Description Usage Arguments Value References See Also Examples
The goal is to solve a linear programming problem having fuzzy constraints trying to assure a minimum (or maximum) value of the objective function.
Max f(x) or Min f(x)
s.t.: Ax<=b+(1β)*t
Where t means we allow not to satisfy the constraint, exceeding the bound b at most in t.
FCLP.classicObjective
solves the problem trying to assure a minimum (maximum) value z0
of the objective function (f(x)>=z0 in maximization problems, f(x)<=z0 in minimization
problems).
FCLP.fuzzyObjective
solves the problem trying to assure a minimum (maximum) value
z0 of the objective function with tolerance t0 (f(x)>=z0(1β)*t0 in maximization
problems, f(x)<=z0+(1β)*t0 in minimization problems).
FCLP.fuzzyUndefinedObjective
solves the problem trying to assure a minimum (maximum)
value of the objective function with tolerance but the user doesn't fix the bound nor the
tolerance. The function estimate a bound and a tolerance and call FCLP.fuzzyObjective
using them.
FCLP.fuzzyUndefinedNormObjective
solves the problem trying to assure a minimum (maximum)
value of the objective function with tolerance but the user doesn't fix the bound nor the
tolerance. The function normalize the objective, estimate a bound and a tolerance and call
FCLP.fuzzyObjective
using them.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42  FCLP.classicObjective(
objective,
A,
dir,
b,
t,
z0 = 0,
maximum = TRUE,
verbose = TRUE
)
FCLP.fuzzyObjective(
objective,
A,
dir,
b,
t,
z0 = 0,
t0 = 0,
maximum = TRUE,
verbose = TRUE
)
FCLP.fuzzyUndefinedObjective(
objective,
A,
dir,
b,
t,
maximum = TRUE,
verbose = TRUE
)
FCLP.fuzzyUndefinedNormObjective(
objective,
A,
dir,
b,
t,
maximum = TRUE,
verbose = TRUE
)

objective 
A vector (c1, c2, …, cn) with the objective function coefficients f(x)=c1*x1+…+cn*xn. 
A 
Technological matrix of Real Numbers. 
dir 
Vector of strings with the direction of the inequalities, of the same length as 
b 
Vector with the right hand side of the constraints. 
t 
Vector with the tolerance of each constraint. 
z0 
The minimum (maximum in a minimization problem) value of the objective function to reach. Only
used in 
maximum 

verbose 

t0 
The tolerance value to the minimum (or maximum) bound for the objective function. Only
used in 
FCLP.classicObjective
returns a solution reaching the given minimum (maximum)
value of the objective function if the solver has found it (trying to maximize β) or NULL
if not. Note that the found solution may not be the optimum for the β returned, trying β in
FCLP.fixedBeta
may obtain better results.
FCLP.fuzzyObjective
returns a solution reaching the given minimum (maximum)
value of the objective function if the solver has found it (trying to maximize β) or NULL
if not. Note that the found solution may not be the optimum for the β returned, trying β in
FCLP.fixedBeta
may obtain better results.
FCLP.fuzzyUndefinedObjective
returns a solution reaching the estimated minimum
(maximum) value of the objective function if the solver has found it (trying to maximize β)
or NULL if not.
FCLP.fuzzyUndefinedNormObjective
returns a solution reaching the estimated
minimum (maximum) value of the objective function if the solver has found it (trying to
maximize β) or NULL if not.
Zimmermann, H. Description and optimization of fuzzy systems. International Journal of General Systems, 2:209215, 1976.
Werners, B. An interactive fuzzy programming system. Fuzzy Sets and Systems, 23:131147, 1987.
Tanaka, H. and Okuda, T. and Asai, K. On fuzzy mathematical programming. Journal of Cybernetics, 3,4:3746, 1974.
FCLP.fixedBeta
, FCLP.sampledBeta
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  ## maximize: 3*x1 + x2 >= z0
## s.t.: 1.875*x1  1.5*x2 <= 4 + (1beta)*5
## 4.75*x1 + 2.125*x2 <= 14.5 + (1beta)*6
## x1, x2 are nonnegative real numbers
obj < c(3, 1)
A < matrix(c(1.875, 4.75, 1.5, 2.125), nrow = 2)
dir < c("<=", "<=")
b < c(4, 14.5)
t < c(5, 6)
max < TRUE
# Problem with solution
FCLP.classicObjective(obj, A, dir, b, t, z0=11, maximum=max, verbose = TRUE)
# This problem has a bound impossible to reach
FCLP.classicObjective(obj, A, dir, b, t, z0=14, maximum=max, verbose = TRUE)
# This problem has a fuzzy bound impossible to reach
FCLP.fuzzyObjective(obj, A, dir, b, t, z0=14, t0=1, maximum=max, verbose = TRUE)
# This problem has a fuzzy bound reachable
FCLP.fuzzyObjective(obj, A, dir, b, t, z0=14, t0=2, maximum=max, verbose = TRUE)
# We want the function estimates a bound and a tolerance
FCLP.fuzzyUndefinedObjective(obj, A, dir, b, t, maximum=max, verbose = TRUE)
# We want the function estimates a bound and a tolerance
FCLP.fuzzyUndefinedNormObjective(obj, A, dir, b, t, maximum=max, verbose = TRUE)

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