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

Abstract

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.

An Approach for the Analysis of Energy Resource Selection Based on Attributes by Using Dombi T-Norm Based Aggregation Operators

“…We also aim to study the Dombi AOs in the context of bipolar fuzzy [43,56] structures. The performance of Dombi AOs when associated with Hamy [57] and Heronian [17] mean can also give us productive results in MADM problems. Further, such AOs-based theories can be utilized in Fintech risks [58], in the evaluation of noise reduction devices [59], and in the evaluation of green supply chains [59,60].…”

“…Liu et al [15] discussed a three-way decision support model based on IVIF information and Xie et al [16] studied the sustainability of the supply chain by prioritizing the risk factors using IVIF information. Hu et al [17] introduced some generalized Heronian means based on IVIF information for MADM problems. Jan et al [18] investigated some very basic theories of IVIF graphs and revised several definitions keeping in view their limitations.…”

Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

“…Fan et al [49] proposed two HM operators to aggregate the linguistic neutrosophic multisets and then discussed their properties. As for interval-valued fuzzy sets, Hu et al [50] presented a study of MADM based on the correlations between attributes under the interval-valued intuitionistic fuzzy environment. Narang et al [51] merged an improved generalized weighted HM operator and generalized geometric weighted HM operators with the traditional combined compromise solution (CoCoSo) method to present a new decision-making model.…”