Multiple-Attribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Generalized Weighted Heronian Mean

Due to the complexity and uncertainty of objective things, interval-valued intuitionistic fuzzy (I-VIF) numbers are often used to describe the attribute values in multiple-attribute decision making (MADM). Sometimes, there are correlations between the attributes. In order to make the decision-making result more objective and reasonable, it is often necessary to take the correlation factors into account. Therefore, the study of MADM based on the correlations between attributes in the I-VIF environment has important theoretical and practical significance. Thus, in this paper, we propose new operators (AOs) for I-VIF information that are able to reflect the completeness of the information, attribute relevance, and the risk preference of decision makers (DMs). Firstly, we propose some new AOs for I-VIF information, including I-VIF generalized Heronian mean (I-VIFGHM), I-VIF generalized weighted Heronian mean (I-VIFGWHM), and I-VIF three-parameter generalized weighted Heronian mean (I-VIFTPGWHM). The properties of the obtained operators, including their idempotency, monotonicity, and boundedness are studied. Furthermore, an MADM method based on the I-VIFGWHM operator is provided. Finally, an example is provided to explain the rationality and feasibility of the proposed method