Dominance degrees for intervals and their application in multiple attribute decision-making

Abstract

Since intervals are used to express decision information in various decision-making problems, it is necessary to give a feasible method to rank them. The most commonly used method is to employ the possibility degree to compare intervals in pairs, then construct a fuzzy preference relation. Generally, the constructed fuzzy preference relation does not keep (additive, multiplicative) consistency. In order to ensure the consistency of decision information, optimization models are constructed by using the logical relationship between the elements of the consistent fuzzy preference relation and their weights. Then, by solving the optimization models, consistent fuzzy preference relations are obtained. The consistent fuzzy preference relations are the proxy of the original inconsistent fuzzy preference relation constructed by the possibility degree. However, such treatment is flawed. The inconsistent fuzzy preference relation generated from the possibility degree can't guarantee the reliability of the result while the proxy consistent fuzzy preference relation would cause bias. To solve this problem, the additive dominance degree and multiplicative dominance degree for intervals are proposed as a result of indirect comparison. The fuzzy preference relations are constructed from the dominance degrees of intervals to ensure the consistency of decision information. In the process of ranking intervals, this can avoid decision-making bias. Furthermore, a new approach to interval multiple attribute decision-making is proposed based on the dominance degrees.