FCLP.Beta: Solves a Fuzzy Linear Programming problem with fuzzy...
In FuzzyLP: Fuzzy Linear Programming

FCLP.fixedBeta

R Documentation

Solves a Fuzzy Linear Programming problem with fuzzy constraints.

Description

The goal is to solve a linear programming problem having fuzzy constraints.

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

s.t.:\quad Ax<=b+(1-\beta)*t

Where t means we allow not to satisfy the constraint, exceeding the bound b at most in t.

FCLP.fixedBeta uses the classic solver (simplex) to solve the problem with a fixed value of \beta.

FCLP.sampledBeta solves the problem in the same way than FCLP.fixedBeta but using several \beta's taking values in a sample of the [0,1] inteval.

Usage

FCLP.fixedBeta(
  objective,
  A,
  dir,
  b,
  t,
  beta = 0.5,
  maximum = TRUE,
  verbose = TRUE
)

FCLP.sampledBeta(
  objective,
  A,
  dir,
  b,
  t,
  min = 0,
  max = 1,
  step = 0.25,
  maximum = TRUE,
  verbose = TRUE
)

Arguments

`objective`	A vector `(c_1, c_2, \ldots, c_n)` with the objective function coefficients `f(x)=c_1 x_1+\ldots+c_n x_n`.
`A`	Technological matrix of Real Numbers.
`dir`	Vector of strings with the direction of the inequalities, of the same length as `b` and `t`. Each element of the vector must be one of "=", ">=", "<=", "<" or ">".
`b`	Vector with the right hand side of the constraints.
`t`	Vector with the tolerance of each constraint.
`beta`	The value of `\beta` to be used.
`maximum`	`TRUE` to maximize the objective function, `FALSE` to minimize the objective function.
`verbose`	`TRUE` to show aditional screen info, `FALSE` to hide aditional screen info.
`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.

Value

FCLP.fixedBeta returns the solution for the given beta if the solver has found it or NULL if not.

FCLP.sampledBeta returns the solutions for the sampled \beta's if the solver has found them. If the solver hasn't found solutions for any of the \beta's sampled, return NULL.

References

Verdegay, J.L. Fuzzy mathematical programming. In: Fuzzy Information and Decision Processes, pages 231-237, 1982. M.M. Gupta and E.Sanchez (eds).

Delgado, M. and Herrera, F. and Verdegay, J.L. and Vila, M.A. Post-optimality analisys on the membership function of a fuzzy linear programming problem. Fuzzy Sets and Systems, 53:289-297, 1993.

Examples

## maximize:   3*x1 + x2
## s.t.:       1.875*x1   - 1.5*x2 <= 4 + (1-beta)*5
##              4.75*x1 + 2.125*x2 <= 14.5 + (1-beta)*6
##               x1, x2 are non-negative 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)
valbeta <- 0.5
max <- TRUE

FCLP.fixedBeta(obj, A, dir, b, t, beta=valbeta, maximum = max, verbose = TRUE)

FCLP.sampledBeta(obj, A, dir, b, t, min=0, max=1, step=0.25, maximum = max, verbose = TRUE)

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