An orness measure for quasi-arithmetic means

IEEE Transactions on Fuzzy Systems

Volumn 14, Issue 6, 2006, Pages 837-848

  Liu, Xinwang ^a  

^a Southeast University   (China)

Author keywords

Aggregation operator; Orness; Quasi arithmetic mean

Indexed keywords

FUNCTION EVALUATION; FUNCTION GENERATORS; MATHEMATICAL OPERATORS; PARAMETERIZATION;

AGGREGATION OPERATOR; EXPONENTIAL FUNCTIONS; QUASI-ARITHMETIC MEANS;

DIGITAL ARITHMETIC;

EID: 33947227224     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2006.879990     Document Type: Article

References (37)

1. D. Dubois and H. Prade, "A review of fuzzy set aggregation connectives," Inf. Sci., vol. 36, no. 1, pp. 85-121, 1985.
2. G. Beliakov, "How to build aggregation operators from data," Int. J. Intell. Syst., vol. 18, no. 8, pp. 903-923, 2003.
3. T. Calvo, A. Kolesárova, M. Komorníkova, and R. Mesiar, T. Calvo, G. Mayor, R. Mesiar, and Heilderberg, Eds., "Aggregation operators: Basic concepts, issues and properties," in Aggregation Operators: New Trends and Applications. New York: Physica-Verlag, 2002, pp. 3-103.
4. T. Calvo and R. Mesiar, "Aggregation operators: Ordering and bounds," Fuzzy Sets Syst., vol. 139, no. 3, pp. 685-697, 2003.
5. J. Chiang, "Aggregating membership values by a Choquet-fuzzy- integral based operator," Fuzzy Sets Syst., vol. 114, no. 3, pp. 367-375, 2000.
6. V. Peneva and I. Popchev, "Properties of the aggregation operators related with fuzzy relations," Fuzzy Sets Syst., vol. 139, no. 3, pp. 615-633, 2003.
7. J.-L. Marichal, Aggregation Operators for Multicriteria Decision Aid Belgium, Inst. Math., Univ. Liege, Liege, 1998, Ph.D..
8. R. R. Yager and J. Kacprzyk, The ordered weighted averaging operators - Theory and applications. Boston, MA: Kluwer Academic, 1997.
9. Z. S. Xu and Q. L. Da, "An overview of operators for aggregating information," Int. J. Intell. Syst., vol. 18, no. 9, pp. 953-969, 2003.
10. R. R. Yager, "On ordered weighted averaging aggregation operators in multicriteria decision making," IEEE Trans. Syst., Man, Cybern., vol. 18, pp. 183-190, 1988.
11. _, "Families of OWA operators," Fuzzy Sets Syst., vol. 59, no. 2, pp. 125-143, 1993.
12. V. Torra, "The weighted OWA operator," Int. J. Intell. Syst., vol. 12, no. 2, pp. 153-166, 1997.
13. X.-W. Liu and L.-H. Chen, "On the properties of parametric geometric OWA operator," Int. J. Approx. Reas., vol. 35, no. 2, pp. 163-178, 2004.
14. F. Herrera, E. Herrera-Viedma, and J. Verdegay, "Direct approach processes in group decision making using linguistic OWA operators," Fuzzy Sets Syst., vol. 79, no. 2, pp. 175-190, 1996.
15. R. R. Yager, "On the valuation of alternatives for decision-making under uncertainty," Int. J. Intell. Syst., vol. 17, no. 7, pp. 687-707, 2002.
16. _, "Fuzzy modeling for intelligent decision making under uncertainty," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 30, no. 1, pp. 60-70, 2000.
17. _, "Decision making with fuzzy probability assessments," IEEE Trans. Fuzzy Syst., vol. 7, pp. 462-467, 1999.
18. D. Filev and R. R. Yager, "On the issue of obtaining OWA operator weights," Fuzzy Sets Syst., vol. 94, no. 2, pp. 157-169, 1998.
19. R. Fullér and P. Majlender, "On obtaining minimal variability OWA operator weights," Fuzzy Sets Syst., vol. 136, no. 2, pp. 203-215, 2003.
20. A. Kolesárová, "Limit properties of quasi-arithmetic means," Fuzzy Sets Syst., vol. 124, no. 1, pp. 65-71, 2001.
21. A. Valls and V. Torra, "Using classification as an aggregation tool in MCDM," Fuzzy Sets Syst., vol. 115, no. 1, pp. 159-168, 2000.
22. J. S. Ume and Y. H. Kim, "Some mean values related to the quasi-arithmetic mean," J. Math. Anal. Applicat., vol. 252, no. 1, pp. 167-176, 2000.
23. L. Godo and V. Torra, "On aggregation operators for ordinal qualitative information," IEEE Trans. Fuzzy Syst., vol. 8, pp. 143-154, 2000.
24. R. Smolikova and M. Wachowiak, "Aggregation operators for selection problems," Fuzzy Sets Syst., vol. 131, no. 1, pp. 23-34, 2002.
25. A. Pradera, E. Trillas, and T. Calvo, "A general class of triangular norm-based aggregation operators: quasi-linear T-S operators," Int. J. Approx. Reas., vol. 30, no. 1, pp. 57-72, 2002.
26. H. Larsen, "Efficient andness-directed importance weighted averaging operators," Int. J. Uncertainty Fuzziness Knowl.-Based Syst., vol. 11, no. Suppl, pp. 67-82, 2003.
27. V. Torra, "Learning weights for the quasi-weighted means," IEEE Trans. Fuzzy Syst., vol. 10, pp. 653-666, 2002.
28. _, "On some relationships between hierarchies of quasiarithmetic means and neural networks," Int. J. Intell. Syst., vol. 14, no. 11, pp. 1089-1098, 1999.
29. J. Dujmović, "Weighted conjunctive and disjunctive means and their application in system evaluation," Univ. Beograd. Publ. Elektrotechn. Fak., vol. 483, pp. 147-158, 1974.
30. J. J. Dujmovic and H. L. Legind, B. D. Baets, Ed., "Properties and modeling of partial conjunction/disjunction," in Current Issues in Data and Knowledge Engineering. Warsaw, Poland: Exit Publishers, 2004, pp. 215-224.
31. J. J. Dujmović, B. D. Baets, J. Fodor, and D. Radojević, Eds., in Proc. Eurof. 2005, Belgrade, Jun. 2005, pp. 56-80.
32. J. J. Dujmović, B. D. Baets, J. Fodor, and D. E. Radojević, "Seven flavors of andness/orness," in Proc. Eurof. 2005, Jun. 2005, pp. 81-92.
33. T. Calvo, G. Mayor, J. Torrens, J. Suner, M. Mas, and M. Carbonell, "Generation of weighting triangles associated with aggregation functions," Int. J. Uncertainty Fuzziness Knowl.-Based Syst., vol. 8, no. 4, pp. 417-451, 2000.
34. J. M. F. Salido and S. Murakami, "Extending Yager's orness concept for the OWA aggregators to other mean operators," Fuzzy Sets Syst., vol. 139, no. 3, pp. 515-542, 2003.
35. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, 2nd ed. Cambridge: Cambridge Univ. Press, 1952.
36. T. Calvo and R. Mesiar, "Weighted means based on triangular conorms," Int. J. Uncertainty Fuzziness Knowl.-Based Syst., vol. 9, no. 2, pp. 183-196, 2001.
37. V. Torra, "OWA operators in data modeling and reidentification, " IEEE Trans. Fuzzy Syst., vol. 12, pp. 652-660, 2004.