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Introduction

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Theory of Fuzzy Computation

Part of the book series: IFSR International Series on Systems Science and Engineering ((IFSR,volume 31))

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Abstract

The fusion of computability theory (CP) with fuzzy set theory (FST) demands a good knowledge of both theories. Thus, this introductory chapter tries to familiarize readers with a number of concepts and ideas that are necessary for the rest of this book. In particular, I start with a review of the events that lead to what is now known as computer science and then I give an overview of FST. The chapter concludes with a description of what the fusion of CP with FST is about and what to expect from it.

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Notes

  1. 1.

    As noted in [41, p. 377], Hilbert actually presented ten of the problems to his audience. All 23 problems are listed in the printed form of his lecture.

  2. 2.

    Nowadays, the term λ-calculus refers to a calculus that is used as a means of describing purely syntactically, the properties of mathematical functions, effectively treating them as rules.

  3. 3.

    His full name was Bertrand Arthur William Russell, third Earl Russell.

  4. 4.

    Although Ivo Düntsch [44] has proposed a logic of rough sets (see Appendix B), still the field is in its infancy.

  5. 5.

    Translation: It is clear then that it is not necessary for every affirmation or negation taken from among opposite propositions that the one be true, the other false. For what is non-existent but has the potentiality of being or not being does not behave after the fashion of what is existent, but in the manner just explained.

  6. 6.

    While working independently from Zadeh, Dieter Klaua [72] discovered his many-valued sets. Interestingly, these sets are in a sense equivalent to Zadeh’s fuzzy sets (see [60] for an overview of Klaua’s work).

  7. 7.

    Strictly speaking when defining a set using its characteristic function we do something similar (see Definition 2.4.3 on p. 34).

  8. 8.

    It is a fact that probability theory is tied to uncertainty, which can be associated with ignorance, while fuzzy sets are associated with vagueness, which has nothing to do with ignorance. Nevertheless, many researchers and thinkers tend to confuse the two terms.

  9. 9.

    In fuzzy theoretic literature, the term crisp is used to denote something that is exact.

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  1. Xanthi, Greece

    Apostolos Syropoulos

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  1. Apostolos Syropoulos
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Syropoulos, A. (2014). Introduction. In: Theory of Fuzzy Computation. IFSR International Series on Systems Science and Engineering, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8379-3_1

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