Quotient Structures of Full Fuzzy Parameterized Soft Groups and Homomorphism Theorems
DOI:
https://doi.org/10.62054/Abstract
Existing foundational work introduced FFPS-groups and examined their basic operations, subgroups, homomorphisms and related structural properties. This paper develops a rigorous treatment of FFPS-homomorphisms by examining the behaviour of kernels and images, the preservation of normal FFPS-subgroups, and the construction of quotient FFPS-groups. Attention is particularly given to the definition of quotient FFPS-groups, where ambiguity may arise if the quotient is formed using parameter-dependent normal approximations. To resolve this, the paper proposes quotient construction based on a fixed normal subgroup , leading to a well-defined quotient FFPS-group over . Furthermore the paper establishes a canonical FFPS-quotient map and provides a refined basis for formulating the First Isomorphism Theorem in the FFPS setting. The results show that FFPS-groups extend classical group theory by allowing algebraic properties such as normality, commutativity and subgroup containment to vary according to fuzzy parameter strength.
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