Monomial geometric programming with fuzzy relation equation constraints

Monomials are widely used. They are basic structural units of geometric programming. In the process of optimization, many objective functions can be denoted by monomials. We can often see them in resource allocation and structure optimization and technology management, etc. Fuzzy relation equations are important elements of fuzzy mathematics, and they have recently been widely applied in fuzzy comprehensive evaluation and cybernetics. In view of the importance of monomial functions and fuzzy relation equations, we present a fuzzy relation geometric programming model with a monomial objective function subject to the fuzzy relation equation constraints, and develop an algorithm to find an optimal solution based on the structure of the solution set of fuzzy relation equations. Two numerical examples are given to verify the developed algorithm. Our numerical results show that the algorithm is feasible and effective.