Solving a posynomial geometric programming problem with fully fuzzy approach

Abstract

In this paper we have investigated a class of geometric programming problems in which all the parameters are fuzzy numbers. In fact, due to impreciseness of the cost components and exponents in geometric programming with their inherently behavior as in economics and many other areas, we have used fuzzy parametric geometric programming. Transforming the primal problem of fuzzy geometric programming into its dual and using the Zadeh's extension principle, we convert the dual form into a pair of mathematical programs. By applying the α-cut on the objective function and r-cut on the constraints in dual form of geometric programming, we obtain an acceptable (α, r) optimal values. Then, we further calculate the lower and upper bounds of the fuzzy objective with emphasize on modification of a method presented in [14, 32]. Finally, we illustrate the methodology of the approach with a numerical example to clarify the idea by drawing the different steps of LR representation of Zαr.

Keywords

• fuzzy logic
• posynomial
• geometric programming
• optimization