Fuzzy weighted average as a fuzzified aggregation operator and its properties

Ondřej Pavlačka; Martina Pavlačková; Vladislav Hetfleiš

Kybernetika (2017)

  • Volume: 53, Issue: 1, page 137-160
  • ISSN: 0023-5954

Abstract

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The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive fuzzy numbers. The usefulness of the obtained results is discussed and illustrated by several numerical examples.

How to cite

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Pavlačka, Ondřej, Pavlačková, Martina, and Hetfleiš, Vladislav. "Fuzzy weighted average as a fuzzified aggregation operator and its properties." Kybernetika 53.1 (2017): 137-160. <http://eudml.org/doc/287950>.

@article{Pavlačka2017,
abstract = {The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive fuzzy numbers. The usefulness of the obtained results is discussed and illustrated by several numerical examples.},
author = {Pavlačka, Ondřej, Pavlačková, Martina, Hetfleiš, Vladislav},
journal = {Kybernetika},
keywords = {aggregation operator; fuzzy weighted average; fuzzy numbers; fuzzy weights},
language = {eng},
number = {1},
pages = {137-160},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Fuzzy weighted average as a fuzzified aggregation operator and its properties},
url = {http://eudml.org/doc/287950},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Pavlačka, Ondřej
AU - Pavlačková, Martina
AU - Hetfleiš, Vladislav
TI - Fuzzy weighted average as a fuzzified aggregation operator and its properties
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 1
SP - 137
EP - 160
AB - The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive fuzzy numbers. The usefulness of the obtained results is discussed and illustrated by several numerical examples.
LA - eng
KW - aggregation operator; fuzzy weighted average; fuzzy numbers; fuzzy weights
UR - http://eudml.org/doc/287950
ER -

