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A Bibliometric Analysis of the Explainable Artificial Intelligence Research Field Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Size-Based Super Level Measures on Discrete Space

Authors : Jana Borzová, Lenka Halčinová, Jaroslav Šupina

Published in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Publisher: Springer International Publishing

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Abstract

We continue in the investigation of a concept of size introduced by Do and Thiele [3]. Our focus is a computation of corresponding super level measure, a key component of size application, on discrete space, i.e., a finite set with discrete topology. We found critical numbers which determine the change of a value of super level measure and we present an algorithm for super level measure computation based on these numbers.

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previous chapter On the Problem of Aggregation of Partial T-Indistinguishability Operators
next chapter What Is the Aggregation of a Partial Metric and a Quasi-metric?
Footnotes
1
Size was originally introduced for complex valued functions. However, non-negative values are sufficient, compare [3, 5].
 
2
The constant \(C_{\mathsf {s}}\) depends only on \(\mathsf {s}\).
 
3
By \(\mathbf 1 _F:\,[n]\rightarrow \{0,1\}\) we denote the characteristic function of the set F.
 
4
Which is equivalent to covering property (COV) in [5].
 
5
I.e., satisfying condition (COV) in [5].
 
Literature
1.
Chen, T., Mesiar, R., Li, J., Stupňanová, A.: Possibility and necessity measures and integral equivalence. Int. J. Approx. Reason. 86, 62–72 (2017)MathSciNetCrossRef
2.
3.
Do, Y., Thiele, C.: \(L^p\) theory for outer measures and two themes of Lennart Carleson united. Bull. Amer. Math. Sci. 52(2), 249–296 (2015)CrossRef
4.
5.
6.
Klement, E.P., Mesiar, R., Spizzichino, F., Stupňanová, A.: Universal integrals based on copulas. Fuzzy Optim. Decis. Making 13(3), 273–286 (2014)MathSciNetCrossRef
7.
Pap, E.: Sublinear means. In: 36th Linz Seminar on Fuzzy Sets Theory: Functional Equations and Inequalities, Linz, 2–6 February 2016, pp. 75–88 (2016)
8.
9.
Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. thesis, Tokyo Institute of Technology (1974)
10.
Metadata
Title
Size-Based Super Level Measures on Discrete Space
Authors
Jana Borzová
Lenka Halčinová
Jaroslav Šupina
Copyright Year
2018
Book
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Print ISBN: 978-3-319-91472-5

Electronic ISBN: 978-3-319-91473-2

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91473-2_19

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