Abstract
We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for <b>R</b> through the <b>sets</b> package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions.
Highlights
Few will deny the importance of sets and set theory, building the fundamentals of modern mathematics
An interesting characteristic of fuzzy sets is that the actual behavior of set operations depends on the underlying fuzzy logic employed, which can be chosen according to domain-specific needs
Fuzzy multisets (Yager 1986) combine both approaches by allowing each element to map to more than one fuzzy membership grade, i.e., D is the power set of multisets over the unit interval
Summary
Few will deny the importance of sets and set theory, building the fundamentals of modern mathematics. The two latter offer set operations such as union and intersection, these are applied to linearly indexable structures (lists and vectors, respectively), interpreting them as sets. The main functions in fso (Roberts 2007) for fuzzy set ordination compute and return, among other information, membership values represented by numeric matrices for some variables of the the input data. The sets package (Meyer and Hornik 2009b) presented here provides a flexible and customizable basic infrastructure for finite sets and the generalizations mentioned above, including basic operations for fuzzy logic.
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