Identification of monotone measures using genetic algorithms

Identification of monotone measures is a very challenging process. Based on an existing data set of a set function (or set functions) defined on the power set of a given finite universal set, to determine a monotone measure, simply switching the values of the given set function that violate the monotonicity is not the optimal way and it also causes some side effects. The paper proposes an algorithm to optimally determine a monotone measure using soft computing technique. In the algorithm, the crux is how to guarantee the monotonicity of the obtained set function. In this connection, a sub-algorithm called reordering algorithm is embedded. According to the lattice structure of the power set of the given universal set, a max-min strategy is adopted to reduce the computational complexity. The proposed approach is illustrated by applying it to several random data sets. Our experiments show that this approach is effective.