Abstract
Geometric programming problems are well-known in mathematical modeling. They are broadly used in diverse practical fields that are contemplated through an appropriate methodology. In this paper, a multi-parametric vector α is proposed for approaching the highest decision maker satisfaction. Hitherto, the simple parameter α , which has a scalar role, has been considered in the problem. The parameter α is a vector whose range is within the region of the satisfaction area. Conventionally, it is assumed that the decision maker is sure about the parameters, but, in reality, it is mostly hesitant about them, so the parameters are presented in fuzzy numbers. In this method, the decision maker can attain different satisfaction levels in each constraint, and even full satisfaction can be reached in some constraints. The goal is to find the highest satisfaction degree to maintain an optimal solution. Moreover, the objective function is turned into a constraint, i.e., one more dimension is added to n-dimensional multi-parametric α . Thus, the fuzzy geometric programming problem under this multi-parametric vector α ∈ ( 0 , 1 ] n + 1 gives a maximum satisfaction level to the decision maker. A numerical example is presented to illustrate the proposed method and the superiority of this multi-parametric α over the simple one.
Highlights
Nowadays, mathematical modeling is the most considered tool in simulation and has inevitable applications in many fields, especially in financial management, economics, wireless networking, and engineering in general [1,2,3]
Mathematical models are classified into two general categories: (I) linear programming (LP) problems and (II) geometric programming (GP) problems that can be defined on crisp and fuzzy numbers
For the sake of this definition, we propose a multi-parametric vector α ∈
Summary
Mathematical modeling is the most considered tool in simulation and has inevitable applications in many fields, especially in financial management, economics, wireless networking, and engineering in general [1,2,3]. Lai [27] proposed a fuzzy approach for finding a satisfactory solution for the linear multilevel decision problem and used the concepts of membership functions as well as the satisfaction degree of individual decision power. Sakawa et al [29] presented an interactive fuzzy programming approach for linear multilevel decision problems This is accomplished by updating the satisfaction degrees of the decision maker by considering the overall satisfaction balance at all levels. In order to improve the satisfaction degree in the solution of a fuzzy geometric programming problem that has various applications in the real world, a novel multi-parametric vector α is proposed. For the sake of this definition, we propose a multi-parametric vector α ∈ Useful remarks on GP and fuzzy sets are provided
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