Redefinition of the concept of fuzzy set based on vague partition from the perspective of axiomatization
This work provides a foundational axiomatic approach to fuzzy set theory, which could impact fields like artificial intelligence and decision-making, though it appears incremental as it builds upon Zadeh's original concept.
The paper tackles the problem of modeling vague phenomena by establishing an axiomatic foundation for membership degree theory and redefining fuzzy sets based on vague partitions, resulting in a new theoretical framework for quantitative recognition of vague attributes.
Based on the in-depth analysis of the essence and features of vague phenomena, this paper focuses on establishing the axiomatical foundation of membership degree theory for vague phenomena, presents an axiomatic system to govern membership degrees and their interconnections. On this basis, the concept of vague partition is introduced, further, the concept of fuzzy set introduced by Zadeh in 1965 is redefined based on vague partition from the perspective of axiomatization. The thesis defended in this paper is that the relationship among vague attribute values should be the starting point to recognize and model vague phenomena from a quantitative view.