Optimization with Fuzzy Data via Evolutionary Algorithms
Witold Kosiński, Theodore E. Simos, George Psihoyios, Ch. Tsitouras · AIP conference proceedings · 2010
Order fuzzy numbers (OFN) that make possible to deal with fuzzy inputs quantitatively, exactly in the same way as with real numbers, have been recently defined by the author and his 2 coworkers. The set of OFN forms a normed space and is a partially ordered ring. The case when the numbers are presented in the form of step functions, with finite resolution, simplifies all operations and the representation of defuzzification functionals. A general optimization problem with fuzzy data is formulated. Its fitness function attains fuzzy values. Since the adjoint space to the space of OFN is finite dimensional, a convex combination of all linear defuzzification functionals may be used to introduce a total order and a real‐valued fitness function. Genetic operations on individuals representing fuzzy data are defined.