The various fuzzy subgroups of a group which are admissible under operator domains are studied. In particular, the classes of all inner automorphisms, automorphisms, and endomorphisms are applied on the fuzzy subgroups of a group. As results, several theorems and examples concerning the fuzzy subgroups following from these kinds of operator domains are obtained. Moreover, we prove that a necess...

Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning input. However, context a non-standard inner product, it becomes difficult to apply due lack initial orthonormal basis. We propose strategies overcome this obstacle and discuss algorithms variants with product. Theoretical analysis experiments demons...