derived from D-overlap functions and irreducible quasi-D-overlap functions proposed by the author lately. The main contributions are: (i) it presents the concept of quasi-D-overlap functions and obtains construction manner of them by means of matrixes; (ii) it illustrates the relationship between quasi-D-overlap functions and 1-Lipschitz semi-quasi-overlap functions; (iii) it gives equivalent characterization of quasi-D-overlap functions and proper quasi-D-overlap functions by dint of matrixes, moreover, it obtains that the convex combination of quasi-D-overlap functions is also a quasi-D-overlap function.
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