Why λ -additive (fuzzy) measures?

Ion Chiţescu

Kybernetika (2015)

  • Volume: 51, Issue: 2, page 246-254
  • ISSN: 0023-5954

Abstract

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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 λ -additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.

How to cite

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Chiţescu, Ion. "Why $\lambda $-additive (fuzzy) measures?." Kybernetika 51.2 (2015): 246-254. <http://eudml.org/doc/270131>.

@article{Chiţescu2015,
abstract = {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.},
author = {Chiţescu, Ion},
journal = {Kybernetika},
keywords = {generalized measure (probability); $\lambda $-additive measure; functional equation; generalized measure (probability); $\lambda $-additive measure; functional equation},
language = {eng},
number = {2},
pages = {246-254},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Why $\lambda $-additive (fuzzy) measures?},
url = {http://eudml.org/doc/270131},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Chiţescu, Ion
TI - Why $\lambda $-additive (fuzzy) measures?
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 2
SP - 246
EP - 254
AB - 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.
LA - eng
KW - generalized measure (probability); $\lambda $-additive measure; functional equation; generalized measure (probability); $\lambda $-additive measure; functional equation
UR - http://eudml.org/doc/270131
ER -

References

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  1. Aczel, J., Lectures on Functional Equations and Their Applications., Dover Publications, Inc. Mineola, New York 2006. Zbl0139.09301
  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., 10.1007/978-0-387-76852-6, Springer (IFSR Internat. Ser. Systems Sci. Engrg. 25) (2009). Zbl1184.28002MR2453907DOI10.1007/978-0-387-76852-6

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