Institute for Research and Applications of Fuzzy Modeling of the University of Ostrava

Institute for Research and Applications of Fuzzy Modeling (IRAFM) is a scientific place of work that is part of the University of Ostrava. It is focused on theoretical research and practical development of various methods of the so-called fuzzy modeling, that is, the formation of models that can include vaguely or imprecisely specified information. Such a situation happens, for example, if a description of an object or process available in a natural language only. Therefore, fuzzy models can be more realistic than classical ones. They can be applied, e.g., for control of complex processes, in multicriterial decision-making, when some criteria may not be quantifiable, in computer vision, for effective approximation of functions that can be much less dependent on initial conditions, for the robust solution of differential equations, for signal filtration and in many other situations.

The institute was founded in Ostrava in September 1996 based on the project of Ministry of Education, Youth, and Sports of the Czech Republic “Support of research in the universities.” The results of IRAFM have significantly contributed to the present state of the art in the area of mathematical fuzzy logic, special algebras of truth values, a theory of approximation of functions, etc. We also introduced a model of semantics of special natural language expressions, the so-called evaluative linguistic expressions (big, very deep, a little smart, etc.) and intermediated quantifiers (most, many, a few, etc.). In the institute, also a very successful theory of the so-called fuzzy transform (F-transform) was introduced, which has a lot of nontrivial applications. The workers of IRAFM gave lectures in over 30 countries in Europe, America, Asia, Australia, New Zealand, and Africa. The results of the institute are publications in scientific journals, scientific monographs, and special software.

Practical results of IRAFM are the original concept of linguistic control, which makes it possible to form a computer algorithm based on the description of control of an industrial process, using which we can successfully control the process. For this purpose, we have developed the software Linguistic Fuzzy Logic Controller (LFLC). Further SW products are LFL Forecaster for analysis and forecasting of time series and LFL Miner for mining information from data. The application of effective algorithms makes an impression that computer as if it understands expressions of natural language. Besides that, we realized many practical applications of our methods in the area of image processing.

IRAFM is also a successful organizer of international conferences and symposia, for example, World Congress IFSA'97 (International Fuzzy Systems Association, 1997, Praha), international conference The Logic of Soft Computing (2005, Ostrava), international conferences EUSFLAT'07 (European Society for Fuzzy Logic and Technology, 2007, Ostrava) and EUSFLAT 2019 in Prague, SFLA'16 (EUSFLAT Summer School on Fuzzy Logic and Applications, 2016, Čeladná), international conference IFSA-EUSFLAT 2021 (International Fuzzy Systems Association-European Society for Fuzzy Logic and Technology, 2021, Bratislava), or international conferences FSTA 2020 and FSTA 2022 (Fuzzy Set Theory and Applications, Liptovský Ján). Furthermore, we co-organize series of conferences ISCAMI (International Student Conference on Applied Mathematics and Informatics), series of Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty, that takes place each year in Japan or the Czech Republic since 1998, and we regularly organize many smaller workshops and meetings.

Current activities of IRAFM

Theoretical foundations

  • Mathematical Fuzzy Logic: formal proving, abstract properties, and models of fuzzy theories, higher-order fuzzy logic (fuzzy type theory), partial fuzzy logic, special algebras (MI- and EQ-algebras).
  • Fuzzy Natural Logic (FNL): mathematical theory whose goal is to model natural human reasoning that proceeds in natural language. FNL stems from the formalism of the fuzzy type theory. Currently, it consists of (a) formal theory of evaluative linguistic expressions, (b) formal theory of fuzzy IF-THEN rules, and approximate reasoning and (c) formal theory of intermediate and generalized quantifiers.
  • Fuzzy Transform a fuzzy approximation of functions: development of methods for approximation of functions, numerical solution of differential and integral equations, signal processing and time series analysis, the theory of fuzzy relations.

Development of special methods and tools

  • Software system LFL Controller, which can be applied to automatic control of technological processes, multicriteria decision-making, or formation of an expert system.
  • Mining linguistic associations from large numerical databases. The software system enabling us to apply our methods is LFL Miner.
  • A robust solution of differential and integral equations.
  • Analysis and forecasting of time series and mining information from them. The software system enabling us to apply our methods is LFL Forecaster.
  • Advanced methods for computer vision. They are based on the theory of fuzzy transform and include image compression, image fusion, edge detection, reconstruction of the damaged image, reading of a corrupted text, and unique methods for identification and recognition of objects.
  • Software “Dragon-fly hunter“ for mobile phones, that helps to recognize observed dragon-fly species and sends this information to specialists.

Updated: 24. 05. 2022