Abstract
In traditional fuzzy logic, to represent, e.g., the experts degree of certainty in different statements, numbers from the interval [0, 1] are used. It is often difficult for an expert to exactly quantify his or her certainty; therefore, instead of a real number, it is more adequate to represent this degree of certainty by an interval. In the first case, we get an interval-valued fuzzy set. In the second case, we get a second-order fuzzy set. Interval-valued fuzzy sets have been actively used in real-life applications. In this chapter the basic operations and properties of interval-valued fuzzy relations are considered. These properties of interval-valued fuzzy relations involve the notion of interval-valued fuzzy aggregations. The important issue will be examinations of properties of the generalized composition of interval-valued fuzzy relations.
You cannot be certain about uncertainty.
Frank Knight
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Notes
- 1.
Studies, in this section, on the possible and necessary comparability of relations and as a consequence possible and necessary properties were inspired by Bernard De Baets and are the results of conversations and cooperation with him.
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Pȩkala, B. (2019). Interval-Valued Fuzzy Relations. In: Uncertainty Data in Interval-Valued Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 367. Springer, Cham. https://doi.org/10.1007/978-3-319-93910-0_2
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DOI: https://doi.org/10.1007/978-3-319-93910-0_2
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Online ISBN: 978-3-319-93910-0
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