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In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided, and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are, respectively, demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers. [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]

Build orientation determination is one of the essential process planning tasks in additive manufacturing since it has crucial effects on the part quality, post-processing, build time and cost, etc. This paper introduces a method based on fuzzy multi-attribute decision making to determine the optimal build orientation from a finite set of alternatives. The determination process includes two major steps. In the first step, attributes that are considered in the determination and heterogeneous relationships of which are firstly identified. A fuzzy decision matrix is then constructed and normalised based on the values of the identified attributes, which are quantified by a set of fuzzy numbers. In the second step, two fuzzy number aggregation operators are developed to aggregate the fuzzy information in the normalised matrix. By comparing the aggregation results, a ranking of all alternative build orientations can then be generated. Two determination examples are used to demonstrate the working process of the proposed method. Qualitative and quantitative comparisons between the proposed method and other methods are carried out to demonstrate its feasibility, effectiveness, and advantages. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]