Use of approximation concepts in fuzzy design problems
This paper presents a fuzzy formulation for design problems. Design variables, as well as problem parameters are modeled as fuzzy numbers characterized by membership functions. An optimization approach and a formulation based on functional requirements on performance parameters are presented. In both cases, numerically efficient algorithms are required to evaluate system responses and their membership functions. Approximation concepts are introduced to develop an efficient numerical methodology in order to define high quality approximations for response functions and membership functions of system responses. Example problems are presented to illustrate and validate the use of approximations in the context of fuzzy design problems. Numerical results show the usefulness and effectiveness of the proposed method.
membership functions engineering design fuzzy optimization mathematical programming representation of uncertainties