
Journal of Convex Analysis 21 (2014), No. 1, 029052 Copyright Heldermann Verlag 2014 LConvexity and LatticeValued Capacities Oleh Nykyforchyn Dept. of Mathematics and Computer Science, Vasyl' Stefanyk Precarpathian National University, Shevchenka 57, IvanoFrankivsk 76025, Ukraine oleh.nyk@gmail.com Dusan Repovs Faculty of Mathematics and Physics, University of Ljubljana, P.O. Box 2964, Ljubljana 1001, Slovenia dusan.repovs@guest.arnes.si [Abstractpdf] $L$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. Keywords: Capacity functor, algebra for a monad, idempotent semimodule, idempotent convexity, plausibility measure. MSC: 18B30, 18C20, 06B35, 52A01 [ Fulltextpdf (257 KB)] for subscribers only. 