Based on the in-depth analysis of the essence and key features of vague phenomena, this paper focuses on establishing the axiomatical foundation of membership degree theory using for modeling vague phenomena, presents an axiomatic system to govern membership degrees and their
interconnections. The concept of vague partition is intro- duced, on this basis, the concept of fuzzy set in Zadeh’s sense is redefined based on vague partition from the perspective of axiomatization. The thesis defended in this paper is that the mutual constraint relationship among vague attribute values
in a vague partition should be the starting point to recognize and model vague phenomena by the quantitative analysis method.

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