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Title: Why $\lambda $-additive (fuzzy) measures? (English)
Author: Chiţescu, Ion
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 51
Issue: 2
Year: 2015
Pages: 246-254
Summary lang: English
Category: math
Summary: The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that $\lambda$-additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity. (English)
Keyword: generalized measure (probability)
Keyword: $\lambda $-additive measure
Keyword: functional equation
MSC: 28A23
MSC: 28E05
MSC: 28E10
MSC: 39B05
MSC: 39B22
MSC: 60A86
idZBL: Zbl 06487076
idMR: MR3350559
DOI: 10.14736/kyb-2015-2-0246
Date available: 2015-06-19T15:17:23Z
Last updated: 2016-01-03
Stable URL:
Reference: [1] Aczel, J.: Lectures on Functional Equations and Their Applications..Dover Publications, Inc. Mineola, New York 2006. Zbl 0139.09301
Reference: [2] Sugeno, M.: Theory of Fuzzy Integrals and Its Applications..Doctoral Dissertation, Tokyo Institute of Technology, 1974.
Reference: [3] Wang, Z.: Une classe de mesures floues - les quasi-mesures..BUSEFAL 6 (1981), 28-37.
Reference: [4] Wang, Z., Klir, G.: Generalized Measure Theory..Springer (IFSR Internat. Ser. Systems Sci. Engrg. 25) (2009). Zbl 1184.28002, MR 2453907, 10.1007/978-0-387-76852-6


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