Algebraic properties of implication-based intuitionistic fuzzy finite state machine over a finite group

An extensive study is performed on the already constituted algebraic structure called the implication-based intuitionistic fuzzy semiautomaton (IB-IFSA) over a finite group that compromises of implication-based intuitionistic fuzzy kernel and implication-based intuitionistic fuzzy subsemiautomaton. In this paper, the necessary and sufficient condition for an implication-based intuitionistic fuzzy normal subgroup to be an implication-based intuitionistic fuzzy kernel of an implication-based intuitionistic fuzzy semiautomaton is developed. In addition, the fundamental and adequate condition for an implication-based intuitionistic fuzzy subgroup to be an implication-based intuitionistic fuzzy subsemiautomaton of an IB-IFSA is formulated. Moreover, the condition for an implication-based intuitionistic fuzzy kernel of the an IB-IFSA to be implication-based intuitionistic fuzzy subsemiautomaton is also established.