3,395 research outputs found
Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
In this paper we study the Pettis integral of fuzzy mappings in arbitrary
Banach spaces. We present some properties of the Pettis integral of fuzzy
mappings and we give conditions under which a scalarly integrable fuzzy mapping
is Pettis integrable
Fuzzy games with a countable space of actions and applications to systems of generalized quasi-variational inequalities
In this paper, we introduce an abstract fuzzy economy (generalized fuzzy
game) model with a countable space of actions and we study the existence of the
fuzzy equilibrium. As applications, two types of results are obtained. The
first ones concern the existence of the solutions for systems of generalized
quasi-variational inequalities with random fuzzy mappings which we define. The
last ones are new random fixed point theorems for correspondences with values
in complete countable metric spaces.Comment: 18 page
Optimal measurements in quantum mechanics
Four common optimality criteria for measurements are formulated using
relations in the set of observables, and their connections are clarified. As
case studies, 1-0 observables, localization observables, and photon counting
observables are considered.Comment: minor correction
Invariant functionals on completely distributive lattices
In this paper we are interested in functionals defined on completely
distributive lattices and which are invariant under mappings preserving
{arbitrary} joins and meets. We prove that the class of nondecreasing invariant
functionals coincides with the class of Sugeno integrals associated with
-valued capacities, the so-called term functionals, thus extending
previous results both to the infinitary case as well as to the realm of
completely distributive lattices. Furthermore, we show that, in the case of
functionals over complete chains, the nondecreasing condition is redundant.
Characterizations of the class of Sugeno integrals, as well as its superclass
comprising all polynomial functionals, are provided by showing that the
axiomatizations (given in terms of homogeneity) of their restriction to
finitary functionals still hold over completely distributive lattices. We also
present canonical normal form representations of polynomial functionals on
completely distributive lattices, which appear as the natural extensions to
their finitary counterparts, and as a by-product we obtain an axiomatization of
complete distributivity in the case of bounded lattices
Art Neural Networks for Remote Sensing: Vegetation Classification from Landsat TM and Terrain Data
A new methodology for automatic mapping from Landsat Thematic Mapper (TM) and terrain data, based on the fuzzy ARTMAP neural network, is developed. System capabilities are tested on a challenging remote sensing classification problem, using spectral and terrain features for vegetation classification in the Cleveland National Forest. After training at the pixel level, system performance is tested at the stand level, using sites not seen during training. Results are compared to those of maximum likelihood classifiers, as well as back propagation neural networks and K Nearest Neighbor algorithms. ARTMAP dynamics are fast, stable, and scalable, overcoming common limitations of back propagation, which did not give satisfactory performance. Best results are obtained using a hybrid system based on a convex combination of fuzzy ARTMAP and maximum likelihood predictions. A prototype remote sensing example introduces each aspect of data processing and fuzzy ARTMAP classification. The example shows how the network automatically constructs a minimal number of recognition categories to meet accuracy criteria. A voting strategy improves prediction and assigns confidence estimates by training the system several times on different orderings of an input set.National Science Foundation (IRI 94-01659, SBR 93-00633); Office of Naval Research (N00014-95-l-0409, N00014-95-0657
Error Bounds and Holder Metric Subregularity
The Holder setting of the metric subregularity property of set-valued
mappings between general metric or Banach/Asplund spaces is investigated in the
framework of the theory of error bounds for extended real-valued functions of
two variables. A classification scheme for the general Holder metric
subregularity criteria is presented. The criteria are formulated in terms of
several kinds of primal and subdifferential slopes.Comment: 32 pages. arXiv admin note: substantial text overlap with
arXiv:1405.113
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