Aggregation of Heterogeneously Related Information with Extended Geometric Bonferroni Mean and Its Application in Group Decision Making

2017 ◽  
Vol 33 (3) ◽  
pp. 487-513 ◽  
Author(s):  
Bapi Dutta ◽  
Felix T. S. Chan ◽  
Debashree Guha ◽  
Ben Niu ◽  
J. H. Ruan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Bonferroni Mean ◽  
Related Information ◽  
Geometric Bonferroni Mean

scholarly journals A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1489
Author(s):  
Shahzad Faizi ◽  
Wojciech Sałabun ◽  
Nisbha Shaheen ◽  
Atiq ur Rehman ◽  
Jarosław Wątróbski
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Geometric Bonferroni Mean ◽  
The Individual ◽  
Heronian Mean

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

scholarly journals Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Mingwei Lin ◽  
Jiuhan Wei ◽  
Zeshui Xu ◽  
Riqing Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Bonferroni Mean ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Special Cases ◽  
Geometric Bonferroni Mean ◽  
Decision Making Model ◽  
Pythagorean Fuzzy Numbers

The partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometric Bonferroni mean (PGBM) operator to the linguistic Pythagorean fuzzy sets (LPFSs) and use them to develop a novel multiattribute group decision-making model under the linguistic Pythagorean fuzzy environment. We first define some novel operational laws for LPFNs, which take into consideration the interactions between the membership degree (MD) and nonmembership degree (NMD) from two different LPFNs. Based on these novel operational laws, we put forward the interaction PBM (LPFIPBM) operator, the weighted interaction PBM (LPFWIPBM) operator, the interaction PGBM (LPFIPGBM) operator, and the weighted interaction PGBM (LPFWIPGBM) operator. Then, we study some properties of these proposed operators and discuss their special cases. Based on the proposed LPFWIPBM and LPFWIPGBM operators, a novel multiattribute group decision-making model is developed to process the linguistic Pythagorean fuzzy information. Finally, some illustrative examples are introduced to compare our proposed methods with the existing ones.

Intuitionistic Fuzzy Power Geometric Bonferroni Means and Their Application to Multiple Attribute Group Decision Making

2015 ◽  
Vol 23 (02) ◽  
pp. 285-315 ◽  
Author(s):  
Yingdong He ◽  
Zhen He ◽  
Chao Jin ◽  
Huayou Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Bonferroni Mean ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Geometric Average ◽  
Multiple Attribute ◽  
Special Cases ◽  
Geometric Bonferroni Mean

The geometric Bonferroni mean (GBM) can capture the interrelationships between input arguments, which is an important generalization of Bonferroni mean (BM). In this paper, we combine geometric Bonferroni mean (GBM) with the power geometric average (PGA) operator under intuitionistic fuzzy environment and present the intuitionistic fuzzy geometric power Bonferroni mean (IFPGBM) and the weighted intuitionistic fuzzy power geometric Bonferroni mean (WIFPGBM). The desirable properties of these new extensions of Bonferroni mean and their special cases are investigated. We list the detailed steps of multiple attribute group decision making with the developed IFPGBM or WIFPGBM, and give a comparison of the new extensions of Bonferroni mean by this paper with the corresponding existing intuitionistic fuzzy Bonferroni means. Finally, examples are illustrated to show the validity and feasibility of the new approaches.

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