A generalized fuzzy extension of EL++

Fuzzy extensions of Description Logics are generally based on precise membership functions which assign a particular real number to an element or a subset of the universe. In some cases where we may only be able to identify approximately appropriate membership degrees the use of precise membership functions become unsuitable. In this paper we propose a generalized fuzzy extension of the description logic EL⁺⁺, named Gf-EL⁺⁺, based on interval-valued fuzzy sets. We present the syntax and the semantics of Gf-EL⁺⁺ which uses an extension of concept subsumption with “interval-valued fuzzy subsumption”. We equally propose a tractable subsumption algorithm for Gf-EL⁺⁺.