"associativity; fuzzy logic; level set; many-valued logic; monoid; Reidemeister closure condition"@en . . "This project intends to investigate associative operations and structures from a geometrical point of view. The main motivation comes from the study of web geometry which is a branch of the differential geometry. As some results have already shown, the concepts of this discipline can be adopted successfully to characterize the associativity of totally ordered monoids and triangular norms in a very intuitive visual way. Thus, there is a good motivation to continue this research and to exploit its potential. The aim of the project is a geometric investigation of questions of structural characterization of associative structures, in particular, totally ordered monoids which play an important role in MTL algebras. These algebras represent semantics of the monoidal t-norm based logic which is a prototypical many-valued logic studied intensively nowadays by many researches. As the outcome of the project, it is expected not only a deeper understanding of associative structures but also a generalization of web geometry to a more general case."@en . . "1"^^ . . "Z\u00E1m\u011Brem tohoto projektu je zkoumat asociativn\u00ED operace a struktury z geometrick\u00E9ho pohledu. Motivac\u00ED je studium geometrie pl\u00E1stv\u00ED, co\u017E je odv\u011Btv\u00ED diferenci\u00E1ln\u00ED geometrie. Jak u\u017E n\u011Bkter\u00E9 v\u00FDsledky uk\u00E1zaly, my\u0161lenky t\u00E9to discipl\u00EDny je mo\u017En\u00E9 \u00FAsp\u011B\u0161n\u011B p\u0159izp\u016Fsobit tak, aby charakterizovaly asociativitu \u00FApln\u011B uspo\u0159\u00E1dan\u00FDch monoid\u016F a troj\u00FAheln\u00EDkov\u00FDch norem n\u00E1zorn\u00FDm a intuitivn\u00EDm zp\u016Fsobem. To d\u00E1v\u00E1 motivaci pokra\u010Dovat v tomto v\u00FDzkumu d\u00E1le a vyu\u017E\u00EDt jeho potenci\u00E1l. C\u00EDlem projektu je v\u00FDzkum charakterizace asociativn\u00EDch struktur, p\u0159edev\u0161\u00EDm \u00FApln\u011B uspo\u0159\u00E1dan\u00FDch monoid\u016F, kter\u00E9 hraj\u00ED d\u016Fle\u017Eitou roli p\u0159i popisu MTL algeber. Tyto algebry tvo\u0159\u00ED s\u00E9mantiky MTL logiky, co\u017E je prototypick\u00E1 v\u00EDcehodnotov\u00E1 logika, kter\u00E1 se v sou\u010Dasn\u00E9 dob\u011B t\u011B\u0161\u00ED z\u00E1jmu velk\u00E9ho mno\u017Estv\u00ED v\u011Bdc\u016F. O\u010Dek\u00E1van\u00FDm v\u00FDstupem projektu bude nejenom hlub\u0161\u00ED porozum\u011Bn\u00ED nespojit\u00FDm asociativn\u00EDm operac\u00EDm ale i zobecn\u011Bn\u00ED geometrie pl\u00E1stv\u00ED pro obecn\u00E9 p\u0159\u00EDpady."@cs . "Geometrie asociativn\u00EDch struktur"@cs . . . "1578"^^ . . "2012-01-01+01:00"^^ . "Geometry of associative structures"@en . . "2014-12-31+01:00"^^ . . "0"^^ . "0"^^ . "1578"^^ . "1"^^ . . "1"^^ . .