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Two critical tasks in multi-criteria group decision making (MCGDM) are to describe criterion values and to aggregate the described information to generate a ranking of alternatives. A flexible and superior tool for the first task is q-rung orthopair fuzzy number (qROFN) and an effective tool for the second task is aggregation operator. So far, nearly thirty different aggregation operators of qROFNs have been presented. Each operator has its distinctive characteristics and can work well for specific purpose. However, there is not yet an operator which can provide desirable generality and flexibility in aggregating criterion values, dealing with the heterogeneous interrelationships among criteria, and reducing the influence of extreme criterion values. To provide such an aggregation operator, Muirhead mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are concurrently introduced into q-rung orthopair fuzzy sets, and an Archimedean power partitioned Muirhead mean operator of qROFNs and its weighted form are presented and a MCGDM method based on the weighted operator is proposed in this paper. The generalised expressions of the two operators are firstly defined. Their properties are explored and proved and their specific expressions are constructed. On the basis of the specific expressions, a method for solving the MCGDM problems based on qROFNs is then designed. Finally, the feasibility and effectiveness of the method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons., Competing Interests: The authors have declared that no competing interests exist.

In this paper, an approach for selection of materials in metal additive manufacturing based on three-way decision-making is proposed. The process of this approach is divided into three stages. First, a decision matrix for a material selection problem in metal additive manufacturing is established based on the basic components of the problem and normalised via a ratio model and a unified rule. Second, the summary loss function, conditional probability, and expected losses of each alternative material are calculated according to the weighted averaging operator, grey relational analysis, and the three-way decision theory, respectively. Third, the three-way decision-making results for the problem are generated according to the developed generation rules and the best material for the problem is selected based on the generated results. The application of the approach is illustrated via a material selection example in metal additive manufacturing. The effectiveness of the approach is demonstrated via a quantitative comparison with several existing approaches. The demonstration results suggest that the proposed approach is as effective as the existing approaches and is more flexible and advantageous in solving a material selection problem in metal additive manufacturing. [ABSTRACT FROM AUTHOR]

Multi-attribute decision-making (MADM) refers to making preference decisions via assessing a finite number of pre-specified alternatives under multiple and usually conflicting attributes. Many problems in the field of additive manufacturing (AM) are essentially MADM problems or can be converted into MADM problems. Recently, a variety of MADM methods have been applied to solve MADM problems in AM. This generates a series of interesting questions: What is the general trend of this research topic from the perspective of published articles every year? Which journals published the most articles on the research topic? Which articles on the research topic are the most cited? What MADM methods have been applied to the field of AM? What are the main strengths and weaknesses of each MADM method used? Which MADM method is the most used one in this field? What specific problems in AM have been tackled via using MADM methods? What are the main issues in existing MADM methods for AM that need to be addressed in future studies? To approach these questions, a review of MADM methods in AM is presented in this paper. Firstly, an overview of existing MADM methods in AM was carried out based on the perspective of specific MADM methods. A statistical analysis of these methods is then made from the aspects of published journal articles, applied specific methods, and solved AM problems. After that, the main issues in the application of MADM methods to AM are discussed. Finally, the research findings of this review are summarised. [ABSTRACT FROM AUTHOR]

Two key steps in multi-criteria decision making (MCDM) are to quantify the considered criteria and to fuse the quantified criterion information to sort all alternatives. One of the most recent and important tools for the first step is linguistic interval-valued intuitionistic fuzzy number (LIVIFN) and one of the most common and effective ways for the second step is aggregation operator (AO). So far, a number of AOs of LIVIFNs have been presented. Each AO can work well under certain conditions. But there is not yet an AO of LIVIFNs that can deal with the situation where the weights of the considered criteria are unknown and the criteria are in different priority levels and concurrently provide satisfying generality and flexibility in the aggregation of criterion information. To this end, a linguistic interval-valued intuitionistic fuzzy Archimedean prioritised and (LIVIFAPA) operator and a linguistic interval-valued intuitionistic fuzzy Archimedean prioritised or (LIVIFAPO) operator, which have such capabilities, are presented in this paper. The formal definitions and generalised expressions of the two AOs are firstly provided. Then their properties are explored and proved and specific expressions are established. After that, a new method for solving the LIVIFNs based MCDM problems is proposed on the basis of the presented AOs. Finally, the proposed method is illustrated via an example about additive manufacturing machine selection and is evaluated via a comparison with existing methods. The major contribution of the paper is the development of the LIVIFAPA and LIVIFAPO operators for MCDM, which can make up for the above shortcoming of the existing AOs of LIVIFNs. [ABSTRACT FROM AUTHOR]