Tractable reasoning with vague knowledge using fuzzy $\mathcal{EL}^{++}$

Abstract Fuzzy Description Logics (fuzzy DLs) are extensions of classic DLs that are capable of representing and reasoning with imprecise and vague knowledge. Though reasoning algorithms for very expressive fuzzy DLs have been developed and optimizations have started to be explored, the efficiency of such systems is still questionable, and the study of tractable languages is an interesting open issue. In this paper we introduce a tractable fuzzy extension of $\mathcal{EL}^{++}$ . We present its syntax and semantics together with a reasoning algorithm for the fuzzy concept subsumption problem to which other problems can be reduced.