An optimization method to estimate the missing elements for the incomplete fuzzy reciprocal preference relation

In this paper, we investigate the missing elements estimation issue of incomplete fuzzy reciprocal preference relation. Based on the multiplicative consistency property, a constrained nonlinear optimization model, which aims for making the induced matrix close to zero, is proposed to estimate the missing elements in the incomplete fuzzy reciprocal preference relation. The numerical example is illustrated to show the correctness and effectiveness of the proposed method. Our method not only estimates the missing elements accurately but also improves the multiplicative consistency, which makes the decision result derived from the incomplete fuzzy reciprocal preference relation could be scientific and effective.

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