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Title: | On the composition of fuzzy power relations | Authors: | Bošnjak Ivica Madarász Rozália |
Issue Date: | 2015 | Journal: | Fuzzy Sets and Systems | Abstract: | © 2014 Elsevier B.V. This paper deals with the "powering" of binary fuzzy relations (i.e. lifting a fuzzy relation R defined on a set X to the relation <sup>R+</sup> defined on the set F(X) of all fuzzy subsets of X). We prove that for any complete residuated lattice L, the composition of the powers of two L-relations is always a subset of the power of their composition. Answering to a question posed by Georgescu, we prove that the converse is not always true. We prove that the composition of the powers of two L-relations is equal to the power of their composition if and only if L is a Heyting algebra. | URI: | https://open.uns.ac.rs/handle/123456789/30162 | ISSN: | 0165-0114 | DOI: | 10.1016/j.fss.2014.09.010 |
Appears in Collections: | PMF Publikacije/Publications |
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