Description Details Super classes Methods See Also Examples
A general FuzzyTuple object for mathematical fuzzy tuples, inheriting from FuzzySet
.
Fuzzy tuples generalise standard mathematical tuples to allow for fuzzy relationships. Whereas a standard, or crisp, tuple assumes that an element is either in a tuple or not, a fuzzy tuple allows an element to be in a tuple to a particular degree, known as the membership function, which quantifies the inclusion of an element by a number in [0, 1]. Thus a (crisp) tuple is a fuzzy tuple where all elements have a membership equal to 1. Similarly to Tuples, elements do not need to be unique and the ordering does matter, FuzzySets are special cases where the ordering does not matter and elements must be unique.
set6::Set
-> set6::FuzzySet
-> FuzzyTuple
equals()
Tests if two sets are equal.
FuzzyTuple$equals(x, all = FALSE)
x
Set or vector of Sets.
all
logical. If FALSE
tests each x
separately. Otherwise returns TRUE
only if all x
pass test.
Two fuzzy sets are equal if they contain the same elements with the same memberships and in the same order. Infix operators can be used for:
Equal | == |
Not equal | != |
If all
is TRUE
then returns TRUE
if all x
are equal to the Set, otherwise
FALSE
. If all
is FALSE
then returns a vector of logicals corresponding to each individual
element of x
.
isSubset()
Test if one set is a (proper) subset of another
FuzzyTuple$isSubset(x, proper = FALSE, all = FALSE)
x
any. Object or vector of objects to test.
proper
logical. If TRUE
tests for proper subsets.
all
logical. If FALSE
tests each x
separately. Otherwise returns TRUE
only if all x
pass test.
If using the method directly, and not via one of the operators then the additional boolean
argument proper
can be used to specify testing of subsets or proper subsets. A Set is a proper
subset of another if it is fully contained by the other Set (i.e. not equal to) whereas a Set is a
(non-proper) subset if it is fully contained by, or equal to, the other Set.
Infix operators can be used for:
Subset | < |
Proper Subset | <= |
Superset | > |
Proper Superset | >=
|
If all
is TRUE
then returns TRUE
if all x
are subsets of the Set, otherwise
FALSE
. If all
is FALSE
then returns a vector of logicals corresponding to each individual
element of x
.
alphaCut()
The alpha-cut of a fuzzy set is defined as the set
A_α = {x ε F | m ≥ α}
where x is an element in the fuzzy set, F, and m is the corresponding membership.
FuzzyTuple$alphaCut(alpha, strong = FALSE, create = FALSE)
alpha
numeric in [0, 1] to determine which elements to return
strong
logical, if FALSE
(default) then includes elements greater than or equal to alpha, otherwise only strictly greater than
create
logical, if FALSE
(default) returns the elements in the alpha cut, otherwise returns a crisp set of the elements
Elements in FuzzyTuple or a Set of the elements.
clone()
The objects of this class are cloneable with this method.
FuzzyTuple$clone(deep = FALSE)
deep
Whether to make a deep clone.
Other sets:
ConditionalSet
,
FuzzyMultiset
,
FuzzySet
,
Interval
,
Multiset
,
Set
,
Tuple
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | # Different constructors
FuzzyTuple$new(1, 0.5, 2, 1, 3, 0)
FuzzyTuple$new(elements = 1:3, membership = c(0.5, 1, 0))
# Crisp sets are a special case FuzzyTuple
# Note membership defaults to full membership
FuzzyTuple$new(elements = 1:5) == Tuple$new(1:5)
f <- FuzzyTuple$new(1, 0.2, 2, 1, 3, 0)
f$membership()
f$alphaCut(0.3)
f$core()
f$inclusion(0)
f$membership(0)
f$membership(1)
# Elements can be duplicated, and with different memberships,
# although this is not necessarily sensible.
FuzzyTuple$new(1, 0.1, 1, 1)
# More important is ordering.
FuzzyTuple$new(1, 0.1, 2, 0.2) != FuzzyTuple$new(2, 0.2, 1, 0.1)
FuzzySet$new(1, 0.1, 2, 0.2) == FuzzySet$new(2, 0.2, 1, 0.1)
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