Formal equivalence classes model of fuzzy relational databases using relational calculus

One of our goals is to formalize an equivalence class(FEC) of the fuzzy relational database(FRDB). FRDB, an extension of RDB using a soft computing technique, fuzzy theory. Using our relational formulas of relational calculus, we can denote its properties by simple and correct formulas. Also, we can prove its properties formally using relational calculus. There are many applications of FRDB such as managing hyperlinks of web pages, customer relationship management (CRM), etc. Our motivation is developing formal verification tools for a software system using FEC of FRDB. We also formalize database operations such as “projection”, “selection”, and “natural join”. We prove several elementary properties of natural join operations using our formalization.