Description Usage Arguments Value References See Also Examples
The goal is to solve a linear programming problem having Trapezoidal Fuzzy Numbers as coefficients in the objective function (f(x)=c1*x1+…+cn*xn).
Max f(x) or Min f(x)
s.t.: Ax<=b
FOLP.posib
uses a possibilistic approach. This approach is based on Trapezoidal Fuzzy Numbers
arithmetic, so the whole objective may be considered as a Fuzzy Number itself. Defining a notion of
maximum for this kind of numbers (a weighted average of the minimum and maximum of the support of
the Trapezoidal number).
1  FOLP.posib(objective, A, dir, b, maximum = TRUE, w1 = 0.5)

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 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. 
maximum 

w1 
Weight to be used, 
FOLP.posib
returns the solution for the given weights if the solver has found it or NULL if not.
Dubois, D. and Prade, H. Operations in fuzzy numbers. International Journal of Systems Science, 9:613626, 1978.
FOLP.ordFun
, FOLP.multiObj
, FOLP.interv
, FOLP.strat
1 2 3 4 5 6 7 8 9 10 11 12 13  ## maximize: [0,2,3]*x1 + [1,3,4,5]*x2
## s.t.: x1 + 3*x2 <= 6
## x1 + x2 <= 4
## x1, x2 are nonnegative real numbers
obj < c(FuzzyNumbers::TrapezoidalFuzzyNumber(0,2,2,3),
FuzzyNumbers::TrapezoidalFuzzyNumber(1,3,4,5))
A<matrix(c(1, 1, 3, 1), nrow = 2)
dir < c("<=", "<=")
b < c(6, 4)
max < TRUE
FOLP.posib(obj, A, dir, b, maximum = max, w1=0.2)

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