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Notes on Vagueness and Mathematics

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Book cover Aspects of Vagueness

Part of the book series: Theory and Decision Library ((TDLU,volume 39))

Abstract

This paper consists of a list of notes on the issue of vagueness, the emphasis being on its relation to “crisp” entities. This is a classical topic, in fact any examination of the interplay of empirical material and theoretical concepts has to take it into account (see,e.g., [4]). In addition to earlier investigations, last decades have brought substantial contributions in the direction of providing technical mathematical and logical explications of aspects of vagueness. This development has been in part initiated by problems in the theory of systems, in computer science, in the area of artificial intelligence, in foundations of mathematics, etc. The most extensive branch of the development has been the theory of fuzzy sets, originating with [9] (for a detailed overview, see [2] and the bibliography in [3]). Among important contributions based on different principles let us mention especially the alternative set theory [8].

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References

  1. Bečvář, J.: 1965, ‘Real-time and complexity problems in automata theory’. Kybernetica 1, 475–498.

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  2. Gaines, B.R.: 1976, ‘Foundations of fuzzy reasoning’. Int.J.Man-Machine Studies 8, 623–668

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  3. Gaines, B.R. and L.J.Kohout: 1977, ‘The fuzzy decade: a bibliography of fuzzy systems and closely related topics’. Int.J.Man-Machine Studies 9, 1–68.

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  4. Körner, S.: 1966, ‘Experience and theory’. Routledge and Kegan Paul, London 1966.

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  5. Parikh,R.: 1977 ‘The problem of vague predidates’ preprint

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  6. Poincaré, H.: 1912, ‘La science et l’hypothèse’. Paris.

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  7. Rüssel, B.: 1923, ‘Vagueness’. Austr.J.of Phil. I, 84–92.

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  8. Vopenca, P.: 1979, ‘Mathematics in the alternive set theory’. Teubner, Leipzig.

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  9. Zadeh, L.A.: 1965, ‘Fuzzy sets’. Information and Control 8, 338–353.

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© 1984 D. Reidel Publishing Company

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Bečvář, J. (1984). Notes on Vagueness and Mathematics. In: Skala, H.J., Termini, S., Trillas, E. (eds) Aspects of Vagueness. Theory and Decision Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6309-2_1

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  • DOI: https://doi.org/10.1007/978-94-009-6309-2_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6311-5

  • Online ISBN: 978-94-009-6309-2

  • eBook Packages: Springer Book Archive

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