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Fuzzy Visual Thinking: Interpreting and Thinking with Fuzzy Pictures and Fuzzy Data

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Fuzzy Pictures as Philosophical Problem and Scientific Practice

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

Abstract

In this chapter I pick up on previous results and extend the discussion in chapter 5 to tackle these questions: How do pictures and their fuzziness enter these activities? How can fuzzy set theory accommodate fuzzy visual thinking? Performing cognitive tasks involves a variety images, some of them are fuzzy perceptions, others are fuzzy pictures. As I have done in my broad discussion of representation and thinking, also here I want to include visual thinking in scientific contexts. Set theory can be used in the formalization of reasoning from images or with images associated with the representational and inferential use of symbolic diagrams, also in the formalization of thinking in a broader set of tasks that include computation and problem-solving using both fuzzy diagrams and fuzzy analogical pictures.

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Notes

  1. 1.

    On the role of diagrams see, for instance, Larkin and Simon [1], Perini [2], Shin [4], Goodwin [5], Blackwell [6].

  2. 2.

    For a brief introduction see Klir and Yuan [7, Chaps. 7 and 9].

  3. 3.

    The diagrammatic structure was introduced by Zadeh in Zadeh [8].

  4. 4.

    See Kosko [9], Bishop [10].

  5. 5.

    I have criticized the conceptual adequacy and application of several causal criteria in Cat [11].

  6. 6.

    From the graphic standpoint, design constraints such as the medium of display and cognitive constraints require that the one-dimensional curve is technically a thin area. Geometry is one thing, graphic depiction another; they constitute different kinds of constrained practices applied in different kinds of contexts.

  7. 7.

    Hassanien et al. [20].

  8. 8.

    For an introduction, see Klir and Yuan [7, Chap. 13].

  9. 9.

    Dubois and Prade [12, Chap. 3].

  10. 10.

    Perini makes this point in Perini [3] about tables.

  11. 11.

    One kind of mapping from fuzzy set diagrams to classic Venn diagrams relies on precisification techniques such as so-called alpha cuts.

  12. 12.

    In Perini [3] Perini defends the hybrid interaction for images in general.

  13. 13.

    Kosslyn [19].

  14. 14.

    Mushrif and Ray [13, 10.2].

  15. 15.

    Tarnawski et al. [14, 6.2].

  16. 16.

    Peters and Pal [15].

  17. 17.

    Dubois and Prade [12], Novak et al. [16], Klir and Yuan [7], Lawry [17].

  18. 18.

    Larkin and Simon [1].

  19. 19.

    Ragin [18], Cat [11].

References

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

    Jordi Cat

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Cat, J. (2017). Fuzzy Visual Thinking: Interpreting and Thinking with Fuzzy Pictures and Fuzzy Data. 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_19

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  • DOI: https://doi.org/10.1007/978-3-319-47190-7_19

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