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The cardinality or "size" of a multiset is the sum of the multiplicities of all its elements. For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6.
In some cases a multiset in this counting sense may be generalized to allow negative values, as in Python. C++'s Standard Template Library implements both sorted and unsorted multisets. It provides the multiset class for the sorted multiset, as a kind of associative container, which implements this multiset using a self-balancing binary search ...
A fuzzy set is a pair (,) where is a set (often required to be non-empty) and : [,] a membership function. The reference set (sometimes denoted by or ) is called universe of discourse, and for each , the value () is called the grade of membership of in (,).
Inclusion–exclusion illustrated by a Venn diagram for three sets. Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections.
A cardinal number that is uncountable and has the property that any collection of sets of that cardinality has a subcollection of the same cardinality with a non-empty intersection. complement (of a set) The set containing all elements not in the given set, within a larger set considered as the universe. complete 1.
In the object-oriented application programming paradigm, which is related to database structure design, UML class diagrams may be used for object modeling. In that case, object relationships are modeled using UML associations, and multiplicity is used on those associations to denote cardinality .
A data structure diagram is a diagram type that is used to depict the structure of data elements in the data dictionary. The data structure diagram is a graphical alternative to the composition specifications within such data dictionary entries. [1] The data structure diagrams is a predecessor of the entity–relationship model (E–R model
Control charts are graphical plots used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1) [1] The hourly status is arranged on the graph, and the occurrence of abnormalities is judged based on the presence of data that differs from the conventional trend or deviates from the control limit line.