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Why \(\lambda\)-additive (fuzzy) measures? (English) Zbl 1363.28022
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.

MSC:
28E05 Nonstandard measure theory
28E10 Fuzzy measure theory
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[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). · Zbl 1184.28002 · doi:10.1007/978-0-387-76852-6
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