×

OWA operators defined on complete lattices. (English) Zbl 1284.03246

Summary: In this paper the concept of an ordered weighted average (OWA) operator is extended to any complete lattice endowed with a t-norm and a t-conorm. In the case of a complete distributive lattice it is shown to agree with a particular case of the discrete Sugeno integral. As an application, we show several ways of aggregating closed intervals by using OWA operators. In a complementary way, the notion of generalized Atanassov’s operators is weakened in order to be extended to intervals contained in any lattice. This new approach allows us to build a kind of binary aggregation functions for complete lattices, including OWA operators.

MSC:

03E72 Theory of fuzzy sets, etc.
03B52 Fuzzy logic; logic of vagueness
06B23 Complete lattices, completions
28E10 Fuzzy measure theory
91B06 Decision theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] K. Atanassov, Intuitionistic Fuzzy Sets, VIIth ITKR Session, Deposited in the Central Science and Technology Library of the Bulgarian Academy of Sciences, Sofia, Bulgaria, 1983, pp. 1684-1697.
[2] Bustince, H.; Calvo, T.; de Baets, B.; Fodor, J.; Mesiar, R.; Montero, J.; Paternain, D.; Pradera, A., A class of aggregation functions encompassing two-dimensional OWA operators, Inf. Sci., 180, 1977-1989, (2010) · Zbl 1205.68419
[3] H. Bustince, J. Fernandez, J. Sanz, M. Galar, R. Mesiar, A. Kolesárová, Multicriteria decision making by means of interval-valued choquet integrals, in: Eurofuse 2011. Advances in Intelligent and Soft Computing, vol. 107, Springer, 2011, pp. 269-278.
[4] Calvo, T.; Mesiar, R., Weighted means based on triangular conforms, Int. J. Uncertainty Fuzzinness Knowl.-Based Syst., 9, 183-196, (2001) · Zbl 1113.03335
[5] Couceiro, M.; Marichal, J.-L., Characterizations of discrete sugeno integrals as polynomial functions over distributive lattices, Fuzzy Sets Syst., 161, 694-707, (2010) · Zbl 1183.28031
[6] De Baets, B.; Mesiar, R., Triangular norms on product lattices, Fuzzy Sets Syst., 104, 61-75, (1999) · Zbl 0935.03060
[7] De Cooman, G.; Kerre, E. E., Order norms on bounded partially ordered sets, J. Fuzzy Math., 2, 281-310, (1993) · Zbl 0814.04005
[8] Deschrijver, G.; Kerre, E. E., Classes of intuitionistic fuzzy t-norms satisfying the residuation principle, Int. J. Uncertainty Fuzziness Knowl.-Based Syst., 11, 6, 691-709, (2003) · Zbl 1074.03022
[9] Deschrijver, G., A representation of t-norms in interval-valued L-fuzzy set theory, Fuzzy Sets Syst., 159, 1597-1618, (2008) · Zbl 1176.03027
[10] Dubois, D.; Prade, H., On the use of aggregation operations in information fusion processes, Fuzzy Sets Syst., 142, 143-161, (2004) · Zbl 1091.68107
[11] Grätzer, G., General lattice theory, (1978), Birkhäuser Verlag Basel · Zbl 0385.06015
[12] Komorníková, M.; Mesiar, R., Aggregation functions on bounded partially ordered sets and their classification, Fuzzy Sets Syst., 175, 48-56, (2011) · Zbl 1253.06004
[13] Yager, R. R., On ordered weighting averaging aggregation operators in multicriteria decision-making, IEEE Trans. Syst. Man Cybern., 18, 183-190, (1988) · Zbl 0637.90057
[14] Yager, R. R.; Gumrah, G.; Reformat, M., Using a web personal evaluation tool—PET for lexicographic multi-criteria service selection, Knowl.-Based Syst., 24, 929-942, (2011)
[15] Zhou, S.-M.; Chiclana, F.; John, R. I.; Garibaldi, J. M., Type-1 OWA operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers, Fuzzy Sets Syst., 159, 3281-3296, (2008) · Zbl 1187.68619
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.