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A Multi-Criteria Three-Way Decision Making Method in a Picture Fuzzy Probabilistic Decision System

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Abstract

Three-way decision is a decision-making method based on human cognitive process, and its basic idea is to divide a universal set into three pair-wise disjoint regions to cognitive information processing. As the complexity of decision-making environment, cognitive information about alternatives given by decision-makers is uncertain and inconsistent. Picture fuzzy point operator (PFPO) is an effective tool to handle this information. In order to obtain more reasonable and effective decision results, this paper proposes three-way decision models and develops a multi-attribute three-way decision method. Then, we use the proposed method to solve a project investment problem. We define new operators on picture fuzzy numbers by a monotonically increasing binary function and a monotonically decreasing unary function. Then, we build three-way decision models based on PFPO and these new operators. Further, we fully consider the relationship between attributes and the classification of alternatives, and present a multi-criteria three-way decision method. In addition, we compare the proposed method with the existing methods by a project investment problem. We show that PFPO can handle inconsistent and changing cognitive information more accurately through an example. In a project investment problem, the decision results obtained by using the proposed method are the same as those obtained by the existing methods, which shows that the method is effective. By the analysis and comparison with these methods, it is proved that the proposed method is very suitable for dealing with multi-attribute decision-making problem with changing picture fuzzy information and consistent with human cognition.

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Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11771263, 61773019) and the Fundamental Research Funds For the Central Universities (Nos. 2018TS059, GK201503013).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, PR China

    Ruirui Zhao, Lina Ma & Shenggang Li

  2. Department of Computer Science, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada

    Lina Ma

  3. Department of Information and Computing Science, China Jiliang University, Hangzhou, 310018, PR China

    Minxia Luo

Authors
  1. Ruirui Zhao
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  2. Lina Ma
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Correspondence to Lina Ma.

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Zhao, R., Ma, L., Li, S. et al. A Multi-Criteria Three-Way Decision Making Method in a Picture Fuzzy Probabilistic Decision System. Cogn Comput 14, 1924–1941 (2022). https://doi.org/10.1007/s12559-021-09900-2

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