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.


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


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