Multi-Attribute Decision-Making Method Based on Complex Interval-Valued q-Rung Orthopair Linguistic Heronian Mean Operators and Their Application

In this manuscript, we firstly proposed a novel concept of complex interval-valued q-rung orthopair linguistic (CIVq-ROL) information by integrating the concepts of complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) information and linguistic set (LS), and it is more generalized than most existing sets, and it is very feasible and valuable for depicting awkward and unreliable information in a difficult situation. Further, we developed some new operational laws of the CIVq-ROF information based on algebraic t-norm and t-conorm. It is also clear that it is a very challenging task to fuse the collection of data into a singleton set in information fusion and decision making, and the Heronian mean (HM) operator is an important aggregation operator, which can not only achieve the aggregation function from the collection of data into a singleton one, but also consider the relationship between any two data. Therefore, based on the CIVq-ROL information and HM operator, we proposed the CIVq-ROL Heronian mean (CIVq-ROLHM), CIVq-ROL weighted HM (CIVq-ROLWHM), CIVq-ROL geometric HM (CIVq-ROLGHM), and CIVq-ROL weighted geometric HM (CIVq-ROLWGHM) operators, and then, the various desirable properties and specific cases of them are also investigated. Furthermore, we developed a multi-attribute decision-making (MADM) procedure for evaluating the finest business in the country from the collection of four different types of electronics-related businesses based on the proposed operators. Finally, various examples are given to show the application of the invented techniques, and a comparative analysis is carried out for the parameters to show the advantages of the proposed approaches.