This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization ...This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.展开更多
基金supported by the National Science Foundation of the United States under Grant No. #DMI- 0553310
文摘This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.
