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Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making

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Abstract

Fuzzy set, intuitionistic fuzzy set, hesitant fuzzy set can be regarded as a special case of dual hesitant fuzzy set. Therefore, dual hesitant fuzzy set is a more comprehensive set. Further, Archimedean t-norm and t-conorm provides generalized operational rules for dual hesitant fuzzy set. And geometric Heronian mean have advantages when considering the interrelationship of aggregation arguments. Thus, it is necessary to extend the geometric Heronian mean operator to the dual hesitant fuzzy environment based on Archimedean t-norm and t-conorm. Comprehensive above, in this paper, the dual hesitant fuzzy geometric Heronian mean operator and dual hesitant fuzzy geometric weighted Heronian mean operator based on Archimedean t-norm and t-conorm are developed. Their properties and special case are investigated. Moreover, a multiple attribute decision making method is proposed. The effectiveness of our method and the influence of parameters on multiple attribute decision making are studied by an example. The superiority of our method is illustrated by comparing with other existing methods.

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Acknowledgements

This study was funded by National Natural Science Foundation Project of China (Grant Number 11701089), Natural Science Foundation of Fujian Province, China (Grant Number 2018J01422), Scientific Research Project of Minnan Normal University (Grant Number MK201715), Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, People’s Republic of China

    Jiongmei Mo & Han-Liang Huang

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  1. Jiongmei Mo
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  2. Han-Liang Huang
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Correspondence to Han-Liang Huang.

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Mo, J., Huang, HL. Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making. Soft Comput 24, 14721–14733 (2020). https://doi.org/10.1007/s00500-020-04819-6

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