Plenary Lecture
On Automated Obtaining of New Vague Functional and Vague Multivalued Dependencies via Resolution Principle
Professor Dzenan Gusic
Department of Mathematics
Faculty of Sciences and Mathematics
University of Sarajevo
Bosnia and Herzegovina
E-mail: dzenang@pmf.unsa.ba
Abstract: In order to describe the real world with imprecise and uncertain data, several extensions of the ordinary relational database model have been considered in literature applying fuzzy set theory. However, a vague set, as a generalized fuzzy set, represents a more powerful tool to process imprecise information than fuzzy set. The integrity constraints like functional and multivalued dependencies play a key role in any database design. We introduce new definitions of vague functional and vague multivalued dependencies which are given on the basis of appropriately selected similarity measures. The definitions are adjusted in order to be applicable to both, the imprecise and precise vague functional and vague multivalued dependencies, respectively. The inference rules are listed after both types of vague dependencies, and are shown to be sound and complete. To prove that a vague dependency follows from some set of vague dependencies used to be very demanding task. As far as it is known, an algorithm or an application that solves the problem automatically, does not exist yet. Now, we offer such an algorithm. We consider vague dependencies as fuzzy formulas. Ultimately, we prove that a vague dependency follows from a set of vague dependencies if and only if the corresponding fuzzy formula is a logical consequence of the corresponding set of fuzzy formulas. However, in order to prove an implication of this kind, one usually applies the resolution principle, that is, an environment where our steps can be fully automated.
Brief Biography of the Speaker: Dzenan Gusic is currently an Associate Professor in the Department of Mathematics of the Faculty of Sciences and Mathematics at the University of Sarajevo, Bosnia and Herzegovina, where he had been since 2007. He received a B.S. in 2007, and an M.S. in 2009. He received his Ph.D. in Analytic Number Theory in 2013. His research interests span both analytic number theory and computer science. Most of his work has been on improving of the error terms in prime (number) geodesic theorems in various settings of locally symmetric spaces, mainly through the application of the properties of zeta functions of Selberg and Ruelle. In the computer sience arena, he had worked on characterizing of fuzzy (vague) functional and multivalued dependencies via fuzzy formulas. Specifically,he has explored the possibility of automatization in the process of obtaining of new fuzzy (vague) dependencies through the resolution principle. Dr. Gusic has published one book, and has authored numerous journal publications, and conference articles in the aforementioned topics. Since 2014, he has served as a Deputy Head of the Department of Mathematics at the University of Sarajevo. He attended numerous conferences on mathematics and informatics that took place in Greece, Hungary, Spain, Italy, North Macedonia, Bosnia and Herezegovina, including the International Congress of Mathematicians ICM 2010, Hyderabad, India.