In today’s world, a huge quantity of data is being generated which requires effective management in terms of storage, manipulation and retrieval. Real world data is often ambiguous and uncertain in nature since it is closer to human intuitions. In a step towards designing database systems to manage real world data, there arises a need to develop an intelligent database model. A symbolic relational database aims at handling such real world data. It is an extension of the classical relational data model and is designed as a subspace of the fuzzy data base model. Design theory of any database consists of finding out the data dependencies and normal forms that enables us to represent data in a consistent and non-redundant fashion. This paper aims at developing higher-level normal forms for the design of symbolic relational databases. The level of normalization worked out in the paper is based on multivalued dependency.

Ever since the development of relational data model, many commercial relational database systems have been introduced. This data model fails to capture the meaning of real world data which is often symbolic or fuzzy in nature as it assumes every data value to be exact. Thus, symbolic relational databases are designed as an extension of the classical relational database model with the aim of capturing the realistic notion of data. The underlying database model used in the design of symbolic relational databases is based on fuzzy sets. The motivation for the application of fuzzy set theory lies in the need to handle information which is vague, incomplete and imprecise.

As we extend the classical relational data model to deal with imprecise information, it is necessary to consider the integrity constraints on the basis of fuzzy concepts. Relational model includes different types of integrity constraints such as functional dependency, multivalued dependency and join dependency, and proposes a set of inference rules for such dependencies.

Symbolic relational databases apply fuzziness on relations in two ways—first elements of the relations called tuples may be subsets of some domain universal sets and second a similarity relation is defined on each domain set. Many authors have studied relational model from the perspective of fuzzy set theory by extending the relational algebra to suit fuzzy databases and have proposed integrity constraints based on fuzzy functional dependency. This paper examines fuzzy relations based on similarity measures. The primary objective is to extend the design theory of relational model to the fuzzy domain by suitably defining the symbolic multivalued dependency. Based on multivalued dependency, the fourth normal form for normalizing symbolic relational database design is proposed. In view of this, the paper is organized as follows: Section 2 of the paper deals with the concept of fuzzy sets. In Section 3, multivalued dependency on symbolic relational databases is defined and analyzed on relational schema. Section 4 is concerned with fourth level of normalization of symbolic relational databases.

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