General Fuzzy Switchboard Transformation Semigroup

Abstract

Commutative and switching processing are central to computation. However, some problems arise when classical versions do not reflect the true needs of current computer science, whereby they cannot predict the flow of the next input information in the specified output. The Switchboard State Machine is a controller that controls the direct flow of information from one state to another and also plays the main part in communication between the subsystems. If the simple system satisfies the two properties of the switching and commutative state machines, the system is therefore a finite switchboard state machine. The general fuzzy switchboard automation (GFSA) was introduced by incorporating the switchboard into the general fuzzy automation. This paper is intended to introduce the concept of a general fuzzy switchboard transformation semigroup (GFSTS) by combining the GFSA and the transformation semigroup. Some related definitions and properties are established. The example of certain products, such as GFSTS cascade products, has also been studied. General Fuzzy Switchboard Poly-Transformation Semigroup (GFSPS) is also introduced since it fulfils the switchboard state machine properties. Some of the definitions and properties associated with the GFSPS are defined. Applications for general fuzzy switchboard automata, such as washing machines, are also provided.