FOLP_Posib: Solves a fuzzy objective linear programming problem using...
In FuzzyLP: Fuzzy Linear Programming

FOLP.posib

R Documentation

Solves a fuzzy objective linear programming problem using Representation Theorem.

Description

The goal is to solve a linear programming problem having Trapezoidal Fuzzy Numbers as coefficients in the objective function (f(x)=c_{1}^{f} x_1+\ldots+c_{n}^{f} x_n).

Max\, f(x)\ or\ Min\ f(x)

s.t.:\quad 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).

Usage

FOLP.posib(objective, A, dir, b, maximum = TRUE, w1 = 0.5)

Arguments

`objective`	A vector `(c_{1}^{f}, c_{2}^{f}, ..., c_{n}^{f})` of Trapezoidal Fuzzy Numbers with the objective function coefficients `f(x)=c_{1}^{f} x_1+\ldots+c_{n}^{f} x_n`. 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`. Each element of the vector must be one of "=", ">=", "<=", "<" or ">".
`b`	Vector with the right hand side of the constraints.
`maximum`	`TRUE` to maximize the objective function, `FALSE` to minimize the objective function.
`w1`	Weight to be used, `w2` is calculated as `w2=1-w1`. `w1` must be in the interval `[0,1]`.

Value

FOLP.posib returns the solution for the given weights if the solver has found it or NULL if not.

References

Dubois, D. and Prade, H. Operations in fuzzy numbers. International Journal of Systems Science, 9:613-626, 1978.

Examples

## maximize:   [0,2,3]*x1 + [1,3,4,5]*x2
## s.t.:         x1 + 3*x2 <= 6
##               x1 +   x2 <= 4
##               x1, x2 are non-negative 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)

FuzzyLP documentation built on Aug. 21, 2023, 1:06 a.m.