fuzzy {sets} | R Documentation |
Fuzzy Logic
fuzzy_logic(new, ...) .N.(x) .T.(x, y) .S.(x, y) .I.(x, y)
x, y |
Numeric vectors. |
new |
A character string specifying one of the available fuzzy logic “families” (see details). |
... |
optional parameters for the selected family. |
A call to fuzzy_logic()
without arguments returns the currently
set fuzzy logic, i.e., a named list with four
components N
, T
, S
, and I
containing the
corresponding functions for negation, conjunction
(“t-norm”), disjunction (“t-conorm”), and
implication (which may not be available).
The package provides several fuzzy logic families.
A concrete fuzzy logic is selected
by calling fuzzy_logic
with a character
string specifying the family name, and optional parameters. Let us
refer to N(x) = 1 - x as the standard negation, and,
for a t-norm T, let S(x, y) = 1 - T(1 - x, 1 - y) by
the dual (or complementary) t-conorm. Available
specifications and corresponding families are as follows, with the
standard negation used unless stated otherwise.
"Zadeh"
"drastic"
"product"
"Lukasiewicz"
"Fodor"
"Frank"
"Hamacher"
alpha
,
beta
and gamma
, respectively. If α is
not given, it is taken as α = (1 + β) / (1 +
gamma).
The default values for β and gamma are 0, so that
by default, the product family is obtained.The following parametric families are obtained by combining the corresponding families of t-norms with the standard negation.
"Schweizer-Sklar"
"Yager"
"Dombi"
"Aczel-Alsina"
"Sugeno-Weber"
By default, the Zadeh family is used.
.N.
, .T.
, .S.
, and .I.
are dynamic
functions, i.e., wrappers that call the corresponding function of the
current fuzzy logic family. Thus, the behavior of code using these
functions will change according to the chosen family.
C. Alsina, M. J. Frank and B. Schweizer (2006), Associative Functions: Triangular Norms and Copulas. World Scientific. ISBN 981-256-671-6.
J. Dombi (1982), A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Sets and Systems 8, 149–163.
J. Fodor and M. Roubens (1994), Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht.
B. Schweizer and A. Sklar (1983), Probabilistic Metric Spaces. North-Holland, New York. ISBN 0-444-00666-4.
x <- c(0.7, 0.8) y <- c(0.2, 0.3) ## Use default family ("Zadeh") .N.(x) .T.(x, y) .S.(x, y) .I.(x, y) ## Switch family and try again fuzzy_logic("Fodor") .N.(x) .T.(x, y) .S.(x, y) .I.(x, y)