Geometric programming with a single-term exponent subject to bipolar max-product fuzzy relation equation constraints

Abstract

We study geometric programming with a single-term exponent subject to bipolar max-product fuzzy relation equation constraints in the area of economics and the covering problem. The structure of its feasible domain is characterized and the lower and upper bound vectors on its solution set are determined. It is shown that each component of one of its optimal solutions is the corresponding component of either the lower bound or the upper bound vector. This interesting property helps us to create a value matrix and present some necessary and sufficient conditions for its consistency checking. Moreover, some sufficient conditions are proposed to detect one of its optimal solutions without solving the problem. A modified branch-and-bound method is extended to solve the problem, in a general case, with use of the value matrix. An efficient algorithm is then designed to solve the problem using the sufficient conditions and the modified branch-and-bound method. Its computational complexity is also analyzed. Finally, some examples are provided to illustrate its importance and the steps of the algorithm.