# Redefinition of the concept of fuzzy set based on vague partition from the perspective of axiomatization

## TL;DR

This paper develops an axiomatic foundation for membership degrees in vague phenomena, introduces the concept of vague partition, and redefines fuzzy sets based on this new perspective, emphasizing the importance of relationships among vague attribute values.

## Contribution

It presents a novel axiomatic system for membership degrees and redefines fuzzy sets through vague partitions, advancing the theoretical understanding of vagueness.

## Key findings

- A new axiomatic system for membership degrees
- Introduction of the vague partition concept
- Redefinition of fuzzy sets based on axiomatization

## Abstract

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.