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Aggregation of fuzzy subgroups
- Source :
- Fuzzy Sets and Systems. 418:170-184
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- 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.
- Subjects :
- 0209 industrial biotechnology
Mathematics::General Mathematics
Logic
Group (mathematics)
Binary relation
02 engineering and technology
Function (mathematics)
Fuzzy logic
Combinatorics
Mathematics::Group Theory
020901 industrial engineering & automation
Monotone polygon
Artificial Intelligence
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
Prime power
Mathematics
Subjects
Details
- ISSN :
- 01650114
- Volume :
- 418
- Database :
- OpenAIRE
- Journal :
- Fuzzy Sets and Systems
- Accession number :
- edsair.doi...........71c4203e3ffeb1bb34c6c5f1e52a024b