The major approaches to designing fuzzy relational databases often employ fuzzy number domains or finite scalar domains with similarity relations. In some situations, treating these values by means of query operations may lead to non-reasonable answers. Therefore, we propose an extended fuzzy relational model with two supplementary attributes, μr and Ie, to solve this problem. Also, the classical properties of redundant-free, uniquely-determined of database interpretation and well-definedness of the relational algebra are preserved in our proposed model. The attribute domains in an extended fuzzy relation allow crisp values, fuzzy number domains, normal fuzzy sets, or linguistic values. Therefore, the proposed model is more general than the existing approaches and more suitable for handling real world applications. Finally, a mechanism for solving query evaluation problems by using self-information is also presented.