Three types of monotonicity of averaging functions

Knowledge-Based Systems

Volumn 72, Issue , 2014, Pages 114-122

  Beliakov, Gleb ^a   Calvo, Tomasa ^b   Wilkin, Tim ^a  

^a DEAKIN UNIVERSITY   (Australia)

^b UNIVERSITY OF ALCALÁ   (Spain)

Author keywords

Aggregation functions; Means; Monotonicity; Weak monotonicity

Indexed keywords

ARTIFICIAL INTELLIGENCE; SOFTWARE ENGINEERING;

AGGREGATION FUNCTIONS; CONSTRUCTION METHOD; IDEMPOTENT; MEANS; MONOTONE FUNCTIONS; MONOTONICITY; MONOTONICITY CONDITIONS;

KNOWLEDGE BASED SYSTEMS;

EID: 84909966897     PISSN: 09507051     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.knosys.2014.08.028     Document Type: Article

References (33)

1. P. Angelov, and R. Yager Density-based averaging - a new operator for data fusion Inform. Sci. 222 2013 163 174
2. D. Barash, and D. Comaniciu A common framework for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift Image Vis. Comput. 22 2004 73 81
3. G. Beliakov Monotonicity preserving approximation of multivariate scattered data BIT 45 2005 653 677
4. G. Beliakov Interpolation of Lipschitz functions J. Comp. Appl. Math. 196 2006 20 44
5. G. Beliakov Construction of aggregation operators for automated decision making via optimal interpolation and global optimization J. Indus. Manage. Optim. 3 2007 193 208
6. G. Beliakov, H. Bustince, and D. Paternain Image reduction using means on discrete product lattices IEEE Trans. Image Process. 21 3 2012 1070 1083
7. G. Beliakov, and T. Calvo Construction of aggregation operators with noble reinforcement IEEE Trans. Fuzzy Syst. 15 2007 1209 1218
8. G. Beliakov, T. Calvo, and J. Lázaro Pointwise construction of Lipschitz aggregation operators with specific properties Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 15 2007 193 223
9. G. Beliakov, G. Li, H.Q. Vu, and T. Wilkin Characterizing compactness of geometrical clusters using fuzzy measures IEEE Trans. Fuzzy Syst. 2014 10.1109/TFUZZ.2014.2336871 in press
10. G. Beliakov, G. Li, H.Q. Vu, T. Wilkin, Fuzzy measures of pixel cluster compactness, in: Proc. of the 11th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Beijing, China, 2014.
11. G. Beliakov, A. Pradera, and T. Calvo Aggregation Functions: A Guide for Practitioners, Studies in Fuzziness and Soft Computing vol. 221 2007 Springer-Verlag Berlin
12. G. Beliakov, and T. Wilkin On some properties of weighted averaging with variable weights Inform. Sci. 281 2014 1 7
13. P.S. Bullen Handbook of Means and Their Inequalities 2003 Kluwer Dordrecht
14. H. Bustince, J. Fernandez, A. Kolesárová, R. Mesiar, Directional monotonicity of fusion functions, Under review, 2014.
15. H. Bustince, J. Fernandez, A. Kolesárová, R. Mesiar, Fusion functions and directional monotonicity, in: Proceedings of IPMU'2014 Conference, Montpellier, France, 2014.
16. H. Bustince, D. Patermain, L. De Miguel, R. Mesiar, Some notions of internal operators, in: Proceedings of EUROFUSE'2013 Conference, 2013, pp. 43-49.
17. T. Calvo, A. Kolesárová, M. Komorníková, and R. Mesiar Aggregation operators: properties, classes and construction methods T. Calvo, G. Mayor, R. Mesiar, Aggregation Operators New Trends and Applications 2002 Physica-Verlag Heidelberg, New York 3 104
18. C. Gini, Le Medie, Unione Tipografico-Editorial Torinese, Milan (Russian translation, Srednie Velichiny, Statistica, Moscow, 1970), 1958.
19. M. Grabisch, J.-L. Marichal, R. Mesiar, and E. Pap Aggregation Functions Encyclopedia of Mathematics and Its Foundations 2009 Cambridge University Press
20. J. Lázaro, T. Rückschlossová, and T. Calvo Shift invariant binary aggregation operators Fuzzy Sets Syst. 142 2004 51 62
21. R.A. Marques Pereira, and R.A. Ribeiro Aggregation with generalized mixture operators using weighting functions Fuzzy Sets Syst. 137 2003 43 58
22. D. Paternain, J. Fernandez, H. Bustince, R. Mesiar, G. Beliakov, Construction of image reduction operators using averaging aggregation functions, Fuzzy Sets Syst., in press. http://dx.doi.org/10.1016/j.fss.2014.03.008.
23. R. Ribeiro, and R. Marques Pereira Generalized mixture operators using weighting functions Eur. J. Oper. Res. 145 2003 329 342
24. P. Rousseeuw Least median of squares regression J. Am. Stat. Assoc. 79 388 1984 871 880
25. P. Rousseeuw, and A. Leroy Robust Regression and Outlier Detection 1987 John Wiley and Sons
26. C. Tomasi, R. Manduchi, Bilateral filtering for gray and color images, in: Proc. of the 6th Int. Conf. on Computer Vision, Bombay, India, January 1998, pp. 839-846.
27. Y. Torra, and V. Narukawa Modeling Decisions Information Fusion and Aggregation Operators 2007 Springer Berlin, Heidelberg
28. J.F. Traub, and H. Wozniakowski A General Theory of Optimal Algorithms 1980 Academic Press New York
29. J. Špirková Weighted operators based on dissimilarity function Inform. Sci. 281 2014 172 181
30. T. Wilkin, Image reduction operators based on non-monotonic averaging functions, in: Proceedings of the 10th IEEE Int. Conf. on Fuzzy Systems, Hyderabad, India, 2013, http://dx.doi.org/10.1109/FUZZ-IEEE.2013.6622458.
31. T. Wilkin, G. Beliakov, Weakly monotone averaging functions, Under review, 2013.
32. T. Wilkin, G. Beliakov, Weakly monotone averaging functions, 2014. ArXiv:1408.0328, < http://arxiv.org/abs/1408.0328 >.
33. P.H. Wolfe Finding the nearest point in a polytope Math. Progr. 11 1976 128 149