The use of parametric programming in fuzzy linear programming
The following problem of fuzzy linear programming \[ ''\max ''\quad c'x,\quad subject\quad to\quad \sum^{n}_{i=1}a_{ij}x_ j\preccurlyeq b_ i\quad(i=1,...,m),\quad x\geq 0, \] whose constraints and goal are not crisp but fuzzy sets characterized by their membership functions, is solved by the parametric programming technique and a complete fuzzy solution (not only the maximizing alternative) is obtained. The advantages of the proposed approach are: (1) The underlying problem is not enlarged. (2) The aspiration level as well as the admissible tolerance of the objective function can be stated after the solution of the parametric problem. (3) It is not necessary to assume piecewise linearity of the membership function of the goal. (4) One obtains a complete fuzzy solution allowing to consider also other possibilities besides the maximizing variant. The presented approach is illustrated by some numerical examples.
scientific article; zbMATH DE number 3848965