Some New Results on Compromise Solutions for Group Decision Problems

Abstract

We report some new results on compromise solutions studied by Yu [Yu, P. L. 1973. A class of decisions for group decision problems. Management Sci. 19 (8, April) 936-946]. The following article focuses on the relation between the compromise solution and its parameter. In particular, we show that, under some nice conditions, the compromise solution is a continuous function of its parameter. A fundamental monotonicity result (Theorem 3.1) concerning compromise solutions is derived. The result enables us to generate the bounds of all compromise solutions. When n = 2, two monotonicity results are derived. These yield a good interpretation of the parameter p. When p is small the "group utility" is emphasized; and when p increases the individual regrets receive more weight. Finally we construct an example to illustrate that the monotonicity results for n = 2 are almost impossible to be generated for n > 2.

Planificación multicriterio de explotaciones agrarias en áreas tropicales protegidas. El caso de la zona protectora Guanare-Masparro (Venezuela)

“…Para problemas con dos objetivos, las soluciones de las demás métricas están contenidas en el subconjunto acotados por L 1 y L ∞ (Yu, 1973). Para el caso de más de dos objetivos pueden existir métricas diferentes de p = 1 y p = ∞, que no están contenidas en el intervalo delimitado por L 1 y L ∞ (Freimer y Yu, 1976). Sin embargo, la literatura reporta esta situación como poco probable en la práctica.…”

Economic Development Prospects of Forest‐Dependent Communities: Analyzing Trade‐offs Using a Compromise‐Fuzzy Programming Framework

“…For the extreme riskneutral compromise solution, all objectives and regrets (deviations of realized objectives from targets) are treated equally and simultaneously; at the risk-averse extreme, the compromise solution emphasizes only the criterion with the largest regret by minimizing that regret (Freimer and Yu 1976). The Pareto optimal risk neutral and risk averse solutions are used to construct fuzzy membership functions that are then used in fuzzy programming to find the middle ground strategy and, importantly, the degree to which the decision maker might be satisfied with this final compromise.…”

Group decision and negotiation support — A methodological survey

“…[80,81,22] to resolve differences between group members. In other GDSS developments, special algorithms were constructed to provide group solutions or identify possible areas of bargaining [7,57].…”