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State operators on generalizations of fuzzy structures |
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| Authors: | Anatolij Dvure?enskij,Dana &Scaron alounová |
| Affiliation: | a Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia b Department of Algebra and Geometry, Faculty of Sciences, Palacký University, t?. 17. listopadu 1192/12, CZ-771 46 Olomouc, Czech Republic c Department of Mathematical Methods in Economy, Faculty of Economics, VŠB-Technical University Ostrava, Sokolská 33, CZ-701 21 Ostrava, Czech Republic |
| Abstract: | We enlarge the language of R?-monoids, which are a non-commutative generalizations of both MV algebras and BL algebras, by adding a unary operation that describes algebraic properties of a state (= an analog of probability measures). The resulting algebras are called stateR?-monoids and state-morphismR?-monoids. We present basic properties of such algebras. We describe subdirectly irreducible algebras, some generators of the varieties of state-morphism R?-monoids, and an interplay between states and state operators. |
| Keywords: | Algebras of fuzzy logics Residuated lattice State operator State-morphism operator Subdirectly irreducible algebras Generators of varieties State |
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