Description Usage Arguments Value References Examples
The goal is to solve a linear programming problem having Trapezoidal Fuzzy Numbers as coefficients in the constraints, the objective function and/or the technological matrix.
Max f(x) or Min f(x)
s.t.: Ax<=b+(1β)*t
This function uses different ordering functions for the objective function and for the constraints.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 
objective 
A vector (c1, c2, ..., cn) of Trapezoidal Fuzzy Numbers with the objective function coefficients f(x)=c1*x1+…+cn*xn. Note that any of the coefficients may also be Real Numbers. 
A 
Technological matrix containing Trapezoidal Fuzzy Numbers and/or 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. 
maximum 

ordf_obj 
Ordering function to be used in the objective function, 
ordf_obj_param 
Parameters need by ordf_obj function, if it needs more than one parameter, use
a named vector. See 
ordf_res 
Ordering function to be used in the constraints, 
ordf_res_param 
Parameters need by ordf_res function, if it needs more than one parameter, use
a named vector. See 
min 
The lower bound of the interval to take the sample. 
max 
The upper bound of the interval to take the sample. 
step 
The sampling step. 
GFLP
returns the solutions for the sampled β's if the solver has found them.
If the solver hasn't found solutions for any of the β's sampled, return NULL.
Gonzalez, A. A studing of the ranking function approach through mean values. Fuzzy Sets and Systems, 35:2941, 1990.
Cadenas, J.M. and Verdegay, J.L. Using Fuzzy Numbers in Linear Programming. IEEE Transactions on Systems, Man, and CyberneticsPart B: Cybernetics, vol. 27, No. 6, December 1997.
Tanaka, H., Ichihashi, H. and Asai, F. A formulation of fuzzy linear programming problems based a comparison of fuzzy numbers. Control and Cybernetics, 13:185194, 1984.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  ## maximize: [1,3,4,5]*x1 + x2
## s.t.: [0,2,3,3.5]*x1 + [0,1,1,4]*x2 <= [2,2,2,3] + (1beta)*[1,2,2,3]
## [3,5,5,6]*x1 + [1.5,2,2,3]*x2 <= 12
## x1, x2 are nonnegative real numbers
obj < c(FuzzyNumbers::TrapezoidalFuzzyNumber(1,3,4,5), 1)
a11 < FuzzyNumbers::TrapezoidalFuzzyNumber(0,2,2,3.5)
a21 < FuzzyNumbers::TrapezoidalFuzzyNumber(3,5,5,6)
a12 < FuzzyNumbers::TrapezoidalFuzzyNumber(0,1,1,4)
a22 < FuzzyNumbers::TrapezoidalFuzzyNumber(1.5,2,2,3)
A < matrix(c(a11, a21, a12, a22), nrow = 2)
dir < c("<=", "<=")
b<c(FuzzyNumbers::TrapezoidalFuzzyNumber(2,2,2,3), 12)
t<c(FuzzyNumbers::TrapezoidalFuzzyNumber(1,2,2,3),0);
max < TRUE
GFLP(obj, A, dir, b, t, maximum = max, ordf_obj="Yager1", ordf_res="Yager3")
GFLP(obj, A, dir, b, t, maximum = max, ordf_obj="Adamo", ordf_obj_param=0.5, ordf_res="Yager3")
GFLP(obj, A, dir, b, t, maximum = max, "Average", ordf_obj_param=c(t=3, lambda=0.5),
ordf_res="Adamo", ordf_res_param = 0.5)
GFLP(obj, A, dir, b, t, maximum = max, ordf_obj="Average", ordf_obj_param=c(t=3, lambda=0.8),
ordf_res="Yager3", min = 0, max = 1, step = 0.2)

beta x1 x2 objective
[1,] 0 2.433193 0.2081575 ?
[2,] 0.25 2.337553 0.4219409 ?
[3,] 0.5 2.241913 0.6357243 ?
[4,] 0.75 2.146273 0.8495077 ?
[5,] 1 2.050633 1.063291 ?
beta x1 x2 objective
[1,] 0 2.433193 0.2081575 ?
[2,] 0.25 2.337553 0.4219409 ?
[3,] 0.5 2.241913 0.6357243 ?
[4,] 0.75 2.146273 0.8495077 ?
[5,] 1 2.050633 1.063291 ?
beta x1 x2 objective
[1,] 0 1.922078 0.5714286 ?
[2,] 0.25 1.75974 0.9285714 ?
[3,] 0.5 1.597403 1.285714 ?
[4,] 0.75 1.435065 1.642857 ?
[5,] 1 1.272727 2 ?
beta x1 x2 objective
[1,] 0 2.433193 0.2081575 ?
[2,] 0.2 2.356681 0.3791842 ?
[3,] 0.4 2.280169 0.550211 ?
[4,] 0.6 2.203657 0.7212377 ?
[5,] 0.8 2.127145 0.8922644 ?
[6,] 1 2.050633 1.063291 ?
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