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Multiple Criteria Decision Making with Probabilities in Interval-Valued Pythagorean Fuzzy Setting

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Abstract

Interval-valued Pythagorean fuzzy set (IVPFS), as an extension of interval-valued intuitionistic fuzzy set (IVIFS) and Pythagorean fuzzy set to deal with uncertainty, has attracted much attention since its introduction, in both theory and application aspects. The present work aims at investigating new distance measures in the IVPFSs and then employing them into multiple criteria decision-making application. To begin with, generalized interval-valued Pythagorean fuzzy weighted distance measure and generalized interval-valued Pythagorean fuzzy ordered weighted distance measure are firstly introduced in the IVPFSs. Afterward, we propose generalized probabilistic interval-valued Pythagorean fuzzy weighted averaging distance (P-GIVPFWAD) operator, generalized probabilistic interval-valued Pythagorean fuzzy order weighted averaging distance (P-GIVPFOWAD) operator and immediate generalized probabilistic interval-valued Pythagorean fuzzy ordered weighted averaging distance (IP-GIVPFOWAD) operator which are new distance measures and are able to integrate the ordered weighted averaging operator, probabilistic weight and individual distance of two interval-valued Pythagorean fuzzy numbers (IVPFNs) in the same formulation. These distance measures are very suitable to deal with the situation where the input data are represented in IVPFNs. Then we present a kind of multiple criteria decision-making method with interval-valued Pythagorean fuzzy information based on the developed distance measures. Finally, a numerical example is provided to explain the feasibility of the proposed method and the validity of the developed method is also analyzed according to the validity criterion of multiple criteria decision making.

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Acknowledgements

The authors are grateful to the anonymous reviewers for their constructive comments and based on which the presentation of this paper has been greatly improved. In the process of revision, we received great help from Dr. Jun Liu at School of Computing and Mmathematics, Ulster University, UK. He made some good suggestions for revision on some relative important issues, whilst the detailed and thorough modification for manuscript are also made. This work is supported by the National Natural Science Foundation of P.R. China (Grant No. 61673320); the Application Basic Research Plan Project of Sichuan Province (No. 2015JY0120); the Scientific Research Project of Department of Education of Sichuan Province (15TD0027, 15ZB0270); and Chinese Scholarship Council of the Ministry of Education ([2016]5112).

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Authors and Affiliations

  1. Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, 641000, Sichuan, People’s Republic of China

    Yi Liu

  2. School of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641000, Sichuan, People’s Republic of China

    Yi Liu & Ya Qin

  3. School of Computing and Mathematics, Ulster University, Jordanstown Campus, BT37 0QR, Northern Ireland, UK

    Yi Liu

  4. School of Computer Sciences, Neijiang Norm University, Neijiang, 641000, Sichuan, People’s Republic of China

    Yun Han

Authors
  1. Yi Liu
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  2. Ya Qin
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  3. Yun Han
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Contributions

YL proposed the ideas of decision making, defined the relevant distance operators, constructed the decision-making method and wrote the paper. YQ main contribution is that made the validity analysis of the decision-making method. YH checked some computing and ensured the correctness of calculation, and also checked the final reversion.

Corresponding author

Correspondence to Yun Han.

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Liu, Y., Qin, Y. & Han, Y. Multiple Criteria Decision Making with Probabilities in Interval-Valued Pythagorean Fuzzy Setting. Int. J. Fuzzy Syst. 20, 558–571 (2018). https://doi.org/10.1007/s40815-017-0349-3

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  • DOI: https://doi.org/10.1007/s40815-017-0349-3

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