The fuzzy clustering analysis based on AFS theory

In the framework of axiomatic fuzzy sets theory, we first study how to impersonally and automatically determine the membership functions for fuzzy sets according to original data and facts, and a new algorithmic framework of determining membership functions and their logic operations for fuzzy sets has been proposed. Then, we apply the proposed algorithmic framework to give a new clustering algorithm and show that the algorithm is feasible. A number of illustrative examples show that this approach offers a far more flexible and effective means for the intelligent systems in real-world applications. Compared with popular fuzzy clustering algorithms, such as c-means fuzzy algorithm and k-nearest-neighbor fuzzy algorithm, the new fuzzy clustering algorithm is more simple and understandable, the data types of the attributes can be various data types or subpreference relations, even descriptions of human intuition, and the distance function and the class number need not be given beforehand.