Geodesic
Why $\lambda $-additive (fuzzy) measures?
Kybernetika, Tome 51 (2015) no. 2, pp. 246-254
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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.
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.
DOI : 10.14736/kyb-2015-2-0246
Classification : 28A23, 28E05, 28E10, 39B05, 39B22, 60A86
Keywords: generalized measure (probability); $\lambda $-additive measure; functional equation 
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Chiţescu, Ion. Why $\lambda $-additive (fuzzy) measures?. Kybernetika, Tome 51 (2015) no. 2, pp. 246-254. doi: 10.14736/kyb-2015-2-0246

[1] Aczel, J.: Lectures on Functional Equations and Their Applications. Dover Publications, Inc. Mineola, New York 2006. | Zbl

[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 | MR | Zbl

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