Abstract
As a common information aggregation tool, the Hamy mean (HM) operator can consider the relationships among multiple input elements, but cannot adjust the effect of elements. In this paper, we integrate the idea of generalized a weighted average (GWA) operator into the HM operator, and reduce the influence of related elements by adjusting the value of the parameter. In addition, considering that extreme input data may lead to a deviation in the results, we further combine the power average (PA) operator with HM, and propose the power generalized Hamy mean (PGHM) operator. Then, we extend the PGHM operator to the trapezoidal fuzzy two-dimensional linguistic environment, and propose two new information aggregation tools, the trapezoidal fuzzy two-dimensional linguistic power generalized Hamy mean (TF2DLPGHM) operator and the weighted TF2DLPGHM (WTF2DLPGHM) operator. Some properties and special cases of these operators are discussed. Furthermore, based on the proposed WTF2DLPGHM operator, a new multi-attribute decision-making method is proposed for lean management evaluation of industrial residential projects. Finally, an example is given to show the specific steps, effectiveness, and superiority of the method.
Highlights
A classic multi-attribute decision-making (MADM) problem can be described as follows: given a group of possible alternatives in advance, with the help of certain information aggregation tool, evaluate these alternatives from the perspective of multiple attributes
Compared with the TF2DLBM operator, the proposed WTF2DLPGHM operator has two advantages: one is to integrate the characteristics of the power average (PA) operator, which can eliminate the influence of unreasonable data on the sorting results; the other is to model the relationship among multiple input elements by adjusting the parameter τ(see Table 9 for details)
In order to make up for this deficiency, we introduce the idea of a generalized weighted average operator into the Hamy mean operator and propose the power generalized Hamy mean (PGHM) operator
Summary
A classic multi-attribute decision-making (MADM) problem can be described as follows: given a group of possible alternatives in advance, with the help of certain information aggregation tool, evaluate these alternatives from the perspective of multiple attributes. With the progress in research, more advanced qualitative information representation models, such as uncertain linguistic variables [16], two-dimensional linguistic variables (2DLVs) [17], linguistic intuitionistic fuzzy numbers [18,19], and hesitant fuzzy linguistic term sets [20] have been proposed; they allow DMs to express evaluation information with two or more linguistic terms. Further studied a partitioned Bonferroni mean operator in the two-dimensional uncertain linguistic environment to describe the relationships between elements. Many studies focus on 2DLVs and 2DULVs, while few focus on TF2DLVs. this paper will further study TF2DLVs and propose a new MADM method in the trapezoidal fuzzy two-dimensional linguistic environment. We extend the PGHM operator to the trapezoidal fuzzy two-dimensional linguistic environment, and propose two new information aggregation tools, the trapezoidal fuzzy two-dimensional linguistic power generalized.
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