Abstract

LL-idempotent analogues of convexity are introduced (LL is a completely distributive lattice). It is proved that the category of algebras for the monad of LL-valued capacities (regular plausibility measures) in the category of compacta is isomorphic to the category of LL-idempotent biconvex compacta and their biaffine maps. For the functor of LL-valued ∪\cup-capacities (LL-possibility measures) a family of monads parameterized by monoidal operations ∗:L×L→L*: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,⊕,∗)(L,\oplus,*)-convex compacta and their affine maps.

Author information

Contact details are reproduced from the original publication and may be historical.

Oleh Nykyforchyn

Dept. of Mathematics and Computer Science, Vasyl' Stefanyk Precarpathian National University, Shevchenka 57, Ivano-Frankivsk 76025, Ukraine

oleh.nyk@gmail.com

Dušan Repovš

Faculty of Mathematics and Physics, University of Ljubljana, P.O. Box 2964, Ljubljana 1001, Slovenia

dusan.repovs@guest.arnes.si

Keywords

  • Capacity functor
  • algebra for a monad
  • idempotent semimodule
  • idempotent convexity
  • plausibility measure

Mathematics Subject Classification

18B30, 18C20, 06B35, 52A01

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Suggested citation

O. Nykyforchyn, D. Repovš. “L-Convexity and Lattice-Valued Capacities.” Journal of Convex Analysis 21 (2014), No. 1, 29–52. https://doi.org/10.68381/jca21002

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.