"http://www.isvav.cz/projectDetail.do?rowId=IAA108270902"^^ . . . "Teorie semiline\u00E1rn\u00EDch svazov\u011B uspo\u0159\u00E1dan\u00FDch prostor\u016F" . . " fuzzy model" . "2011-03-18+01:00"^^ . "Theory of Semilinear Lattice-ordered Spaces"@en . "semilinear space" . "24"^^ . . . . "24"^^ . . . " module" . "The 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 the applicant 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."@en . . " approximation" . . "Theory of semilinear spaces and their endomorphisms was developed. Use of the Galois connections theory in the solvability of fuzzy relation equations. Correct fuzzy relational models were analyzed. The theory of generalized determinants was developed."@en . " semiring" . . "0"^^ . "IAA108270902" . . "2011-12-31+01:00"^^ . "semilinear space; semiring; lattice; module; approximation; fuzzy model; principle of duality"@en . . "1"^^ . . . "2013-06-28+02:00"^^ . "2009-01-01+01:00"^^ . . . "0"^^ . " lattice" . . "Byla vytvo\u0159ena teorie semiline\u00E1rn\u00EDch prostor\u016F a jejich endomorphism\u016F. Byla pou\u017Eita teorie Galoisov\u00FDch konex\u00ED v \u0159e\u0161itelnosti soustav fuzzy rela\u010Dn\u00EDch rovnic. Byly vytv\u00E1\u0159eny korektn\u00ED fuzzy rela\u010Dn\u00ED modely. Byla rozpracov\u00E1na teorie zobecn\u011Bn\u00FDch determinant\u016F."@cs . "Hlavn\u00EDm c\u00EDlem p\u0159edkl\u00E1dan\u00E9ho projektu je vytvo\u0159it plnohodnotnou teorii semiline\u00E1rn\u00EDch l-prostor\u016F, kter\u00E1 umo\u017En\u00ED analyzovat fuzzy logick\u00E9 modely reprezentovan\u00E9 jist\u00FDm typem line\u00E1rn\u00EDch forem, zkoumat jejich vlastnosti a poskytnout jejich zd\u016Fvodn\u011Bn\u00ED. V\u00FDznamn\u00FDm rysem, pro kter\u00FD jsou fuzzy logick\u00E9 modely atraktivn\u00ED, je pr\u016Fhledn\u00E1 interpretovatelnost kone\u010Dn\u00E9ho v\u00FDsledku. Tato atraktivnost v\u0161ak vy\u017Eaduje znalost r\u016Fzn\u00FDch oblast\u00ED, kter\u00E9 vedle fuzy logiky zahrnuj\u00ED uspo\u0159\u00E1dan\u00E9 algebraick\u00E9 struktury a teorii aproximace. D\u016Fvodem je to, \u017Ee fuzzy logick\u00E9 modely kop\u00EDruj\u00ED expertn\u00ED znalost o modelovan\u00E9m probl\u00E9mu, kter\u00E1 v\u0161ak nen\u00ED p\u0159\u00EDmo spojen\u00E1 s vlastn\u00EDm probl\u00E9mem. V p\u0159edkl\u00E1dan\u00E9m projektu chceme roz\u0161\u00ED\u0159it z\u00E1klady teorie semiline\u00E1rn\u00EDch l-prostor\u016F navr\u017Eenou ve v\u011Bdeck\u00FDch \u010Dl\u00E1nc\u00EDch navrhovatele a vytvo\u0159it ji ve stylu, kter\u00FD byl prov\u011B\u0159en v teorii line\u00E1rn\u00EDch prostor\u016F. O\u010Dek\u00E1v\u00E1me, \u017Ee nov\u00E1 teorie odkryje spole\u010Dnou povahu v\u0161ech fuzzy logick\u00FDch model\u016F." .