Using genetic algorithms for λ-fuzzy measure fitting and extension

Constructing fuzzy measures in systems is an important topic in system research. Revising a set function to be a desirable fuzzy measure is one of the practicable strategies of the construction. In this paper, the following fitting problem is investigated: given a universal set and a set function, which is not necessarily a λ-fuzzy measure, defined on a class of subsets of the universal set, we want to find a regular λ-fuzzy measure on the power set of the universal set such that it is as close as possible to the original set function. This is, essentially, an optimization problem. A genetic algorithm is used to search the optimal solution. As a special case, when the set function is already a regular λ-fuzzy measure on the original domain that is a proper subclass of the power set we can obtain a regular λ-fuzzy measure extension on the power set