Abstract: Using the method and principle of intervalvalued fuzzy set, we introduced the concepts of representable intervalvalued overlap and grouping functions, combined with overlap and grouping functions generated by the multiplicative generator pairs, under the boundary conditions, we gave the solutions to the functional equations I(G(x,y),z)=O(I(x,z),I(y,z))  and I(x,O₁(y,z))=O₂(I(x,y),I(x,z)), and discussed the related properties of overlap and groupling functions.

Key words: fuzzy implication, overlap function, grouping function, distributivity, functional equation