AN ELEMENTARY STUDY OF p-FUZZY WSOFT tau-ALGEBRAS AND THEIR p-FUZZY SOFT omega-SUBALGEBRAS

In this paper, first we generalize the existing notion of fuzzy subalgebra of an algebra in such a way that the fuzzy subalgebra of an algebra can be of a subtype of the type of the parent algebra and the underlying set of the fuzzy subalgebra can be a proper subset of the underlying set of the parent algebra via the notions of gf-omega-algebra and gf-omega-subalgebra of a gf-tau-algebra and study some (lattice) algebraic properties of the collection of all gf-omega-subalgebras of a gf-tau-algebra and then using these notions we introduce the notions of pfs-tau-algebra and pfs-omega-subalgebra of a pfs-tau-algebra which generalize the notions of p-soft tau-algebra, p-soft omega-subalgebra of a p-soft tau-algebra and the currently existing notions of (normal) fuzzy soft group, fuzzy soft ring, fuzzy soft (left, right) ideal etcetera. Further, we study some (lattice) algebraic properties of pfs-omega-subalgebras of a pfs-tau-algebra.