Neutrosophic Geometric Programming (NGP) Problems Subject to (⋁, . ) Operator; the Minimum Solution

Abstract

This paper comes as a second step serves the purpose of constructing a neutrosophic optimization model for the relation geometric programming problems subject to (max, product) operator in its constraints. This essay comes simultaneously with my previous paper entitled (Neutrosophic Geometric Programming (NGP) with (max-product) Operator, An Innovative Model) which contains the structure of the maximum solution. The purpose of this article is to set up the minimum solution for the (RNGP) problems, the author faced many difficulties, where the feasible region for this type of problems is already nonconvex; furthermore, the negative signs of the exponents with neutrosophic variables 𝑥𝑗 ∈ [0,1] ∪ 𝐼 . A new technique to avoid the divided by the indeterminacy component (𝐼) was introduced; Separate the neutrosophic geometric programming into two optimization models, introducing two new matrices named as the distinguishing matrix and the facilitation matrix. All these notions were important for finding the minimum solution of the program. Finally, two numerical examples were presented to enable the reader to understand this work.

Keywords

• relational neutrosophic geometric programming (rngp); (⋁
• . ) operator; neutrosophic relation equations; distinguishing matrix; facilitation matrix; minimum solution; incompatible problem