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Implicators based on binary aggregation operators in interval-valued fuzzy set theory
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DOI：10.1016/j.fss.2005.02.002.png)
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In this paper we introduce aggregation operators on the lattice L*, which is the underlying lattice of both interval-valued fuzzy sets and intuitionistic fuzzy sets in the sense of Atanassov. We consider some particular classes of binary aggregation operators based on t-norms on the unit interval. We investigate the properties of the implicators generated by these classes. In particular, representations in terms of implicators on [0, 1] are obtained, and the Smets-Magrez axioms are studied. We compare the results with those obtained for implicators generated by already known classes of t-norms on L*. (c) 2005 Elsevier B.V. All rights reserved.
Keyword:
aggregation operator on L*
binary aggregation operator
implicator
Smets-Magrez axioms
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