On a Particular Class of Lattice-Valued Possibilistic Distributions

0350092 - ÚI 2012 RIV CZ eng J - Journal Article
Kramosil, Ivan
On a Particular Class of Lattice-Valued Possibilistic Distributions.
Neural Network World. Roč. 21, č. 5 (2011), s. 407-427. ISSN 1210-0552
R&D Projects: GA ČR GEICC/08/E018
Institutional research plan: CEZ:AV0Z10300504
Keywords : possibilistic distribution * possibilistic measure * lattice-valued uncertainty degrees * complete lattice * boolean ordering * lexicographic ordering * possibilistic entropy function
Subject RIV: BA - General Mathematics
Impact factor: 0.646, year: 2011

Investigated are possibilistic distributions taking as their values sequences from the infinite Cartesian product of identical copies of a fixed finite subset of the unit interval of real numbers. Uniform and lexicographic partial orderings on the space of these sequences are defined and the related complete lattices introduced. Lattice-valued entropy function is defined in the common pattern for both the orderings, naturally leading to different entropy values for the particular ordering applied in the case under consideration. The mappings on possibilistic distributions with uniform partial ordering under which the corresponding entropy values are conserved as well as approximations of possibilistic distributions with respect to this entropy function are also investigated.
Permanent Link: http://hdl.handle.net/11104/0006123