16,557 research outputs found
Decomposition approaches to integration without a measure
Extending the idea of Even and Lehrer [3], we discuss a general approach to
integration based on a given decomposition system equipped with a weighting
function, and a decomposition of the integrated function. We distinguish two
type of decompositions: sub-decomposition based integrals (in economics linked
with optimization problems to maximize the possible profit) and
super-decomposition based integrals (linked with costs minimization). We
provide several examples (both theoretical and realistic) to stress that our
approach generalizes that of Even and Lehrer [3] and also covers problems of
linear programming and combinatorial optimization. Finally, we introduce some
new types of integrals related to optimization tasks.Comment: 15 page
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
The idempotent Radon--Nikodym theorem has a converse statement
Idempotent integration is an analogue of the Lebesgue integration where
-additive measures are replaced by -maxitive measures. It has
proved useful in many areas of mathematics such as fuzzy set theory,
optimization, idempotent analysis, large deviation theory, or extreme value
theory. Existence of Radon--Nikodym derivatives, which turns out to be crucial
in all of these applications, was proved by Sugeno and Murofushi. Here we show
a converse statement to this idempotent version of the Radon--Nikodym theorem,
i.e. we characterize the -maxitive measures that have the
Radon--Nikodym property.Comment: 13 page
Fuzzy Interval-Valued Multi Criteria Based Decision Making for Ranking Features in Multi-Modal 3D Face Recognition
Soodamani Ramalingam, 'Fuzzy interval-valued multi criteria based decision making for ranking features in multi-modal 3D face recognition', Fuzzy Sets and Systems, In Press version available online 13 June 2017. This is an Open Access paper, made available under the Creative Commons license CC BY 4.0 https://creativecommons.org/licenses/by/4.0/This paper describes an application of multi-criteria decision making (MCDM) for multi-modal fusion of features in a 3D face recognition system. A decision making process is outlined that is based on the performance of multi-modal features in a face recognition task involving a set of 3D face databases. In particular, the fuzzy interval valued MCDM technique called TOPSIS is applied for ranking and deciding on the best choice of multi-modal features at the decision stage. It provides a formal mechanism of benchmarking their performances against a set of criteria. The technique demonstrates its ability in scaling up the multi-modal features.Peer reviewedProo
Generalized Lebesgue integral
AbstractA new definition of integral-like functionals exploiting the ideas of the Lebesgue integral construction and extending the idea of pan-integrals is given. Some convergence theorems for sequence of measurable functions are discussed. As a result, a theoretical basis for applications of the generalized Lebesgue integral is provided. Several types of integrals known from the literature are shown to be special cases of generalized Lebesgue integral
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