Abstract
Abstract
Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their ambiguous representations, for which taking pseudo-inverse is involutive, form categories. Self-dualities and contravariant equivalences for these categories are obtained. Possible interpretations and applications to processing of imperfect information are discussed.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Geometry and Topology,Algebra and Number Theory
Reference17 articles.
1. Akian, M.: Densities of invariant measures and large deviations. Trans. Amer. Math. Soc. 351(11), 4515–4543 (1999)
2. Bergmann, M.: Introduction to many-valued and fuzzy logic: Semantics, algebras, and derivation systems. Cambridge University Press, New York (2008)
3. Edalat, A.: Domains for computation in mathematics, physics and exact real arithmetic. Bull. Symb. Logic 3(4), 401–452 (1997)
4. Erné, M.: Z-distributive function spaces preprint (1998)
5. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S., Lattices, Continuous: Domains encyclopedia of mathematics and its applications, vol. 93. Cambridge University Press, New York (2003)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Compatibilities between continuous semilattices;Carpathian Mathematical Publications;2021-01-04