Abstract: The extension set is a new set approach to the resolution of the contradictory and noncompatible problems. It mainly investigates the matrix representation of the extension set operation. First, some operations such as set intersect ∩、set union ∪ and set complement C, based on the max and min of the absolute value, were introduced to extension sets，and their serial properties were also proved. Then, the matrix representation of extension transformations was defined on the finite extension set universe, and some properties of the composition extension relations, extension transformation and extension equivalence were discussed.

Key words: extension sets；correlated function；extension matrix；extension equivalence；extension transformation