Epistemic vs Aleatory: Granular Computing and Ideas Beyond That

Vladik Kreinovich, University of Texas at El Paso

Many practical problems are naturally reduced to solving systems of equations. There are many efficient techniques for solving well-defined systems of equations, i.e., systems in which we know the exact values of all the parameters and coefficients. In practice, we usually know these parameters and coefficients with some uncertainty—uncertainty usually described by an appropriate granule: interval, fuzzy set, rough set, etc. Many techniques have been developed for solving systems of equations under such granular uncertainty. Sometimes, however, practitioners use previously successful techniques and get inadequate results. In this paper, we explain that to obtain an adequate solution, we need to take into account not only the system of equations and the granules describing uncertainty: we also need to take into account the original practical problem—and for different practical problems, we get different solutions to the same system of equations with the same granules.

Speaker biosketch

Vladik Kreinovich is a professor of computer science at the University of Texas at El Paso. He was educated at Leningrad State University (currently known as St. Petersburg University) and received a doctorate in mathematics from the Sobolev Institute of Mathematics, affiliated with Novosibirsk State University in Novosibirsk. His research spans several areas of computer science, computational statistics and computational mathematics generally, including interval arithmetic, fuzzy mathematics, probability theory, and probability bounds analysis. His research addresses computability issues, algorithm development, verification, and validated numerics for applications in uncertainty processing, data processing, intelligent control, geophysics and other engineering fields. He has been extremely productive with over 2,400 scholarly publications. In 2015, the Society For Design and Process Science gave him its Zadeh Award.