Fuzzy Geometric Programming: a possibility approach

Geometric programming provides a powerful tool for solving a variety of engineering optimization problems. Many applications of geometric programming are engineering design problems in which some of the problem parameters are estimate of actual values. In applications of geometric programming, some coefficients and/or exponents may not be precisely known. However, the coefficients and/or exponents in the real-life problems are often imprecise and ambiguous. The impreciseness and ambiguity associated with the coefficients and/or exponents in geometric programming can be represented with fuzzy variables. Fuzzy geometric programming can be used to deal with such Situations. In this paper, we propose chance constrained geometric programming model (i.e., the possibility) for solving fuzzy geometric programming model in which the some coefficients and/or exponents are assumed to be characterized by fuzzy variables. In fuzzy environments, the crisp coefficients and/or exponents in conventional geometric programming model become fuzzy variables. And then a deterministic equivalent model is obtained in order to solve the model.

Keywords:

Geometric programming , Fuzzy set , Optimization , possibility