Abstract
The theory of fuzzy finite switchboard automata (FFSA) is introduced by the use of general algebraic structures such as complete residuated lattices in order to enhance the process ability of FFSA. We established the notion of homomorphism, strong homomorphism and reverse homomorphism and shows some of its properties. The subsystem of FFSA is studied and the set of switchboard subsystem-forms a complete -sublattices is shown. The algorithm of FFSA with complete residuated lattices is given and an example is provided.
Highlights
Many researchers studied on fuzzy finite automata with membership value in a Complete Residuated Lattices (CRL) [2,4,9,11,13,14,15,17,19,20,21,22]
As a continuation of the fuzzy finite automata (FFA), the concept of fuzzy finite switchboard state machine (FFSSM) that is made up of switching and commutative state machines has been studied by Sato and Kuroki [3,6]
If the system fulfilled the two properties which are fuzzy commutative automata and fuzzy switching automata, it can be called as finite switchboard automata
Summary
A finite state machine is a mathematical computation model that is used to design the computer programs along with sequential logic circuits. In general fuzzy finite state machine (FFSM) or fuzzy finite automata (FFA) has membership grades in an interval [0,1] but there is a possibility to extended the membership values into more general algebraic structures. Qiu studied those so-called theories and their characterizations where he considered its membership grades under the fact of complete residuated lattices [17,20]. Many researchers studied on fuzzy finite automata with membership value in a Complete Residuated Lattices (CRL) [2,4,9,11,13,14,15,17,19,20,21,22].
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