It is of much interest to derive the priority vector from a multiplicative reciprocal preference relation (MRPR) originating from the analytic hierarchy process. There exists a conflict between the prioritization methods and the transitivity property of the entries in inconsistent MRPRs. In this paper, we attempt to weaken the conflict and enhance the effectiveness of the prioritization methods. The main contribution is to introduce the concept of indirect weak transitivity standard of MRPRs. When an MRPR possesses indirect weak transitivity about an alternative, a consistent MRPR is constructed as a proxy of inconsistent ones. When an MRPR does not possess indirect weak transitivity about any alternative, an adjustment algorithm is proposed to produce a new MRPR with indirect weak transitivity about an alternative. Numerical results are reported to show the procedure of eliciting priorities from an MRPR with indirect weak transitivity. The observation reveals that the proposed indirect weak transitivity standard could be used to assist the decision-maker in determining the outcome with more rationality.
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The authors would like to thank the anonymous reviewers for the valuable suggestions improving the quality of the paper. The work was supported by the National Natural Science Foundation of China (Nos. 71871072, 71761001, 71761002), the Guangxi Natural Science Foundation for Distinguished Young Scholars (No. 2016GXNSFFA380004), 2017 Guangxi high school innovation team and outstanding scholars plan, and the Guangxi Colleges and Universities Key Laboratory of Mathematics and its Applications.
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Lan, J., Chen, Z. & Liu, F. An indirect weak transitivity standard for inconsistent multiplicative reciprocal preference relations. Granul. Comput. (2021). https://doi.org/10.1007/s41066-021-00266-2
- Analytic hierarchy process (AHP)
- Multiplicative reciprocal preference relation (MRPR)
- Indirect weak transitivity
- Prioritization method