Representation and construction of homogeneous and quasi-homogeneous -ary aggregation functions
Kybernetika (2021)
- Volume: 57, Issue: 6, page 958-969
- ISSN: 0023-5954
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topSu, Yong, and Mesiar, Radko. "Representation and construction of homogeneous and quasi-homogeneous $n$-ary aggregation functions." Kybernetika 57.6 (2021): 958-969. <http://eudml.org/doc/297594>.
@article{Su2021,
abstract = {Homogeneity, as one type of invariantness, means that an aggregation function is invariant with respect to multiplication by a constant, and quasi-homogeneity, as a relaxed version, reflects the original output as well as the constant. In this paper, we characterize all homogeneous/quasi-homogeneous $n$-ary aggregation functions and present several methods to generate new homogeneous/quasi-homogeneous $n$-ary aggregation functions by aggregation of given ones.},
author = {Su, Yong, Mesiar, Radko},
journal = {Kybernetika},
keywords = {aggregation functions; invariantness; homogeneity; quasi-homogeneity},
language = {eng},
number = {6},
pages = {958-969},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Representation and construction of homogeneous and quasi-homogeneous $n$-ary aggregation functions},
url = {http://eudml.org/doc/297594},
volume = {57},
year = {2021},
}
TY - JOUR
AU - Su, Yong
AU - Mesiar, Radko
TI - Representation and construction of homogeneous and quasi-homogeneous $n$-ary aggregation functions
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 6
SP - 958
EP - 969
AB - Homogeneity, as one type of invariantness, means that an aggregation function is invariant with respect to multiplication by a constant, and quasi-homogeneity, as a relaxed version, reflects the original output as well as the constant. In this paper, we characterize all homogeneous/quasi-homogeneous $n$-ary aggregation functions and present several methods to generate new homogeneous/quasi-homogeneous $n$-ary aggregation functions by aggregation of given ones.
LA - eng
KW - aggregation functions; invariantness; homogeneity; quasi-homogeneity
UR - http://eudml.org/doc/297594
ER -
References
top- Aczél, J., Lectures on Functional Equations and their Applications., Acad. Press, New York 1966. MR0208210
- Alsina, C., Frank, M. J., Schweizer, B., Associative Functions., Triangular Norms and Copulas, World Scientific Publishing Co., Singapore 2006. MR2222258
- Dujmovic, J. J., , Univ. Beograd Publ. Elektrotech. Fak. 483 (1974), 147-158. MR0378884DOI
- Ebanks, B. R., 10.1155/S0161171298000489, Int. J. Math. Math. Sci. 21 (1998), 351-358. MR1609715DOI10.1155/S0161171298000489
- Even, Y., Lehrer, E., , Economic Theory 56 (2014), 1, 33-58. MR3190759DOI
- Grabisch, M., Marichal, J. L., Mesiar, R., Pap, E., Aggregation Functions., Cambridge University Press, New York 2009. Zbl1206.68299MR2538324
- Klement, E. P., Mesiar, R., Pap, E., Triangular Norms., Kluwer Academic Publisher, Dordrecht 2000. Zbl1087.20041MR1790096
- Lima, L., Bedregal, B., Bustince, H., Barrenechea, E., Rocha, M., , Inform. Sci. 355-356 (2016), 328-347. DOI
- Nelsen, R. E., An Introduction to Copulas. Second edition., Springer, New York 2006. MR2197664
- Mayor, G., Mesiar, R., Torrens, J., , Kybernetika 44 (2008), 6, 745-755. MR2488902DOI
- Mesiar, R., Li, J., Pap, E., , Int. J. Approx. Reasoning 54 (2013), 357-364. Zbl1267.28018MR3021836DOI
- Mesiar, R., Rückschlossová, T., , Fuzzy Sets and Systems 142 (2004), 63-73. MR2045343DOI
- Rückschlossová, T., Rückschloss, R., Homogeneous aggregation operators., Kybernetika 42(3) (2006), 279-286. MR2253389
- Xie, A., Su, Y., Liu, H., , Fuzzy Sets and Systems 287 (2016), 203-212. MR3447027DOI
- Su, Y., Zong, W., Mesiar, R., , Fuzzy Sets and Systems, in press. DOI
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