This paper introduces a complete extended relational database model based on probability theory and fuzzy theory, called FPRDB, for representing and handling vague and uncertain information of objects in real world applications. FPRDB is built by first extending probabilistic triples with fuzzy sets, associating the probability of such fuzzy sets for expressing and computing uncertain degree of imprecise information. | Journal of Computer Science and Cybernetics, , (2016), 189–207 DOI: A FUZZY PROBABILISTIC RELATIONAL DATABASE MODEL AND ALGEBRA NGUYEN HOA Department of Information Technology, Saigon University; nguyenhoa@ Abstract. This paper introduces a complete extended relational database model based on probability theory and fuzzy theory, called FPRDB, for representing and handling vague and uncertain information of objects in real world applications. FPRDB is built by first extending probabilistic triples with fuzzy sets, associating the probability of such fuzzy sets for expressing and computing uncertain degree of imprecise information. Then, schemas, fuzzy probabilistic relations, fuzzy probabilistic functional dependencies and algebraic operations are defined coherently and consistently for FPRDB. A set of the properties of the relational algebraic operations in FPRDB is also formulated and proven. Keywords. Probability distribution, fuzzy probabilistic triple, fuzzy probabilistic relation, fuzzy probabilistic functional dependency, fuzzy probabilistic relational algebraic operation. 1. INTRODUCTION It is true that the real world is pervaded by uncertain and imprecise information that we have to face, and make decisions on, in daily life [1, 2]. Although, the classical relational database model is very useful for modeling, designing and implementing large-scale systems, it is restricted for representing and handling uncertain and imprecise information [3, 4]. For example, applications of the classical relational database model cannot deal with queries such as “find all patients who are young ”; nor “find all players who are 80-90% likely to be the top scorers of the English Premier League, in year 2016”, etc, where young is an imprecise notion [5, 6]. Up to now, there have been many relational database models studied and built based on the probability theory for modeling objects about which information may be .
