Algebraic study of fuzzy finite switchboard automata - Ebas, Nur Ain (2020)
A finite switchboard automaton has an explicit mechanism which is switchboard that acts as a controller to predict the next input for the interaction within the systems. The classical version of the algebraic automata is a part of theoretical computer science which is not effectively reflecting the practical demands of the computation at the algebraic level. It unable to formalize the controller to predict the flow of the next input information into a designated output. In other words, the algebraic approach is still lacking in terms of their properties. Thus, it is necessary to understand the modeling of switching and commutative mechanisms as a controller in a machine. Fuzzy set theory can be applied to solve the control problems. This research studied on how one can incorporate the fuzzy set into finite switchboard automata and develop algebraic properties. Further, the general algebraic structure such as complete residuated lattices (CRL) has been utilized to enhance the membership grade of the fuzzy finite switchboard automata (FFSA). This research also proposed a specific algorithm for FFSA by the use of CRL. In an automata theory, some machines seldom have the possibility of overlapping transitions to the same state upon the same symbol from the different current states that are called as multi-memberships. Thus, this research considers the multi-memberships in the FFSA which lead to overcome these issues by introducing the theory of the general fuzzy switchboard automata (GFSA) and investigates the topological study of GFSA with the help of switchboard subsystems. The newly defined Kuratowski fuzzy closure operation is used to establish fuzzy topology on a GFSA. Semigroup actions are closely related to automata. By extending the algebraic properties of GFSA, the General Fuzzy Switchboard Transformation Semigroup (GFSTS) has been introduced and the concept of the covering and the products are established. The objectives of this research are achieved. The properties of the switchboard automata and subsystem need to satisfy in order to make the machine well operating.