Member attribute is used to describe the property of dimension members. It is not fully understood or well defined by OLAP research community. This paper focuses on a special kind of member attributes that could also be used as dimensions called attribute dimensions. To facilitate this kind of multidimensional data modeling from real-world applications, the classic multidimensional data structure is extended and a group of algebraic operations are introduced to formulate corresponding multidimensional queries. In this extended model, the attribute dimension is regarded as a special ?view? and can be stated either statically or dynamically based on member attribute. With this approach, both ROLAP and MOLAP can benefit from storage saving and reduced processing time. Compared with current OLAP products and research papers, built-in integrity restraint on member attribute and multidimensional data set makes this extended model unique.