Two Reasoning Methods for Extended Fuzzy ALCH

This paper introduces cut sets of fuzzy concepts and fuzzy roles as atomic concepts and atomic roles to build extended fuzzy $\cal{ALCH}$$\cal{(EFALCH)}$, a new fuzzy extension of $\cal{ALCH}$. It talks about two reasoning methods for $\cal{ EFALCH}$. The first one presents a sound and complete algorithm for $\cal{EFALCH}$ reasoning tasks and proves the complexity is PSPACE-complete. The second one reduces $\cal{EFALCH}$ into $\cal{ ALCH}$, which can be performed in polynomial time and keep the semantic consistency, and then uses $\cal{ALCH}$ reasoning method to solve $\cal{EFALCH}$ reasoning tasks.