960 research outputs found
Belief functions on lattices
We extend the notion of belief function to the case where the underlying
structure is no more the Boolean lattice of subsets of some universal set, but
any lattice, which we will endow with a minimal set of properties according to
our needs. We show that all classical constructions and definitions (e.g., mass
allocation, commonality function, plausibility functions, necessity measures
with nested focal elements, possibility distributions, Dempster rule of
combination, decomposition w.r.t. simple support functions, etc.) remain valid
in this general setting. Moreover, our proof of decomposition of belief
functions into simple support functions is much simpler and general than the
original one by Shafer
Bipolarization of posets and natural interpolation
The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of . We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy. A second aim of the paper is to define a general mechanism for the bipolarization of ordered structures. Bisets (or signed sets), as well as bisubmodular functions, bicapacities, bicooperative games, as well as the Choquet integral defined for them can be seen as particular instances of this scheme. Lastly, an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper.Interpolation; Choquet integral; Lattice; Bipolar structure
Expanding FLew with a Boolean connective
We expand FLew with a unary connective whose algebraic counterpart is the
operation that gives the greatest complemented element below a given argument.
We prove that the expanded logic is conservative and has the Finite Model
Property. We also prove that the corresponding expansion of the class of
residuated lattices is an equational class.Comment: 15 pages, 4 figures in Soft Computing, published online 23 July 201
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