Expression of Fuzziness for Optimization and its Application to Multicriteria Optimum Design.
Teruo Sunaga, Eiji Kondo, Takanori KIYOTA · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C · 1993
Instead of the membership function, its reciprocal function minus one, called the unsatisfying function, is introduced. By use of the function, the formulation and the calculation of the optimization problem with the concept of fuzziness is shown to be simpler than in the case using the membership function, because the unsatisfying function is similar to the penalty function in the mathematical programming. For a multicriteria optimization problem, the aspiration levels of the objectives are regarded as restriction values. For all the restrictions of the problem, the unsatisfying functions beyond the restriction values are prepared. The calculation method of the least squares of the unsatisfying functions and the interactive solution method are proposed. Furthermore, it is shown that the technological knowledge of precision and error can be utilized. Finally, a beam design problem is described for the application of these methods.