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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:
 2.8e+06 Nonstandard measure theory 2.8e+11 Fuzzy measure theory
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##### 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). · Zbl 1184.28002 · doi:10.1007/978-0-387-76852-6
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