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On weak consistency of interval additive reciprocal matrices

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Abstract

When one estimates the importance of alternatives under rational choice, it is natural to avoid self-contradiction from the viewpoint of psychology. Due to the vagueness encountered in a manner analogous to human thought, decision makers always exhibit limited rationality. The judgements could be expressed as interval-valued comparison matrices within the framework of analytic hierarchy process. In this study, for additive reciprocal matrices (ARMs), three axiomatic properties are proposed to characterize the additive consistency and the multiplicative consistency under fully rational behavior. For interval additive reciprocal matrices (IARMs), the concept of weak consistency is used to capture the limited rationality. By weakening some axiomatic properties of consistent ARMs, the reasonable properties of IARMs with weak consistency are presented. Two kinds of IARMs satisfying the properties of weak consistency are analyzed and some comparisons are offered. It is observed that the consistency of ARMs can be defined exactly and characterized by using the axiomatic properties. The properties of characterizing the consistency degree of IARMs should be captured by weakening the axiomatic ones of consistent ARMs. The proposed approach visualizes the development process starting from cardinal consistency of numeric-valued preference relations to weak consistency of interval-valued comparison matrices.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Nos. 71571054, 71871072), 2017 Guangxi high school innovation team and outstanding scholars plan, the Guangxi Natural Science Foundation for Distinguished Young Scholars (No. 2016GXNSFFA380004), and the Innovation Project of Guangxi Graduate Education (No. YCSW2019045).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, Guangxi, China

    Fang Liu, Jia-Wei Zhang, Qin Yu & Ya-Nan Peng

  2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6R 2G7, Canada

    Witold Pedrycz

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Witold Pedrycz

  4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Witold Pedrycz

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  1. Fang Liu
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  2. Jia-Wei Zhang
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  3. Qin Yu
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  4. Ya-Nan Peng
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  5. Witold Pedrycz
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Correspondence to Fang Liu.

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Liu, F., Zhang, JW., Yu, Q. et al. On weak consistency of interval additive reciprocal matrices. Fuzzy Optim Decis Making 19, 153–175 (2020). https://doi.org/10.1007/s10700-020-09314-z

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