Abstract
In this chapter we presented basic notions and definitions constituting the basis of fuzzy set theory. Particular attention has been paid to cardinality of fuzzy sets, and we presented various approaches to defining it. We also introduced the notion of aggregation operator and presented the most important types of aggregators.
There are many misconceptions about fuzzy logic. The principal misconception is that fuzzy logic is fuzzy. The stated definition underscores that fuzzy logic is precise. In fuzzy logic precision is achieved through association of fuzzy sets with membership functions and, more generally, association of granules with generalized constraints. What this implies is that fuzzy logic is what may be called precisiated logic.
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Dyczkowski, K. (2018). Elements of Fuzzy Set Theory. In: Intelligent Medical Decision Support System Based on Imperfect Information. Studies in Computational Intelligence, vol 735. Springer, Cham. https://doi.org/10.1007/978-3-319-67005-8_3
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DOI: https://doi.org/10.1007/978-3-319-67005-8_3
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