Although the model-theoretic semantics of the languages used in the Semantic Web are crisps, the need arise to extend them to represent fuzzy data, in the same way fuzzy logic extend first-order-logic. We will define a fuzzy counterpart of the RDF Model Theory for RDF (section 2) and RDF Schema (section 3). Last, we show how to implement the extended semantics in inference rules (section 4). year = {2005}, pages = {12--22}, masid = {1856198} } Although the model-theoretic semantics of the languages used in the Semantic Web are crisps, the need arise to extend them to represent fuzzy data, in the same way fuzzy logic extend first-order- logic. We will define a fuzzy counterpart of the RDF Model Theory for RDF (section 2) and RDF Schema (section 3). Last, we show how to implement the extended semantics in inference rules (section 4).