The ordered modular averages

IEEE Transactions on Fuzzy Systems

Volumn 19, Issue 1, 2011, Pages 42-50

  Mesiar, Radko ^a,b   Mesiarová Zemánková, Andrea ^c  

^a UNIVERSITY OF OSTRAVA   (Czech Republic)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^c INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Comonotone modularity; copula; modularity; symmetric capacity

Indexed keywords

ADDITIVITY; AGGREGATION FUNCTIONS; COMONOTONE MODULARITY; CONSTRUCTION METHOD; COPULA; MODULARITY; NEUTRAL ELEMENTS; ORDERED WEIGHTED AVERAGE; SYMMETRIC CAPACITY;

EID: 79551649338     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2010.2077641     Document Type: Article

References (27)

1. B. S. Ahn, "The OWA aggregation with uncertain descriptions on weights and input arguments" IEEE Trans. Fuzzy Syst., vol. 15, no. 6, pp. 1130- 1134, Dec. 2007.
2. G.Beliakov, "Learning weights in the generalizedOWAoperators," Fuzzy Optim. Decis. Making, vol. 4, pp. 119-130, 2005.
3. G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A Guide for Practitioners. New York: Springer-Verlag, 2007.
4. T. Calvo and R. Mesiar, " Stability of aggregation operators," in Proc. Int. Conf. Fuzzy Logic Technol., Leicester, U.K., 2001, pp. 475-478.
5. T. Calvo, A. Koleśarov́a, M. Komorńikov́a, and R. Mesiar, "Aggregation operators: Properties, classes and construction methods," in Aggregation Operators, T. Calvo, G. Mayor, R. Mesiar, Eds. Heidelberg, Germany: Physica-Verlag, 2002, pp. 3-107.
6. M. Couceiro and J.-L. Marichal, " Asociative polynomial funcations over bounded distributive lattices," Order, 2010, DOI:10.1007/s11083-010- 9150-8.
7. D. Dubois, H. Prade, and C. Testemale, " Weighted fuzzy pattern matching," Fuzzy Sets Syst., vol. 28, pp. 313-331, 1988.
8. M. Grabisch, "Fuzzy integral in multicriteria decision making," Fuzzy Sets Syst., vol. 69, pp. 279-298, 1995.
9. M. Grabisch, J.-L. Marichal, R. Mesiar, and E. Pap, Aggregation Functions. Cambridge, U.K.: Cambridge Univ. Press, 2009.
10. M. Grabisch, "OWA operators and nonadditive integrals," to appear in [27]
11. H. Imaoka, "On a subjective evaluation model by a generalized fuzzy integral" Int. J. Uncertain. Fuzziness Knowl.-Based Syst., vol. 5, pp. 517- 529, 1997.
12. E. P. Klement, A. Koleśarov́a, R. Mesiar, and C. Sempi, " Copulas constructed from horizontal sections," Comm. Statist. Theory Methods, vol. 36, no. 13-16, pp. 2901-2911, 2007.
13. E. P. Klement, A. Koleśarov́a, R. Mesiar, and A. Stup̌ nanov́a, "Lipschitz continuity of discrete universal integrals based on copulas," Int. J. Uncertain. Fuzziness Knowl.-Based Syst., vol. 18, no. 1, pp. 39-52, 2010.
14. E. P. Klement, R. Mesiar, and E. Pap, " Measure-based aggregation operators," Fuzzy Sets Syst., vol. 142, no. 1, pp. 3-14, 2004.
15. E. P. Klement, R. Mesiar, and E. Pap, " A universal integral as common frame for Choquet and Sugeno integral," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 178-187, Feb. 2010.
16. J. M. Meriǵo and A. M. Gil-Lafuente, " The induced generalized OWA operator," in Proc. New Dimensions Fuzzy Logic Related Technologies. Proc. 5th EUSFLAT Conf., Ostrava, Czech Republic, 2007, pp. 463-470.
17. T. Murofushi and M. Sugeno, " Some quantities represented by theChoquet integral," Fuzzy Sets Syst., vol. 56, pp. 229-235, 1993.
18. R. B. Nelsen, An Introduction to Copulas. New York: Springer-Verlag, 1999.
19. K. F. Siburg and P. Stoimenov, " Gluing copulas," Commun. Statist.: Theory Methods, vol. 37, no. 19, pp. 3124-3134, 2008.
20. V. Torra, "The weighted OWA operator," Int. J. Intell. Syst., vol. 12, pp. 153-166, 1997.
21. R. R. Yager, "On ordered weighted averaging aggregation operators in multicriteria decision making" IEEE Trans. Syst., Man Cybern., vol. 18, no. 1, pp. 183-190, Jan./Feb. 1988.
22. R. R. Yager and D. P. Filev, Essentials of Fuzzy Modeling and Control. New York: Wiley-Interscience, 1994.
23. R. R. Yager and D. P. Filev, " Induced ordered weighted averaging operators," IEEE Trans. Syst., Man Cybern., vol. 29, no. 2, pp. 141-150, Apr. 1999.
24. R. R.Yager and J. Kacprzyk, The OrderedWeighted Averaging Operators: Theory and Applications. Boston, MA: Kluwer, 1997.
25. R. R. Yager, "Using stress functions to obtain OWA operators," IEEE Trans. Fuzzy Syst., vol. 15, no. 6, pp. 1122-1129, Dec. 2007.
26. R. R. Yager, "Time series smoothing and OWA aggregation," IEEE Trans. Fuzzy Syst., vol. 16, no. 4, pp. 994-1007, Aug. 2008.
27. R. R. Yager, J. Kacprzyk, and G. Beliakov, Recent Developmen ts in the Ordered Weighted Averaging Operators: Theory and Practice. NewYork: Springer-Verlag, in press.