References

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  1. Baas, S., Kwakernaak, H., 10.1016/0005-1098(77)90008-5, Automatica 13 (1977), 47-58. MR0439026DOI10.1016/0005-1098(77)90008-5
  2. Beliakov, G., Pradera, A., Calvo, T., Aggregation Functions: A Guide for Practitioners., Springer-Verlag, Berlin 2007. 
  3. Calvo, T., Mayor, G., (eds.), R. Mesiar, 10.1007/978-3-7908-1787-4, Physica-Verlag, Heidelberg 2002. Zbl0983.00020MR1936384DOI10.1007/978-3-7908-1787-4
  4. Campos, L. M. De, Heute, J. F., Moral, S., 10.1142/s0218488594000146, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 2 (1994), 167-196. MR1282406DOI10.1142/s0218488594000146
  5. Dong, W. M., Wong, F. S., 10.1016/0165-0114(87)90163-1, Fuzzy Sets and Systems 21 (1987), 183-199. Zbl0611.65100MR0871975DOI10.1016/0165-0114(87)90163-1
  6. Dubois, D., 10.1016/j.fss.2012.09.003, Fuzzy Sets and Systems 213 (2013), 106-108. MR3007014DOI10.1016/j.fss.2012.09.003
  7. Dubois, D., Prade, H., 10.1109/tac.1981.1102744, IEEE Trans. Automat. Control 26(1981), 4, 926-936. MR0635852DOI10.1109/tac.1981.1102744
  8. Fodor, J. C., Roubens, M., 10.1007/978-94-017-1648-2_3, Kluwer Academic Publishers, Dordrecht 1994. Zbl0827.90002DOI10.1007/978-94-017-1648-2_3
  9. Ghazinoory, S., Zadeh, A. E., Kheirkhah, A. S., 10.1016/j.ins.2010.01.012, Inform. Sci. 180 (2010), 9, 1582-1590. DOI10.1016/j.ins.2010.01.012
  10. Grabisch, M., Marichal, J. L., Mesiar, R., Pap, E., 10.1017/cbo9781139644150, Cambridge University Press, Cambridge 2009. Zbl1206.68299MR2538324DOI10.1017/cbo9781139644150
  11. Guh, Y.-Y., Hong, C. C., Wang, K. M., Lee, E. S., 10.1016/0898-1221(96)00171-x, Comp. Math. Appl. 32 (1996), 115-123. DOI10.1016/0898-1221(96)00171-x
  12. Guh, Y. Y., Hon, C. C., Lee, E. S., 10.1016/s0165-0114(98)00333-9, Fuzzy Sets and Systems 117 (2001), 1, 157-160. MR1891319DOI10.1016/s0165-0114(98)00333-9
  13. Hung, K. C., Julian, P., Chien, T., Jin, W. T. H., 10.1016/j.eswa.2009.04.069, Expert Systems Appl. 37 (1) (2010), 202-213. DOI10.1016/j.eswa.2009.04.069
  14. Chang, P. T., Hung, K. C., 10.1016/j.camwa.2004.10.042, Comp. Math. Appl. 49 (2005), 1797-1814. MR2154685DOI10.1016/j.camwa.2004.10.042
  15. Kao, C., Liu, S. T., 10.1016/s0165-0114(99)00137-2, Fuzzy Sets and Systems 120 (2001), 3, 435-444. Zbl1103.90411MR1829262DOI10.1016/s0165-0114(99)00137-2
  16. Kaufmann, A., Gupta, M. M., Introduction to Fuzzy Arithmetic: Theory and Applications. (Second edition), Van Nostrand Reinhold, New York 1991. MR1132439
  17. Klir, G. J., Pan, Y., 10.1007/s005000050038, Soft Computing 2 (1998), 100-108. DOI10.1007/s005000050038
  18. Klir, G. J., Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications., Prentice Hall, New Jersey, 1996. Zbl0915.03001MR1443433
  19. Lin, C. H., Tan, B., Hsieh, P. J., 10.1111/j.1540-5414.2005.00081.x, Decision Sciences 36 (2005), 3, 489-511. DOI10.1111/j.1540-5414.2005.00081.x
  20. Liu, F., Mendel, J. M., 10.1109/tfuzz.2007.896229, IEEE Trans. Fuzzy Systems 16 (2008), 1, 1-12. DOI10.1109/tfuzz.2007.896229
  21. Liu, X., Mendel, J. M., Wu, D., 10.1016/j.ins.2011.10.006, Inform. Sci. 187 (2012), 151-170. Zbl1248.03072MR2869869DOI10.1016/j.ins.2011.10.006
  22. Pavlačka, O., Talašová, J., Application of the Fuzzy Weighted Average of Fuzzy Numbers in Decision Making Models., In: New Dimensions in Fuzzy Logic and Related Technologies. Vol II. (M. Štěpnička,, V. Novák, and U. Bodenhofer, eds.) Proc. 5th EUSFLAT Conference, Ostravská univerzita, Ostrava 2007, pp. 455-462. 
  23. Pavlačka, O., Talašová, J., 10.1016/j.fss.2009.12.008, Fuzzy Sets and Systems 161 (11) (2010), 1585-1603. Zbl1186.90144MR2608263DOI10.1016/j.fss.2009.12.008
  24. Pavlačka, O., 10.1016/j.ins.2011.06.022, Inform. Sci. 181 (22) (2011), 4969-4992. Zbl1241.68117MR2832874DOI10.1016/j.ins.2011.06.022
  25. Pavlačka, O., 10.1016/j.fss.2012.08.003, Fuzzy Sets and Systems 213 (2013), 102-105. Zbl1291.91052MR3007013DOI10.1016/j.fss.2012.08.003
  26. Ricci, R. G., Mesiar, R., 10.1016/j.fss.2011.06.008, Fuzzy Sets and Systems 181 (2011), 1-13. Zbl1236.68236MR2823722DOI10.1016/j.fss.2011.06.008
  27. Sachs, T., Tiong, R. L. K., 10.1061/(asce)0733-9364(2009)135:1(56), J. Construction Engrg. Management-Asce 135 (2009), 1, 56-71. DOI10.1061/(asce)0733-9364(2009)135:1(56)
  28. Talašová, J., NEFRIT - Multicriteria Decision Making Based on Fuzzy Approach., Central Europ. J. Oper. Res. 8 (2000), 4, 297-319. Zbl0981.90035MR1832867
  29. Wang, Y. M., Elhag, T. M. S., 10.1016/j.eswa.2005.09.040, Expert Systems Appl. 31 (2006), 2, 309-319. DOI10.1016/j.eswa.2005.09.040
  30. Wang, Y. M., Elhag, T. M. S., 10.1016/j.fss.2006.06.008, Fuzzy Sets and Systems 157 (2006), 2456-2471. Zbl1171.68764MR2254175DOI10.1016/j.fss.2006.06.008
  31. Wei, C. C., Chang, H. W., 10.1016/j.eswa.2010.06.081, Expert Systems Appl. 38 (2011), 1, 429-434. DOI10.1016/j.eswa.2010.06.081
  32. Wu, W. Y., Lin, C. H., Kung, J. Y., Lin, C. T., A new fuzzy TOPSIS for fuzzy MADM problems under group decisions., J. Intelligent and Fuzzy Systems 18 (2007), 2, 109-115. Zbl1119.68193MR2327710
  33. Xu, Q., Ma, L., Nie, W. F., Li, P., Zhang, J. W., Sun, J. Z., 10.1007/11424857_32, In: Computational Science and Its Applications - ICCSA 2005, Part 3, Lecture Notes in Computer Science, vol. 3482, Springer-Verlag, Berlin 2005, pp. 292-298. DOI10.1007/11424857_32

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