8.1 Introduction

The normalization, being one kind of constraints, is proposed in traditional relational databases. Among various normalized forms, first normal form (1NF) is the most fundamental one, which assumes that each attribute value in a relational instance must be atomic, As we know, the real-world applications are complex, and data types and their relationships are rich as well as complicated. The 1NF assumption limits the expressive power of traditional relational database model. Therefore, some attempts to relax 1NF limitation are made and one kind of data model, called non-first normal (or nested) relational database model have been introduced, where attribute values may be atomic or set-valued and even relations themselves (Colby, 1990; Makinouchi, 1977; Ozsoyoglu, Ozsoyoglu and Matos, 1987; Roth, Korth and Batory, 1987; Schek and Scholl, 1986). Such database model is also called NF ² one simply. NF ² data models based on relational data model can model complex structures of objects and the relationship among them.

A NF ² data model containing fuzzy information accommodates uncertainty and complexity of the real-world objects simultaneously. Therefore, some researches have concentrated on introducing imprecise and uncertain information into NF relational databases. In (Levene, 1992; Roth, Korth and Silberschatz, 1989), a NF ² database model with null values is presented. In (Yazici et al, 1999), uncertain null values, set values, range values (partial values and value intervals), and fuzzy values are all modeled in NF ² data model and the extended NF ² algebra...