Projects & Grants

Internal Grant Competition DGC
START-UP grant

Theory of Semilinear Lattice-ordered Spaces
Project IdIAA108270902
Main solverprof. Irina Perfiljeva, CSc., dr. h. c., prof. h. c.
Period1/2009 - 12/2011
ProviderStandardní grantový projekt GA AV
AnotationThe main goal of the proposed project is to develop a powerful theory of semilinear l-spaces which enables to analyze fuzzy logic models represented by linear-like forms, investigate their properties, and provide their justification. The essential feature which makes fuzzy logic models attractive is clear interpretability of a final result. However, this attractiveness requires knowledge in various fields which, besides formal fuzzy logic, include ordered algebraic structures and the theory of approximation. The reason is that a fuzzy logic model copies expert knowledge about a modeled problem, which is not directly connected with the problem itself. In the proposed project we want to extend foundations of the theory of semilinear l-spaces proposed in the scientific papers of theapplicant and develop it in the style which proved itself in the theory of linear spaces. We expect that the new theory will reveal the common nature of all fuzzy logic models.