Statistical Estimations of Lattice-Valued Possibilistic Distributions

0361642 - ÚI 2012 RIV DE eng C - Conference Paper (international conference)
Kramosil, Ivan - Daniel, Milan
Statistical Estimations of Lattice-Valued Possibilistic Distributions.
Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Heidelberg: Springer, 2011 - (Liu, W.), s. 688-699. Lecture Notes in Artificial Intelligence, 6717. ISBN 978-3-642-22151-4. ISSN 0302-9743.
[ECSQARU 2011. European Conference /11./. Belfast (GB), 29.06.2011-01.07.2011]
R&D Projects: GA ČR GEICC/08/E018; GA ČR GAP202/10/1826
Institutional research plan: CEZ:AV0Z10300504
Keywords : complete lattice * upper-valued semilattice * lattice-valued possibilistic distribution * random samples from upper-valued semilattices * probabilistic algorithms * Monte-Carlo methods
Subject RIV: BA - General Mathematics

The most often applied non-numerical uncertainty degrees are those taking their values in complete lattices, but also their weakened versions may be of interest. In what follows, we introduce and analyze possibilistic distributions and measures taking values in finite upper-valued possibilistic lattices, so that only for finite sets of such values their supremum is defined. For infinite sets of values of the finite lattice in question we apply the idea of the so called Monte-Carlo method: sample at random and under certain conditions a large enough finite subset of the infinite set in question, and take the supremum over this finite sample set as a "good enough" estimation of the undefined supremum of the infinite set. A number of more or less easy to prove assertions demonstrate the conditions when and in which sense the quality of the results obtained by replacing non-existing or non-accessible supremum values by their random estimations tend to the optimum results supposing that the probabilistic qualities of the statistical estimations increase as demanded by Monte-Carlo methods.
Permanent Link: http://hdl.handle.net/11104/0198909