Analysis of functional dependencies in relational databases using fuzzy logic

The research presented in this dissertation is finding of fuzzy functional dependencies in the fuzzy relational database models. The goal is reviewing and analyzing of recent results in this field and developing our own algorithm for identification of dependencies between attributes in the fuzzy relations based on fuzzy implication in fuzzy logic. The problem of fuzzy functional dependency analzsing in fuzzy relational database models is not recent. In this area there is a significant number of papers and authors dealt with mentioned issue in the last two decades. However, literature analysis showed that there is no algorithm that would enable the identification of attribute relationships in relational schemas. This restriction was the motive for the development of our methodology in the analysis of fuzzy functional dependencies over a given set of attributes. Solving this, not so new problem, is not only research challenge having theoretical importance, but it also has practical significance. Implementation of logical database models provided by the previous theory and integration to other areas and fields (GIS, Rudarenje podataka, Information Retrieval, reducing data redundansy, estimation of NULL values...) are crucial aims in this paper. The initial assumption was that the theory of fuzzy sets and particular fragment of fuzzy logic are the perfect solution when database managers can’t unambiguously determine the relationships between data and attributes within the relation. In the field of artificial intelligence, fuzzy sets and fuzzy logic are studied in terms of fuzzy relational database design within the intelligent systems because fuzzy set theory and fuzzy logic are powerful tools for manipulating and representing imprecise and uncertain information. Finding potential dependencies between attributes in fuzzy relations is actually rudarenje podataka technique related to hidden and useful knowledge used for decision making. This dissertation presents a new technique for identification of existing dependencies between pairs of tuples using different fuzzy implications which characterization is described by author. Fuzzy implications meeting established acceptance criteria are used for estimation of linguistic strength θ when fuzzy functional dependency X →θ Y is satisfied. For demonstration of proposed methodology and research verification we performed experiment on real data under two different models: fuzzy database model based on proximity relatio