WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 20, 2021
Complex Fuzzy Groups Based on Rosenfeld’s Approach
Authors: , , ,
Abstract: Complex fuzzy sets (CFS) generalize traditional fuzzy sets (FS) since the membership functions of CFS reduces to the membership functions of FS. FS values are always at [0, 1], unlike CFS which has values in the unit disk of C. This paper merges notion and concept in group theory and presents the notion of a complex fuzzy subgroup of a group. This proposed idea represents a more general and better optional mathematical tool as one of the approaches in the fuzzy group. However, this research defines the notion of complex fuzzy subgroupiod, complex fuzzy normal subgroup, and complex fuzzy left(right) ideal. Therefore, the lattice, homomorphic preimage, and image of complex fuzzy subgroupiod and ideal are introduced and studied its properties. Finally, complex fuzzy subgroups and their properties are presented and investigated.
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Keywords: Fuzzy sets, fuzzy subgroups and groups, fuzzy subgroupoid and ideal, complex fuzzy subgroupoid and ideal, Complex fuzzy sets, fuzzy subgroups
Pages: 368-377
DOI: 10.37394/23206.2021.20.38