Possibilistic Measures Taking Their Values in Spaces Given by Inclusion-Closed Fragments of Power-Sets

Authors: Ivan Kramosil
Publication year: 2009
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Projects: Mathematical foundation of inference and decision under uncertainty
Bibliographic citation: KRAMOSIL, Ivan. Possibilistic Measures Taking Their Values in Spaces Given by Inclusion-Closed Fragments of Power-Sets. In: SOSSAI, C., CHEMELLO, G., eds. Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Berlin: Springer, 2009, S. 688-699. Lecture Notes in Artificial Intelligence, 5590. ISBN 978-3-642-02905-9. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-642-02906-6_59
DOI: 10.1007/978-3-642-02906-6_59
ID: 327311

Abstract

Possibilistic distributions and measures with non-numerical membership degrees have been developed mostly under the simplifying assumption that these degrees are taken from a complete lattice. In this paper the conditions imposed on the space of possibilistic values are weakened in such a way that this space is defined by an inclusion-closed system of subsets of a space X. Let us note that the system of all finite subsets of an infinite space X (an incomplete lattice) or the system of all subsets of X the cardinality of which does not exceed a fixed number are examples of inclusion-closed systems of subsets of X.