M. Premkumar

This paper introduces a novel framework called the Ҟ‐Ϙ group acting on neutrosophic‐complex fuzzy subsets, expanding classical group theory to incorporate fuzziness, uncertainty, and indeterminacy. We formulate the algebraic structure and key properties of complex fuzzy subgroups within this neutrosophic environment, examining how closure, associativity, identity, and inverse elements operate when influenced by degrees of truth, falsity, and indeterminacy. The work further integrates the concept of homomorphisms by exploring how these complex fuzzy subgroups behave under structure‐preserving mappings. In particular, we investigate the homomorphic images and preimages of such subgroups and establish fundamental results that confirm the stability of their structural characteristics under transformations. Additionally, we develop the notion of direct products for the Ҟ‐Ϙ group operating neutrosophic‐complex fuzzy subgroups. Our findings show that the direct product construction retains the essential features of the underlying neutrosophic‐complex fuzzy subgroup, and this property extends naturally from the product of two subgroups to finite collections of them. The proposed framework enhances the interaction between fuzzy algebra and neutrosophic logic, offering a broader and more flexible mathematical model for analyzing complex group structures under uncertainty.

We are proposed the ȶ-norm of the FPS – SA and the PS – Is of the PS-Algebra (PSA), and analyze their respective characteristics. Additionally, we as a species define the Cartesian products of FPS – SAs and PS – Is of PSA. These are discussed in specifics, combined with additional algebraic features. Additionally, the ȶ-norm defines the interconnection and intersection of PS Sub Algebra (PSSA) and PSI of PSA.

The normal greatest element of the post of fuzzy T-sub algebra in T-algebra as well as the normal fuzzy T-sub algebra in T-algebra are defined in this article. Additionally, the normal greatest element of the post of fuzzy T-sub algebra in T-algebra is explored.