A (Basis for a) Philosophy of a Theory of Fuzzy Computation

Apostolos Syropoulos 1
  • 1 , Xanthi, Greece


Vagueness is a linguistic phenomenon as well as a property of physical objects. Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the fuzzy Turing machine. This conceptual computing device gives an idea of what computing under vagueness means, nevertheless, it is not the most natural model. Based on the properties of this and other models of vague computing, an attempt is made to formulate a basis for a philosophy of a theory of fuzzy computation.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Granik, A. and Caulfield, H.J. (2001), Fuzziness in Quantum Mechanics, arXiv:quant-ph/0107054v1.

  • [2] Alvarez, D.S. and Skarmeta, A:F.G. (2004), A fuzzy language, Fuzzy Sets and Systems, 141, 335–390.

  • [3] James F. Baldwin, Trevor P. Martin, and Maria Vargas-Vera (1999). Fril++ a Language for Object-Oriented Programming with Uncertainty. In Anca L. Ralescu and James G. Shanahan (editors), Fuzzy Logic in Artificial Intelligence, volume 1566 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, 62–78.

  • [4] Max Black (1937). Vagueness. An Exercise in Logical Analysis. Philosophy of Science, 4(4): 427–455.

  • [5] Mark A. Changizi (2003). The Brain from 25,000 Feet, volume 317 of Synthese Library. Springer Netherlands.

  • [6] David F. Clark (1991). HALO–a fuzzy programming language. Fuzzy Sets and Systems, 44:199–208.

  • [7] Richard Dietz and Sebastiano Moruzzi, editors (2010). Cuts and Clouds: Vaguenesss, its Nature and its Logic. Oxford University Press, Oxford, UK.

  • [8] Dragan D. Djakovic (1988). RASP–A Language with Operations on Fuzzy Set. Computer Languages, 13(3–4): 143–147.

  • [9] Alexander S. Green, Peter LeFanu Lumsdaine, Neil J. Ross, Peter Selinger, and Benoît Valiron (2013). An introduction to quantum programming in quipper. In Gerhard W. Dueck and D. Michael Miller, editors, Reversible Computation, volume 7948 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, 110–124.

  • [10] Mika Hirvensalo (2004). Quantum Computing. Springer-Verlag, Berlin, 2nd edition.

  • [11] Dominic Hyde and Mark Colyvan (2008). Paraconsistent Vagueness: Why Not? The Australasian Journal of Logic, 6:107–121.

  • [12] Rosanna Keefe and Peter Smith (editors) (1999). Vagueness: A Reader. The MIT Press.

  • [13] George J. Klir and Bo Yuan (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall (Sd).

  • [14] Edward Jonathan Lowe (1994). Vague Identity and Quantum Indeterminacy. Analysis, 54(2): 110–114.

  • [15] Rafael Morales-Bueno, José-Luis Pérez-de-la-Cruz, Ricardo Conejo, and Buenaventura Clares (1997). A family of fuzzy programming languages. Fuzzy Sets and Systems, 87: 167–179.

  • [16] Toby Ord and Tien D. Kieu (2005). The Diagonal Method and Hypercomputation. The British Journal for the Philosophy of Science, 56(1): 147–156.

  • [17] Gheorghe Păun (2002). Membrane Computing: An Introduction. Springer-Verlag, Berlin, Germany, EU.

  • [18] Pironio, S. and Acín, A. and Massar, S. and de la Giroday, A. Boyer and Matsukevich, D.N. and Maunz, P. and Olmschenk, S. and Hayes, D. and Luo, L. and Manning, T.A. and Monroe, C. (2010). Random numbers certified by Bell’s theorem. Nature, 464: 1021–1024.

  • [19] Jarosław Pykacz (2011). Towards many-valued/fuzzy interpretation of quantum mechanics. International Journal of General Systems, 40(1): 11–21.

  • [20] Jarosław Pykacz, Bart D’Hooghe, and Roman R. Zapatrin. Quantum Computers as Fuzzy Computers (2001). In: B. Reusch, editor, Fuzzy Days 2001, volume 2206 of Lecture Notes in Computer Science, Springer, Berlin, Germany, EU, 526–535.

  • [21] Bertrand Russell (1923). Vagueness. Australasian Journal of Philosophy, 1(2): 84–92.

  • [22] Eugene S. Santos (1969). Probabilistic Turing Machines and Computability. Proceedings of the American Mathematical Society, 22(3): 704–710.

  • [23] Stewart Shapiro (1983). Mathematics and reality. Philosophy of Science, 50(4): 523–548.

  • [24] Nicholas J.J. Smith (2008). Vagueness and Degrees of Truth. Oxford University Press.

  • [25] Roy Sorensen. Vagueness. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Fall 2008 edition, 2008.

  • [26] Zenon A. Sosnowski (1990). FLISP–A language for processing fuzzy data. Fuzzy Sets and Systems, 37(1): 23–32.

  • [27] Apostolos Syropoulos (2008). Hypercomputation: Computing Beyond the Church-Turing Barrier. Springer New York, Inc., Secaucus, NJ, USA.

  • [28] Apostolos Syropoulos (2014). Theory of Fuzzy Computation. IFSR International Series on Systems Science and Engineering. Springer, New York.

  • [29] Apostolos Syropoulos (2017). On vague computers. In Andrew Adamatzky, editor, Emergent Computation: A Festschrift for Selim G. Akl, Springer International Publishing, Cham, Switzerland, 393–402.

  • [30] Alan M. Turing (1936). On Computable Numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42: 230–265.

  • [31] Raymond Turner. The philosophy of computer science. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Fall 2013 edition, 2013. http://plato.stanford.edu/archives/fall2013/entries/computer-science/.

  • [32] Jean Paul Van Bendegem (1970). Why the largest number imaginable is still a finite number. Logique et Analyse.

  • [33] Kees van Deemter (2010). Not Exactly: In Praise of Vagueness. Oxford University Press.

  • [34] Thomas Vetterlein, Harald Mandl, and Klaus-Peter Adlassnig (2010). Fuzzy Arden Syntax: A fuzzy programming language for medicine. Artificial Intelligence in Medicine, 49: 1–10.

  • [35] Jiří Wiedermann (2004). Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines. Theoretical Computer Science, 317: 61–69.

  • [36] Lotfi Askar Zadeh (1968). Fuzzy Algorithms. Information and Control, 12: 94–102.

  • [37] Lotfi Askar Zadeh (1995). Discussion: Probability Theory and Fuzzy Logic Are Complementary Rather Than Competitive. Technometrics, 37(3): 271–276.

  • [38] Steven French and Décio Krause (2003). Quantum Vagueness. Erkenntnis, 59: 97–124.


Journal + Issues