A new approach for multiple objective decision making

The proposed TOPSIS for MODM algorithm is developed for solving multiple objective decision-making problems by considering two reference points of the positive ideal solution and the negative ideal solution simultaneously. The basic principle of compromise of TOPSIS for MODM is that the chosen solution should be as close to the positive ideal solution as possible and so far away from the negative ideal solution as possible. Thus, the authors can reduce a k-objective decision-making problem into an auxiliary bi-objective decision-making problem. That is: instead of k incommensurable and confiicting objective function, they consider two commensurable but conflicting objective functions (distance functions). Then, by using the max-min operator, the authors can obtain a compromise solution for the auxiliary bi-objective problem and the original k-objective problem. To illustrate the TOPSIS algorithm, a numerical nutrition problem is solved.