Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Effectiveness of a geometric programming algorithm for optimization of machining economics models
Computers and Operations Research
An infeasible interior-point algorithm for solving primal and dual geometric programs
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Solving Posynomial Geometric Programming Problems via Generalized Linear Programming
Computational Optimization and Applications
Optimal design of a CMOS op-amp via geometric programming
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
CMOS op-amp sizing using a geometric programming formulation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fuzzy pricing and marketing planning model: A possibilistic geometric programming approach
Expert Systems with Applications: An International Journal
Solving portfolio optimization problem based on extension principle
IEA/AIE'10 Proceedings of the 23rd international conference on Industrial engineering and other applications of applied intelligent systems - Volume Part I
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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 estimates of actual values. When the parameters in the problem are imprecise, the calculated objective value should be imprecise as well. This paper develops a procedure to derive the fuzzy objective value of the fuzzy posynomial geometric programming problem when the exponents of decision variables in the objective function, the cost and the constraint coefficients, and the right-hand sides are fuzzy numbers. The idea is based on Zadeh's extension principle to transform the fuzzy geometric programming problem into a pair of two-level of mathematical programs. Based on duality algorithm and a simple algorithm, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs. The upper bound and lower bound of the objective value are obtained by solving the pair of geometric programs. From different values of @a, the membership function of the objective value is constructed. Two examples are used to illustrate that the whole idea proposed in this paper.