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CEEPUS курс за студентите от ФМИ


Central European Exchange Program for University Studies

Course Title:          Boolean algebras, ordered structures and

Lecturer:                 Prof. dr Andreja Tepavcevic,
                                University of Novi Sad,

Time schedule:     07.07.2015      Tuesday         12:00-17:00              

Place:                     room 534, floor 5, FMI


Course Description:

In this course, basics of Boolean algebras, lattices and other ordered structures will be introduced. Some aspects of Boolean optimization will be presented. As an application these structures will be considered as truth values of fuzzy structures, in particular fuzzy relations. Fuzzy relational databases are a new field of investigation in information technology.  In the history of fuzzy mathematics, fuzzy relations were early considered to be useful in various applications, therefore have been extensively investigated. Among many applications, we are here focused to fuzzy relational equations, particularly those which are connected to control problems. Fuzzy control essentially consists of an input, processing and output stages. It is usually rule based, and frequently fuzzy IF-THEN rules appear in this context, mostly in the processing stage. Practically, fuzzy rule bases use several antecedents that are combined using fuzzy operators or (fuzzifying if-then rules) fuzzy relations. In particular, the Mamdani approach to fuzzy controllers starts from a fuzzy relation which is deduced from actual control process and which from an input value creates an output value using a suitable compositional rule of inference. In concrete applications of fuzzy control, it is frequent that output values are determined in advance by input values, and the problem is to find a fuzzy relation which performs such a transition. There have been numerous scientific contributions in this field in the last two decades. Among several theoretical approaches to fuzzy control, we are focused to those transforming if-then rules into fuzzy relations.

The aim of this course is to present several aspects of this topic. An insight to the development of investigations concerning fuzzy relations and fuzzy relational databases will be given. Next, a theoretical background to fuzzy relational equations in the most general framework of lattice valued membership will be elaborated. Then some techniques for solving different equations and inequations will be explained. In the second part the applications of these, mostly in control problems will be presented.


  • Boolean algebras
  • Lattices and Ordered Sets
  • Boolean optimization
  • Fuzzy relations with membership values in lattices
  • Fuzzy relational  equations and inequations: from the beginning of fuzziness  to the role in the contemporary science and technology
  • Eigen fuzzy sets; clossednes of fuzzy sets under fuzzy relations
  • Fuzzy relational databases


Intended audience:

This course would be presented in such a way that anybody with knowledge of basic university mathematics can follow it. This course can be useful for master, graduate and postgraduate students as well as researchers wishing to broaden their views and to learn new ideas and techniques.


Biography of presenter:

Andreja Tepavcevic the head of Chair in applied algebra, Department of Mathematics and Informatics, University of Novi Sad. She got her Ph. D.in Mathematics 1993 at University of Novi Sad, Serbia. She is a professor at Faculty of Science in Novi Sad since 2003. Her research interests are in: Fuzzy Set Theory, Universal Algebra, Lattice Theory and applications. She has been teaching several courses to bachelor, master and doctoral students of Applied Mathematics, Informatics and Biology, supervised four Ph.D., three master and three graduate thesis and was an external adviser of two doctoral thesis and one master thesis defended abroad. She is an author of about 100 research papers and five university textbooks. She participated at about 70 conferences and gave invited lectures at about 20 universities and was a member of organizing and program committees for several seminars and conferences and a member of editorial board of 3 international journals.


FREE for students of the Faculty of Mathematics and Informatics, Plovdiv University.  


For Information:    Assoc. Prof. Dr. Elena Somova
                                  tel. 261 259; 0889 338997
                                  e-mail: eledel@uni-plovdiv.bg

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