Geodesic
L-Convexity and Lattice-Valued Capacities
Journal of convex analysis, Tome 21 (2014) no. 1, pp. 29-52

Voir la notice de l'article provenant de la source Heldermann Verlag

$L$-idempotent analogues of convexity are introduced ($L$ is a completely distributive lattice). It is proved that the category of algebras for the monad of $L$-valued capacities (regular plausibility measures) in the category of compacta is isomorphic to the category of $L$-idempotent biconvex compacta and their biaffine maps. For the functor of $L$-valued $\cup$-capacities ($L$-possibility measures) a family of monads parameterized by monoidal operations $*:L\times L\to L$ is introduced and it is shown that the category of algebras for each of these monads is isomorphic to the category of $(L,\oplus,*)$-convex compacta and their affine maps.
Classification : 18B30, 18C20, 06B35, 52A01
Mots-clés : Capacity functor, algebra for a monad, idempotent semimodule, idempotent convexity, plausibility measure 
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     author = {O. Nykyforchyn and D. Repovs},
     title = {L-Convexity and {Lattice-Valued} {Capacities}},
     journal = {Journal of convex analysis},
     pages = {29--52},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a1/}
}
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O. Nykyforchyn; D. Repovs. L-Convexity and Lattice-Valued Capacities. Journal of convex analysis, Tome 21 (2014) no. 1, pp. 29-52. http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a1/