On I-vague products

Abstract

The notions of I-vague product of groups with membership and non-membership functions taking values in a complete involuntary dually residuated lattice ordered semigroup are introduced. This generalizes the notions with truth values in a complete Boolean algebra as well as those usual vague sets whose membership and non-membership functions taking values in the unit interval [0, 1]. We prove that if the complete involuntary dually residuated lattice ordered semigroup is infinitely meet distributive, then the set of all I-vague normal groups of a group with I-vague product forms a semilattice.