Aggregation of fuzzy subgroups

Aggregation of fuzzy subgroups

Given an aggregation function, and two fuzzy subgroups of a group, this study investigates whether the aggregation of them is also a fuzzy subgroup. It is proven that if the cardinal of the group is a prime power, then it is always a fuzzy subgroup. For a general group, it is proven that the existen...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 418; pp. 170 - 184
Main Authors: Bejines, C., Chasco, M.J., Elorza, J.
Format: Journal Article
Language:English
Published: Elsevier B.V 15-08-2021
Subjects:
Aggregation function
Fuzzy subgroup
Lattice
Triangular norm
Fuzzy subgroup
Aggregation function
Lattice
Triangular norm
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Summary:Given an aggregation function, and two fuzzy subgroups of a group, this study investigates whether the aggregation of them is also a fuzzy subgroup. It is proven that if the cardinal of the group is a prime power, then it is always a fuzzy subgroup. For a general group, it is proven that the existence of a binary relation between the fuzzy subgroups determines if their aggregation is a fuzzy subgroup. Moreover, given two fuzzy subgroups, if the aggregation of them is a fuzzy subgroup for some strictly monotone aggregation function, then it is a fuzzy subgroup for any aggregation function. The present study also examines conditions on the aggregation function that characterise the case where the aggregation of two arbitrary fuzzy subgroups is also a fuzzy subgroup.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2020.05.017