Article
MSC:
28A23,
28E05,
28E10,
39B05,
39B22,
60A86 | MR 3350559 | Zbl 06487076 | DOI: 10.14736/kyb-2015-2-0246
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Keywords:
generalized measure (probability); $\lambda $-additive measure; functional equation
generalized measure (probability); $\lambda $-additive measure; functional equation
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.
References:
[1] Aczel, J.: Lectures on Functional Equations and Their Applications. Dover Publications, Inc. Mineola, New York 2006. Zbl 0139.09301
[2] Sugeno, M.: Theory of Fuzzy Integrals and Its Applications. Doctoral Dissertation, Tokyo Institute of Technology, 1974.
[3] Wang, Z.: Une classe de mesures floues - les quasi-mesures. BUSEFAL 6 (1981), 28-37.
[4] Wang, Z., Klir, G.: Generalized Measure Theory. Springer (IFSR Internat. Ser. Systems Sci. Engrg. 25) (2009). DOI 10.1007/978-0-387-76852-6 | MR 2453907 | Zbl 1184.28002
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