An improvement method for selecting the best alternative in Decision Making

Multiple attributes group decision making problems aim to find the best alternative for the experts from a solution set of alternatives. Because the attribute value and decision-makers evaluation with respect to the alternatives are usually vague and imprecise, fuzzy multiple attributes group decision making have been widely investigated, in which, ordering fuzzy evaluation results in fuzzy decision making is an important method to find the best alternative for the experts, difference fuzzy expressions for evaluation in fuzzy decision making problems correspond with difference aggregation operator and ranking method. In this paper, we analyze some algebraic properties of a kind of ranking method in fuzzy multiple attributes group decision-making, and prove that the ranking method is pre-ordering, its’drawback in fuzzy decision making is no unique alternative to be best alternative. Then, we provide an equivalence relation on fuzzy evaluation values based on the ranking method, and propose a linearly ordering on equivalence classes of fuzzy evaluation values. Based on the linearly ordering, we propose an improve method to handle fuzzy multiple attributes group decision-making when its ordering is pre-ordering. Some numerical examples illustrate that our method can be used to improve the best alternative of fuzzy decision making when its ordering is pre-ordering.