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Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees

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Abstract

This paper develops a Pythagorean fuzzy (PF) mathematical programming method to solve multi-attribute group decision-making problems under PF environments. The main work is summarized as four aspects: (1) Considering the fuzziness and hesitancy in pairwise comparisons of alternatives, we firstly introduce PF sets to depict the fuzzy truth degrees of alternative comparisons. (2) According to the information entropy, individual subjective attribute weight vectors of decision makers (DMs) are calculated and integrated into a collective one by a cross-entropy optimization model. Then DMs’ weights are objectively derived from the collective subjective attribute weight vector. (3) PF group consistency and inconsistency indices are defined based on PF-positive ideal solution (PFPIS) and PF-negative ideal solution (PFNIS), respectively. To determine comprehensive attribute weights, a biobjective PF mathematical programming model is constructed through minimizing two inconsistency indices based on PFPIS and PFNIS simultaneously. A linear programming method is technically developed to solve this model. (4) Using the cross-entropy again, collective relative closeness degrees of alternatives are explicitly derived to rank the alternatives. Finally, an example of green supplier selection is analyzed to verify the effectiveness of the proposed method.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 61263018, 11461030 and 71661010), Young scientists Training object of Jiangxi province (No. 20151442040081), the Natural Science Foundation of Jiangxi Province of China (No. 20161BAB201028), “Thirteen five” Programming Project of Jiangxi province Social Science (2016) (Nos. 16GL08 and 16GL19), the Science and Technology Project of Jiangxi province educational department of China (Nos. GJJ150463 and GJJ150466), and the Jiangxi Provincial Humanities and Social Sciences Research Project (No. JC162020).

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Authors and Affiliations

  1. College of Information Technology, Jiangxi University of Finance and Economics, Nanchang, 330013, China

    Shu-Ping Wan & Zhen Jin

  2. School of Science, Nanchang Institute of Technology, Nanchang, 330099, China

    Zhen Jin

  3. School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China

    Jiu-Ying Dong

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  1. Shu-Ping Wan
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  2. Zhen Jin
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  3. Jiu-Ying Dong
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Correspondence to Zhen Jin.

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Wan, SP., Jin, Z. & Dong, JY. Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees. Knowl Inf Syst 55, 437–466 (2018). https://doi.org/10.1007/s10115-017-1085-6

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