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This book presents a comprehensive discussion on the characterization of vagueness in pictures. It reports on how the problem of representation of images has been approached in scientific practice, highlighting the role of mathematical methods and the philosophical background relevant for issues such as representation, categorization and reasoning. Without delving too much into the technical details, the book examines and defends different kinds of values of fuzziness based on a complex approach to categorization as a practice, adopting conceptual and empirical suggestions from different fields including the arts. It subsequently advances criticisms and provides suggestions for interpretation and application. By describing a cognitive framework based on fuzzy, rough and near sets, and discussing all of the relevant mathematical and philosophical theories for the representation and processing of vagueness in images, the book offers a practice-oriented guide to fuzzy visual reasoning, along with novel insights into the field of interpreting and thinking with fuzzy pictures and fuzzy data.

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1. Introduction: visual uncertainty, categorization, objectivity and practices and values of imprecision.- 2. From ordinary to mathematical categorization in the visual world... of words, pictures and practices.- 3. Vagueness and fuzziness in words and predication.- 4. Representations: from words to images.- 5. Epistemology, aesthetics and pragmatics of scientific and other images: visualization, representation and reasoning.- 6. Visual representation: from perceptions to pictures.- 7. Vague pictures: epistemology, aesthetics and pragmatics of fuzziness, from fuzzy perception to fuzzy pictures.- 8. Blur as vagueness: seeing images vaguely and seeing vague images; perception and representation.- 9. Vague pictures as pictures.- 10. Vague pictures as vague representations and representing.- 11. The cognitive values of imprecision: towards a scientific epistemology, aesthetics and pragmatics of fuzziness, contextual lessons from the history of picture-making practices.- 12. Introduction: fuzzy-set representation and processing of fuzzy images; nonlinguistic vagueness as scientific practice; scientific epistemology, aesthetics, methodology and technology of fuzziness.- 13. Application of mathematics in the representation of images: from geometry to set theory.- 14. Cognitive framework of set-theoretic methodology of analysis and synthesis: categorization, classification and many faces of digital geometry.- 15. Conceptual resources and philosophical grounds in set-theoretic models of vagueness: fuzzy, rough and near sets.- 16. Analytic and synthetic forms of vague categorization.- 17. From intrinsic to extrinsic vague categorization and content.- 18. Pictorial representation and simplicity of categorization.- 19. Fuzzy visual thinking: interpreting and thinking with fuzzy pictures and fuzzy data.- 20. Pictorial approximation: pictorial accuracy, vagueness and fuzziness.- 21. Pictorial vagueness as scientific practice: picture-making and the mathematical practice of fuzzy categorization.- 22. Conclusion.

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