Multi-criteria decision making with Hamacher aggregation operators based on multi-polar fuzzy Z-numbers

Abstract

Multi-polar fuzzy sets are crucial for capturing and representing diverse opinions or conflicting criteria in decision-making processes with greater flexibility and precision. While, Z-numbers are important for effectively modeling uncertainty by incorporating both the reliability of information and its degree of fuzziness, enhancing decision-making in uncertain environments. To date, no model in the literature exhibits the properties of multi-polar fuzzy sets and Z-numbers. In this article, we introduce a new concept of multi-polar fuzzy Z-number and Hamacher operations for multi-polar fuzzy Z-numbers. Based on the Hamacher operations, we propose aggregation operators for multi-polar fuzzy Z-numbers, namely, multi-polar fuzzy Z-number Hamacher weighted averaging operator, multi-polar fuzzy Z-number Hamacher ordered weighted averaging operator, multi-polar fuzzy Z-number Hamacher weighted geometric operator and multi-polar fuzzy Z-number Hamacher ordered weighted geometric operator. Additionally, we develop a decision-making model based on the proposed Hamacher aggregation operators. Further, we apply the proposed technique to a couple of case studies to check the validity and authenticity of the proposed methodology. Finally, we compare the outcomes of the study with several existing techniques to assess the accuracy of the proposed model.