Minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm

作者：Li Pingke^*; Fang Shu Cherng

来源：Journal of Systems Science and Complexity, 2009, 22(1): 49-62.

DOI：10.1007/s11424-009-9146-x

• Fractional optimization
• fuzzy relational equations
• triangular norms

This paper shows that the problem of minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1 linear 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 with an objective function being monotone in each variable separately. This method could be extended as well to the case in which the triangular norm is non-Archimedean.

• 出版日期2009-3
• 单位清华大学; 大连理工大学