The institute has been established in Ostrava in September 1996 under the support of the Ministry of Education of the Czech Republic. The results of people from Ostrava region, part of them now working in IRAFM, are internationally renowned. The results of IRAFM have significantly contributed to the state of the art of soft computing methods, namely to the theory of mathematical fuzzy logic and the related algebraic functions, fuzzy approximation, general theory of fuzzy IF-THEN rules, general theory of linguistic meaning, approximate reasoning, and multi-criteria decision-making. The workers of IRAFM gave lectures in more than 25 countries in Europe, America and Asia. We also organize international conferences and meetings, for example IFSA’97 (International Fuzzy Systems Association) World Congress (1997, Prague), International Conference “The logic of soft computing” (2005, Ostrava), International Conference EUSFLAT 2007 (European Society for Fuzzy Logic and Technology), (2007, Ostrava).
Current activities of IRAFM
- Mathematical fuzzy logic in narrow sense (FLn): formal proving, abstract properties and models of fuzzy theories, fuzzy type theory (higher-order fuzzy logic), fuzzy partial logic, special algebras (MI- and EQ-algebras).
- Fuzzy natural logic (FNL): a mathematical theory that provides models of terms and rules that come with natural language and allow us to reason and argue in it. At the same time, the theory copes with vagueness of natural language semantics. Its paradigm extends the concept of natural logic suggested by G. Lakoff in 1970. FNL uses the formalism of fuzzy type theory and currently consists of (a) a formal theory of evaluative linguistic expressions, (b) a formal theory of fuzzy IF-THEN rules and approximate reasoning and (c) a formal theory of intermediate and generalized fuzzy quantifiers.
- Fuzzy transform and fuzzy approximation: development of methods for approximation of functions, numerical solution of differential equations, fuzzy relations formalized within fuzzy logic; The leading theory is that of fuzzy transform.
Development of special methods and tools
- Software system LFL Controller. It can be applied in automatic control, decision-making, and construction of models on the basis of principles provided by fuzzy logic. The system is integrated with Matlab/Simulink.
- Control of various kinds of processes on the basis of known linguistically specified control strategy.
- Managerial decision-making.
- Classification on the basis of qualitative and quantitative information.
- Mining linguistically characterized associations from large numerical data bases.
- Robust solution of differential equations.
- Analysis and forecasting of time series. The software system realizing our methods is LFL Forecaster.
- Signal filtering.
- Advanced methods for computer vision. They are based on the theory of fuzzy transform and include: data compression, fusion of images, edge detection, image reconstruction, recognition of damaged text in the wild and other methods.
- Development of new evolutionary algorithms for global optimization in fuzzy models.
Past activities of IRAFM
- Foundations of conceptual analysis of vague data: study of fuzzy concept lattices and related structures.
- Mathematical programming and fuzzy optimization: development of theoretical foundations, methods and algorithms.
- Higher abstract theories of fuzzy automata
The outputs of the institute consist of scientific publications and monographs as well as optimized computer routines making it possible to develop fuzzy models.