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Representation and Aggregation of Multi-source Information of Modern Smart Cities Based on the Intuitionistic Polygonal Fuzzy Set

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Abstract

The aggregation of multi-source information can be realized by means of the ordered representation of polygonal fuzzy sets and their linear operations, especially the ordered representation plays an important role in multi-attribute decision analysis. An intuitionistic fuzzy set is not only a generalization of traditional fuzzy set, but also can overcome some defects of fuzzy phenomena described by binary logic. In this paper, we first propose the ordered representation and its arithmetic operations of n-intuitionistic polygonal fuzzy sets (n-IPFS) based on the idea of equidistant dissection, and give a method to solve the ordered representation of n-IPFS through an example. Secondly, a mathematical linear function describing multi-source information of modern smart city is given through an ordered representation of n-IPFS, a new normalization method and calculation formula are proposed for the intuitionistic polygonal decision matrix. Then, by using n-IPFS arithmetic operations the aggregation method of weighted average operator and geometric average operator of multi-source information is given. Finally, the effectiveness of the proposed method is verified by aggregating multi-source information, and thus an intuitionistic fuzzy set and polygonal fuzzy set are unified and applied to decision-making problem of multi-source information of modern smart cities.

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Funding

This work has been supported by the National Natural Science Foundation of China (Grant No. 61374009).

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Authors and Affiliations

  1. School of Management, Tianjin Normal University, Tianjin, 300387, China

    Xiaoping Li

  2. School of Mathematics, Teacher’s College, Eastern Liaoning University, Dandong, 118003, China

    Yanhong Li

  3. School of Mathematics, Tonghua Normal University, Tonghua, Jilin, 134002, China

    Yujie Tao

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  1. Xiaoping Li
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  2. Yanhong Li
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  3. Yujie Tao
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Correspondence to Yujie Tao.

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Li, X., Li, Y. & Tao, Y. Representation and Aggregation of Multi-source Information of Modern Smart Cities Based on the Intuitionistic Polygonal Fuzzy Set. Int. J. Fuzzy Syst. 23, 967–983 (2021). https://doi.org/10.1007/s40815-020-01001-w

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  • DOI: https://doi.org/10.1007/s40815-020-01001-w

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