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Fuzzy Pictures as Philosophical Problem and Scientific Practice pp 139–146Cite as

Conceptual Resources and Philosophical Grounds in Set-Theoretic Models of Vagueness: Fuzzy, Rough and Near Sets

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 348))

Abstract

The conclusions of my discussion of pictorial precision and certainty in informal philosophical analysis extend to the application of fuzzy formalism. In fact, they do so more broadly. In image analysis fuzzy formalism has been applied as part of different generalizations of set theory: near sets, rough sets and fuzzy sets, and their possible combinations. They are all different kinds of Cantor sets in which membership is established by a law that enables the grouping into a whole. Both fuzzy sets and rough sets generalize classical set theory; and near sets are more general than rough sets.

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Notes

  1. 1.

    Sen and Pal [1].

  2. 2.

    Ibid.

  3. 3.

    Ibid.

  4. 4.

    Cat [2].

  5. 5.

    Pawlak [3].

  6. 6.

    Peters [4].

  7. 7.

    Maji and Pal [5].

  8. 8.

    Maji and Pal [5], 2.2.

  9. 9.

    Ibid., 2.5.

  10. 10.

    Ibid., 2.7.

  11. 11.

    Zadeh [6].

  12. 12.

    McNeill and Freiberger [7]; for a more detailed study see Seising [8].

  13. 13.

    Black [8]. Also Black’s references track a combination of scientific and philosophical issues and resources that may be found, in turn, in Duhem, Russell and others.

  14. 14.

    Pawlak [3].

  15. 15.

    Peters and Pal [9], 1.5–6.

  16. 16.

    Poincaré [10].

  17. 17.

    Ibid., ch. 2.

  18. 18.

    Merleau-Ponty [11].

  19. 19.

    Peters and Pal [9], 1.5–6.

  20. 20.

    G. Matheron, in Fashandi and Peters (2010), 4.4.

  21. 21.

    I have examined the case of causality in Cat (2006).

References

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Authors and Affiliations

  1. Department of History and Philosophy of Science, Indiana University, Bloomington, USA

    Jordi Cat

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  1. Jordi Cat
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Cat, J. (2017). Conceptual Resources and Philosophical Grounds in Set-Theoretic Models of Vagueness: Fuzzy, Rough and Near Sets. In: Fuzzy Pictures as Philosophical Problem and Scientific Practice. Studies in Fuzziness and Soft Computing, vol 348. Springer, Cham. https://doi.org/10.1007/978-3-319-47190-7_15

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  • DOI: https://doi.org/10.1007/978-3-319-47190-7_15

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