A study on graph cellular automaton using rough set theory and fuzzy set theory

Abstract

In this thesis, the concept of automata theory and cellular automata newlinewas explored using rough set theory and fuzzy set theory. This was newlineeffectively achieved by defining a rough finite state automata with the aid of newlinean information system with decision variables. Also the properties and a newlinelanguage generated by such an automata are discussed in detail. The class of newlinerough finite state automaton captures the uncertainty using the rough newlinetransition map. To adhere the dynamical behavior of the system, a new newlinemathematical model called Non-homogeneous Rough Finite State Automata newline(NRFSA) was introduced. The dynamical behavior of any system can be newlineexpressed in terms of an information system at time t and the defined newlineconcepts are elaborated with suitable examples. To investigate the NRFSA newlineusing ! cut partition tree, fuzzy membership matrix is defined for an newlineinformation system at time .t.. The ! cut partition tree generated out of newlinethis fuzzy membership matrix leads to define a non-homogeneous rough finite newlinestate automaton for each quot#quot[0,1]. The properties and the language generated newlineby such an automaton are analyzed in detail. Using the Basic Linear Rules, newlinethe k$% generation GCA is introduced. These methods enable us to capture the newlinecomplete characterization of the future generations. In real time problems at newlineeach time .t. the system dynamically changes its behavior. Our objective is to newlineprovide a suitable mathematical model namely Non homogeneous Rough newlineGraph Cellular Automaton (NRGCA) that provides an appropriate solution in newlinepredicting the systems having dynamical behavior. The generations of newlinenon-homogeneous rough graph cellular automaton are also defined and as an newlineapplication the spreading rate of COVID19 according to various factors is newlineanalyzed. Using the generations of NRGCA the definite and possible newlinetransitions between suspicious, infected and recovere