L-graph Automata And Some Applications

Abstract

Abstract This paper defines a novel graph constructed on a residuated lattice using a specific definition of the fuzzy graph (called $L$-graph). These types of graphs also have applications in libraries, pharmacies and machine facilities. Among these applications, this research presents the $L$-graph automaton related to the $L$-graph constructed by a minimum zero forcing set. The $L$-graph automaton is used to find efficient searching for diseases that have the most similar symptoms. It has been demonstrated that if two $L$-graphs are isomorphic, then the related $L$-graph automata are isomorphic but not necessarily vice versa. New notions, $L^{\prime\prime}$-graph automata, pseudo-isomorphism and self-sufficiency are proved. Besides, by taking advantage of the properties of the residuated lattice, it has been proven that the two $L$-graph automata are equivalent if and only if the $L^{\prime}$-graph automata contracted of $L$-graph automata are equivalent. Ultimately, in light of the above, some related theorems are proved and several examples are provided to illustrate these new notions.