An Extension of Semantic Proximity for Fuzzy Multivalued Dependencies in Fuzzy Relational Database

TL;DR

This paper extends the concept of semantic proximity to fuzzy multivalued dependencies in fuzzy relational databases, addressing data integrity issues with a new formula and proving the completeness of inference rules.

Contribution

It introduces a modified semantic proximity formula and defines fuzzy multivalued dependencies based on an extended semantic proximity with an alpha degree, enhancing data integrity in fuzzy databases.

Findings

Proposed a new semantic proximity formula for fuzzy dependencies

Defined fuzzy multivalued dependencies with extended semantic proximity

Proved the completeness of inference rules for these dependencies

Abstract

Following the development of fuzzy logic theory by Lotfi Zadeh, its applications were investigated by researchers in different fields. Presenting and working with uncertain data is a complex problem. To solve for such a complex problem, the structure of relationships and operators dependent on such relationships must be repaired. The fuzzy database has integrity limitations including data dependencies. In this paper, first fuzzy multivalued dependency based semantic proximity and its problems are studied. To solve these problems, the semantic proximity's formula is modified, and fuzzy multivalued dependency based on the concept of extension of semantic proximity with \alpha degree is defined in fuzzy relational database which includes Crisp, NULL and fuzzy values, and also inference rules for this dependency are defined, and their completeness is proved. Finally, we will show that fuzzy functional dependency based on this concept is a special case of fuzzy multivalued dependency in fuzzy relational database.