Some Issues on Multiplicative Consistency of Interval Reciprocal Relations

Consistency plays an important part in decision making with interval reciprocal relation also called interval fuzzy preference relation. In this paper, we give the definition of perfect multiplicative consistent interval reciprocal relation and discuss its properties. A method is proposed to construct a set of multiplicative consistent reciprocal relations from a perfect consistent interval reciprocal relation. Then we develop methods to get the perfect multiplicative consistent interval reciprocal relation from the inconsistent one and estimate the missing values from an incomplete interval reciprocal relation. Finally, a group decision-making method is proposed based on perfect multiplicative consistent interval reciprocal relations. Some examples are also given to compare the proposed methods with the existing ones.

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