Journal
INFORMATION SCIENCES
Volume 181, Issue 6, Pages 1116-1124Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2010.11.024
Keywords
Atanassov's intuitionistic fuzzy sets; Aggregation operators; Interval-valued fuzzy sets; OWA; Triangular norms
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Funding
- Government of Spain [TIN2010-15055]
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Atanassov's intuitionistic fuzzy set (AIFS) is a generalization of a fuzzy set. There are various averaging operators defined for AIFSs. These operators are not consistent with the limiting case of ordinary fuzzy sets, which is undesirable. We show how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. We provide two generalizations of the existing methods for other averaging operators. We relate operations on AIFS with operations on interval-valued fuzzy sets. Finally, we propose a new construction method based on the Lukasiewicz triangular norm, which is consistent with operations on ordinary fuzzy sets, and therefore is a true generalization of such operations. (C) 2010 Elsevier Inc. All rights reserved.
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