The Decomposition Algorithm Of AFS Structure And Its Applications To Failure Diagnosis

The theory of fuzzy sets and systems has been studied widely and applied in many fields as a new mathematics method since it was proposed by Professor L. A. Zadeh, an American cyberneticist, in 1965. AFS (Axiomatic Fuzzy Set) theory was proposed first in [26-31] as a new analytic method of fuzzy mathematics. In the framework of AFS theory, the membership functions and their logic operations for fuzzy concepts can be impersonally determined according to original data and facts. AFS theory has been applied to data mining, pattern recognition and failure diagnosis.When we study failure diagnosis of system based on AFS theory, the complexity of AFS structure increases the difficulty in calculation and analysis for the real-world applications. Therefore our focus is on how to reduce the complexity of AFS structure effectively. In [28], the author has proved the feasibility in mathematics. In this paper, we propose a direct sum decomposition algorithm of AFS structure based on the research in [28], which decomposes a complex AFS structure into several independent sub-AFS structures, thus the elements in the same sub-AFS structure are dependent on each other, the elements in the different sub-AFS structures are independent. This implies that each sub-AFS structure is a connected system. Then we apply AFS theory to diagnose failures of marine diesel engine. The example shows that the decomposition algorithm is objective, uniform, easy to control and coincidence with experts' experiences. Especially in more complex systems, this decomposition algorithm will show more superiority.