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On the normalization of a priority vector associated with a reciprocal relation

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  • Michele Fedrizzi
  • Matteo Brunelli

Abstract

In this paper we show that the widely used normalization constraint SUM(i=1,n) wi = 1 does not apply to the priority vectors associated with reciprocal relations, whenever additive transitivity is involved. We show that misleading applications of this type of normalization may lead to unsatisfactory results and we give some examples from the literature. Then, we propose an alternative normalization procedure which is compatible with additive transitivity and leads to better results.

Suggested Citation

  • Michele Fedrizzi & Matteo Brunelli, 2009. "On the normalization of a priority vector associated with a reciprocal relation," DISA Working Papers 0905, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2009.
    • Handle: RePEc:trt:disawp:0905
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    References listed on IDEAS

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    1. B. Baets & H. Meyer & B. Schuymer, 2006. "Cyclic Evaluation of Transitivity of Reciprocal Relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 217-238, April.
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    Cited by:

    1. Huayou Chen & Ligang Zhou, 2012. "A Relative Entropy Approach to Group Decision Making with Interval Reciprocal Relations Based on COWA Operator," Group Decision and Negotiation, Springer, vol. 21(4), pages 585-599, July.
    2. Yulan Wang & Huayou Chen & Ligang Zhou, 2013. "Logarithm Compatibility of Interval Multiplicative Preference Relations with an Application to Determining the Optimal Weights of Experts in the Group Decision Making," Group Decision and Negotiation, Springer, vol. 22(4), pages 759-772, July.

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