Abstract
Interpretation of the basic structures of fuzzy logic, notably that of possibility distribution, is an essential requirement to clarify their value as an important tool in automated reasoning. Despite its evident value, as shown by the multiplicity and importance of its applications, much of the discussion to this day about such notions as “possibility” or the “fuzzy paradigm” typically relies on illustrative examples while failing to provide clarifying insights into important conceptual matters. In this paper we review an interpretation of the basic notions of fuzzy logic in terms of metric and utilitarian notions such as similarity and utility that clarifies major semantic issues while establishing links to existing formal frameworks such as the notion of possible worlds and the theory of metric spaces. We remark that these ideas were present, albeit in an implicit fashion, in the pioneering applications of fuzzy logic to system control. We review also recent extensions of similarity-based interpretations to fuzzy evidence.
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Ruspini, E.H. (2013). On the Meaning of Fuzziness. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35644-5_25
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DOI: https://doi.org/10.1007/978-3-642-35644-5_25
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