Possibility programming by the comparison of fuzzy numbers (Q1802451)

A fuzzy mathematical programming problem (possibilistic programming problem) is investigated: \(\tilde c_ 1x_ 1\tilde +\dots \tilde +\tilde c_ n x_ n\to\max\), subject to \(\tilde a_{i1}x_ 1\tilde + \dots \tilde +\tilde a_{in}x_ n\tilde \leq \tilde b_ i\) \((i=1,2,\dots,m)\), \(x_ j\geq 0\) \((j=1,2,\dots,n)\). In this problem triangular or trapezoidal fuzzy coefficients \(\tilde c_ j\), \(\tilde a_{ij}\), \(\tilde b_ i\) are considered as well as special inequality relations between right and left hand sides of the constraints \(\tilde \leq\), the variables \(x_ j\) are crisp. The approach appears to be powerful due to its simplicity and its relatively small requirement of computer time. The presented approach is demonstrated on simple numerical examples.