Comprehensive Fuzzy Turing Machines, An Evolution to the Concept of Finite State Machine Control (1908.01994v1)

Abstract: The Turing machine is an abstract concept of a computing device which introduced new models for computation. The idea of Fuzzy algorithms defined by Zadeh and Lee was followed by introducing Fuzzy Turing Machine (FTM) to create a platform for a new fuzzy computation model. Then, in his investigations on its computational power, Wiedermann showed that FTM is able to solve undecidable problems. His suggested FTM structure, which highly resembles the original definition was one of the most well-known classical definitions of FTM lately.To improve some of its weaknesses and vague points which will be discussed extensively in this paper, we will develop a more complete definition for fuzzy Turing machines. Our proposed definition of FTM, which encompasses the conventional definition, is motivated from the definition of General Fuzzy Automata (GFA) introduced by Doostfatemeh and Kremer. As it improved the conventional definition of fuzzy automata, especially the problem of membership assignment and multi-membership resolution, we also improved the same aspects of FTM through the definition of Comprehensive Fuzzy Turing Machine (CFTM). In addition, we address on some possible vaguenesses in FTM was not the subject of focus in fuzzy automata. As example, we investigate the issue of multi-path and multi-direction which are possible in case of nondeterminism. Finally, we show the simplicity, applicability and computational efficiency of the CFTM through an explanatory example.