T5: Lattice and Poset Valued Fuzzy Structures: From Theory to Applications
 

Branimir Seselja
University of Novi Sad, Serbia

Andreja Tepavcevic
University of Novi Sad, Serbia

Abstract:
Fuzzy sets theory in the framework of ordered sets and lattices as co-domains will be presented. Fuzziness arising from ordered structures will be explained and many useful and easy order-theoretic techniques, which are applied to fuzzy structures, will be described. Short introduction to lattices will be given with stress to frequently used ones: complete chains (e.g., unit interval) and residuated lattices. Classical constructions and notions from fuzzy sets developed within ordered structure context will be given: e.g., set-theoretic operations including t-norms, p-cuts, fuzzy relations and properties etc. Answers will be given to the question: How to apply and use real functions if the unit interval is replaced by lattices and posets. Usefulness and applications of lattice-valued fuzzy structures will be elaborated throughout several examples in biology, social sciences, and medicine.

Outline:

  • Ordered sets and lattices: short introduction with characteristic examples
  • Fuzzy sets: poset and lattice-valued ones
  • Operations and relations on fuzzy power set
  • Fuzzy relations: general, similarity and order
  • Working with lattice valued structures: from real interval to residuated lattice
  • Applications:
    • Dealing with concepts (social sciences)
    • Distribution of species (biology)
    • preparing diagnosis (medicine)

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

 

Vitas:

Branimir Seselja is the head of Chair in applied algebra at the Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Serbia. His specialization is Universal algebra, Lattice theory and algebraic aspect of Fuzzy set theory. He has published more than 100 articles in journals specialized in the above topics, he has given many invited lectures at universities worldwide, participated at numerous conferences. Among his publications is a monograph on weak congruences (together with A. Tepavcevic), Lattice theory, and several overview texts on algebraic aspects of fuzziness (http://www.im.ns.ac.yu/Faculty/seseljab).

 
 

Andreja Tepavcevic 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 and Biology, supervised two Ph.D., three master and three graduate thesis and was an external adviser of one doctoral thesis and one master thesis defended abroad. She is an author of about 80 research papers and five university textbooks. She participated at about 60 conferences and gave invited lectures at about 15 universities and was a member of organizing and program committees for several seminars and conferences.