An Enhancement to the Concept of Membership Assignment in Fuzzy Turing Machines

Implementation of Fuzzy sets concepts in various branches of science and technology has led to their applicability and flexibility. The Turing machine is an abstract concept of a computing device which introduced new models for computation. The idea of the definition of Fuzzy Turing Machine (FTM) is to create a platform for a new fuzzy computation model, which incorporates the concepts of fuzzy logic. ‎Following its introduction and investigation of its computational power by ‎‎ Wiedermann, he showed ‎that ‎FTM ‎is ‎able ‎to ‎‎solve undecidable ‎problems (Wiedermann,2004)‎.‎ ‎‎In this paper, we look into the Wiedermann definition ‎of FTM as one of the most well known classical definitions of FTM along with other classical definitions based on it, and their benefits and weaknesses. Later, we will develop a more complete definition for fuzzy Turing machines which covers those vague aspects of the conventional definitions. 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 ‎(Doostfatemeh and Kremer,2005)‎. It improved the conventional definition of fuzzy automata, especially the problem of membership assignment and multi-membership resolution‎, the same as what we have performed here in the present paper to improve the FTM.