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2015 | OriginalPaper | Buchkapitel

1. Generalized Fuzzy Measurability

verfasst von : Anca Croitoru, Nikos Mastorakis

Erschienen in: Computational Problems in Science and Engineering

Verlag: Springer International Publishing

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Abstract

In this paper we introduce two concepts of generalized measurability for set-valued functions, namely \(\varphi\)-μ-total-measurability and \(\varphi\)-μ-measurability relative to a non-negative function \(\varphi: \mathcal{P}_{0}(X) \times \mathcal{P}_{0}(X) \rightarrow [0,+\infty )\) and a non-negative set function \(\mu: \mathcal{A}\rightarrow [0,+\infty )\) and present some relationships between them. We also define different types of convergences for sequences of set-valued functions and prove some relationships among them and a theorem of Egorov type. Finally, we introduce two semi-metrics on a space of set-valued functions and then compare them.

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Metadaten
Titel
Generalized Fuzzy Measurability
verfasst von
Anca Croitoru
Nikos Mastorakis
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-15765-8_1

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