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• W2053717907 abstract "In this paper we study fuzzy Turing machines with membership degrees in distributive lattices, which we called them lattice-valued fuzzy Turing machines. First we give several formulations of lattice-valued fuzzy Turing machines, including in particular deterministic and non-deterministic lattice-valued fuzzy Turing machines (l-DTMcs and l-NTMs). We then show that l-DTMcs and l-NTMs are not equivalent as the acceptors of fuzzy languages. This contrasts sharply with classical Turing machines. Second, we show that lattice-valued fuzzy Turing machines can recognize n-r.e. sets in the sense of Bedregal and Figueira, the super-computing power of fuzzy Turing machines is established in the lattice-setting. Third, we show that the truth-valued lattice being finite is a necessary and sufficient condition for the existence of a universal lattice-valued fuzzy Turing machine. For an infinite distributive lattice with a compact metric, we also show that a universal fuzzy Turing machine exists in an approximate sense. This means, for any prescribed accuracy, there is a universal machine that can simulate any lattice-valued fuzzy Turing machine on it with the given accuracy. Finally, we introduce the notions of lattice-valued fuzzy polynomial time-bounded computation (lP) and lattice-valued non-deterministic fuzzy polynomial time-bounded computation (lNP), and investigate their connections with P and NP. We claim that lattice-valued fuzzy Turing machines are more efficient than classical Turing machines." @default.
• W2053717907 created "2016-06-24" @default.
• W2053717907 creator A5067652312 @default.
• W2053717907 date "2009-12-01" @default.
• W2053717907 modified "2023-09-26" @default.
• W2053717907 title "Lattice-valued fuzzy Turing machines: Computing power, universality and efficiency" @default.
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• W2053717907 doi "https://doi.org/10.1016/j.fss.2009.08.003" @default.
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