Abstract
This paper introduces an approach for group decision-making problems (GDMP) without weighted aggregation operators. This approach is more suitable for scenarios with infinite number of individuals. A mathematical model approach is established based on the new concept of s⁎-optimal concession equilibrium solution without weighted aggregation operators for group decision-making problems. It is of practical significance for all decision-makers (experts) to find an optimal solution or to sort out all the candidate solutions. We prove that the s⁎-optimal concession equilibrium solution is equivalent to solving a single objective optimization problem, and, under certain conditions, the s⁎-optimal equilibrium solution always exists. Moreover, it is proven that the s⁎-optimal concession equilibrium solution is equivalent to the robust optimal solution of the group weight aggregation and the optimal solution under the worst weighted aggregation operators.
Highlights
The group decision-making problem has always been a hot topic in the research of decision theory and an important branch of scientific research
This paper introduces an approach for group decision-making problems (GDMP) without weighted aggregation operators
This paper introduces a new concept of solution to GDMP: s-concession equilibrium solution and s-optimal concession equilibrium solution
Summary
The group decision-making problem has always been a hot topic in the research of decision theory and an important branch of scientific research. The motivation and innovation of this paper are that the proposed optimal concession equilibrium solution is a natural law of the consistency of group interests without weighted aggregation operators and when the candidate is infinite, this method avoids the difficulty of calculating the weights so that it is more effective in solving group decision-making problems. According to Theorem 8, we obtain a method to find out an s∗-optimal concession equilibrium solution to GDMP. We prove that the s∗-optimal concession equilibrium solution is essentially a robust optimal solution for all group decision weights. Theorem 13 shows that the s∗-optimal concession equilibrium solution x∗ to GDMP at the concession value ε is the optimal solution to the problem (S), that is, an optimal concession equilibrium solution based on the weight of all group decision-makers. From the viewpoint of robustness, the s∗-optimal concession equilibrium solution is the robust solution for the decisionmakers under the worst weights in Λ
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