2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

Abstract

KEYWORDS Aggregation operators;Multiple-attribute decision making; Bonferroni mean; 2-dimensional uncertain linguistic variables.Abstract. 2-Dimensional Uncertain Linguistic Variables (2DULVs) are powerful tools to express the fuzzy or uncertain information, and the weighted Bonferroni mean can not only take the attribute importance into account, but also capture the interrelationship between the attributes. However, the traditional Bonferroni mean can only deal with the crisp numbers. In this paper, Bonferroni mean was extended to process the 2DULVs. Firstly, we proposed the Normalized Weighted Geometric Bonferroni Mean (NWGBM) operator and the Generalized Normalized Weighted Geometric Bonferroni Mean (GNWGBM) operator, which had the characteristic of reducibility and considered the interrelationships between two attributes. Then, we introduced the computation rules, characteristics, the expected value, and comparison method of the 2DULVs. Further, we developed the 2-Dimensional Uncertain Linguistic Normalized Weighted Geometric Bonferroni Mean (2DULNWGBM) and the 2-Dimensional Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean (2DULGNWGBM), and explored some properties and discussed some special cases of them. Finally, we developed a new decision making method based on these operators. An example is given to compare the method with the existing methods.

The Trapezoidal Fuzzy Two-Dimensional Linguistic Power Generalized Hamy Mean Operator and Its Application in Multi-Attribute Decision-Making

“…Yin et al [30] further studied a partitioned Bonferroni mean operator in the two-dimensional uncertain linguistic environment to describe the relationships between elements. Liu [31] proposed two-dimensional uncertain linguistic generalized normalized weighted geometric Bonferroni mean.…”

Schur m-power convexity of generalized geometric Bonferroni mean involving three parameters

“…It is well known that the Bonferroni mean and geometric Bonferroni mean have important applications in multicriteria decision-making problems and have led to many meaningful results. See, for example, Xu and Yager [5], Xia, Xu and Zhu [3,6], Tian et al [7], Dutta et al [8], Liang et al [9], and Liu [10].…”

Archives of Control Sciences

“…To address such type of issues, Bonferroni mean (BM) operator [48] and geometric Bonferroni mean (GBM) operator [49], has prominent characteristics to capture the interrelationship among the multi-input arguments. In the past few years, the BM and GBM have received more and more attentions, many important results both in theory and application are developed [50][51][52][53][54][55][56][57][58]. Therefore, by considering the advantages of the DHPFSs and the BM, GBM operator during the information fusion process, the present study enhanced these works in that direction.…”