Generalized Bonferroni mean operators in multi-criteria aggregation

Beliakov, Gleb; Liu, James N. K.; Mordelová, Juliana; Rückschlossová, Tatiana; Yager, Ronald R.

doi:10.1016/j.fss.2010.04.004

Cited by 190 publications

(142 citation statements)

References 8 publications

Supporting

Mentioning

142

Contrasting

Order By: Relevance

“…Beliakov et al [37] introduced GBM, which can consider the correlations of any three aggregated arguments because the traditional BM can only determine the interrelationship between any two arguments. Nevertheless, Xia et al [38] highlighted that the GBM introduced by Beliakov et al [37] has a drawback.…”

Section: Gbmmentioning

confidence: 99%

“…Nevertheless, Xia et al [38] highlighted that the GBM introduced by Beliakov et al [37] has a drawback. Therefore, Xia et al [38] introduced a new form of GBM.…”

Section: Gbmmentioning

confidence: 99%

“…However, BM and HM can only consider the interrelationship between any two arguments. Beliakov et al [37] introduced the generalized Bonferroni mean (GBM) to overcome the drawback of BM; GBM has also been extended to IFSs [38]. However, to the best of our knowledge, no research has been conducted on GBM in the Pythagorean fuzzy environment.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

et al. 2017

View full text Add to dashboard Cite

The Pythagorean fuzzy set as an extension of the intuitionistic fuzzy set characterized by membership and nonmembership degrees has been introduced recently. Accordingly, the square sum of the membership and nonmembership degrees is a maximum of one. The Pythagorean fuzzy set has been previously applied to multiattribute group decision-making. This study develops a few aggregation operators for fusing the Pythagorean fuzzy information, and a novel approach to decision-making is introduced based on the proposed operators. First, we extend the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduce the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Second, a new generalization of the Bonferroni mean, namely, the dual generalized Bonferroni mean, is proposed by considering the shortcomings of the generalized Bonferroni mean. Furthermore, we investigate the dual generalized Bonferroni mean in the Pythagorean fuzzy sets and introduce the dual generalized Pythagorean fuzzy Bonferroni mean and dual generalized Pythagorean fuzzy Bonferroni geometric mean. Third, a novel approach to multiattribute group decision-making based on proposed operators is proposed. Lastly, a numerical instance is provided to illustrate the validity of the new approach.

show abstract

Section: Gbmmentioning

confidence: 99%

“…Nevertheless, Xia et al [38] highlighted that the GBM introduced by Beliakov et al [37] has a drawback. Therefore, Xia et al [38] introduced a new form of GBM.…”

Section: Gbmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

et al. 2017

View full text Add to dashboard Cite

show abstract

“…As mentioned above, the BM and GBM can consider the interrelationships of any two input arguments. Further, Beliakov et al [40] extended the BM to the Generalized BM (G-BM) by taking the interrelationships of any three arguments into account.…”

Section: Preliminaries 21 Uncertain Linguistic Variablesmentioning

confidence: 99%

“…Xu and Yager [39] developed some BM operators for the intuitionistic fuzzy information. Beliakov et al [40] proposed the Generalized Bonferroni Mean (G-BM). Xu and Chen [41] extended the BM to Interval-valued Intuitionistic Fuzzy (IIF) sets.…”

Section: Introductionmentioning

confidence: 99%

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

Лю

2017

Scientia Iranica

View full text Add to dashboard Cite

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.

show abstract

Generalized intuitionistic fuzzy Bonferroni means

Mao

Zhang

Zhu

2011

Int. J. Intell. Syst.

136

View full text Add to dashboard Cite

Intuitionistic fuzzy set is a widely used tool to express the membership, nonmembership, and hesitancy information of an element to a set. To aggregate the intuitionistic fuzzy information, a lot of aggregation techniques have been developed, especially, the ones which reflect the correlations of the aggregated arguments are the hot research topics, among which Bonferroni mean (BM) is an important aggregation technique. However, the classical BM ignores some aggregation information and the weight vector of the aggregated arguments. In this paper, we introduce the generalized weighted BM and the generalized intuitionistic fuzzy weighted BM, both of which focus on the group opinion. Paying more attention to the individual opinions, we further define the generalized weighted Bonferroni geometric mean and the generalized intuitionistic fuzzy weighted Bonferroni geometric mean. Various families of the existing operators can be obtained when the parameters of the developed aggregation techniques are assigned different values. Finally, we propose an approach to multicriteria decision making on the basis of the proposed aggregation techniques and an example is also given to illustrate our results. C 2011 Wiley Periodicals, Inc.

show abstract

Generalized Bonferroni mean operators in multi-criteria aggregation

Cited by 190 publications

References 8 publications

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

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

Generalized intuitionistic fuzzy Bonferroni means

Contact Info

Product

Resources

About