Abstract
The notion of fuzziness lies at the core of fuzzy computability theory. Thus, one should have a basic understanding of the ideas involved. This chapter serves both as a crash course in fuzzy set theory, for those readers that have no previous knowledge of the concepts involved, and as a précis of fuzzy set theory, for those readers familiar with the relevant notions. The exposition that follows is based on [75], while the material for Sect. 3.1 is borrowed from [49, 137].
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- 1.
Recall that an equivalence relation R on a set X is a subset of X ×X (i.e., R ⊆ X ×X) such that \(a R a\) for all \(a \in X\), \(a R b\) implies \(b R a\) for all a, b ∈ X, and \(a R b\) and \(b R c\) imply \(a R c\) for all a, b, c ∈ X.
References
Barr, M.: Fuzzy set theory and topos theory. Can. Math. Bull. 29, 501–508 (1986)
Gerla, G.: Fuzzy ogic: Mathematical Tools for Approximate Reasoning. Kluwer Academic Publishers, Dordrecht (2001)
Goguen, J.: L-fuzzy sets. J. Math. Anal. Appl. 18, 145–174 (1967)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)
Kosko, B.: Fuzziness vs. probability. Int. J. Gen. Syst. 17(2), 211–240 (1990)
Smyth, M.: Effective given domains. Theor. Comput. Sci. 5, 257–274 (1977)
Vickers, S.: Topology via logic. In: Cambridge Tracts in Theoretical Computer Science, vol. 6. Cambridge University Press, Cambridge (1990)
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Syropoulos, A. (2014). Elements of Fuzzy Set Theory. 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_3
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DOI: https://doi.org/10.1007/978-1-4614-8379-3_3
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