Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

Considering the characteristics such as fuzziness and greyness in real decision-making, the interval grey triangular fuzzy number is easy to express fuzzy and grey information simultaneously. And the partition Bonferroni mean (PBM) operator has the ability to calculate the interrelationship among the attributes. In this study, we combine the PBM operator into the interval grey triangular fuzzy numbers to increase the applicable scope of PBM operators. First of all, we introduced the definition, properties, expectation, and distance of the interval grey triangular fuzzy numbers, and then we proposed the interval grey triangular fuzzy numbers partitioned Bonferroni mean (IGTFPBM) and the interval grey triangular fuzzy numbers weighted partitioned Bonferroni mean (IGTFWPBM), the adjusting of parameters in the operator can bring symmetry effect to the evaluation results. After that, a novel method based on IGTFWPBM is developed for solving the grey fuzzy multiple attribute group decision-making (GFMAGDM) problems. Finally, we give an example to expound the practicability and superiority of this method.

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Multiple Attribute Group Decision-Making Methods Based on Trapezoidal Fuzzy Two-Dimensional Linguistic Partitioned Bonferroni Mean Aggregation Operators

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph15020194 ◽

2018 ◽

Vol 15 (2) ◽

pp. 194 ◽

Cited By ~ 11

Author(s):

Kedong Yin ◽

Benshuo Yang ◽

Xuemei Li

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Two Dimensional ◽

Bonferroni Mean ◽

Multiple Attribute

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GLDS method for multiple attribute group decision making under 2-Tuple linguistic neutrosophic environment

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202748 ◽

2021 ◽

pp. 1-16

Author(s):

Jianping Fan ◽

Feng Yan ◽

Meiqin Wu

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Distance Measure ◽

Group Decision ◽

Weighted Average ◽

Aggregation Operator ◽

Low Carbon ◽

Multiple Attribute ◽

Power Aggregation Operator ◽

Linguistic Neutrosophic Numbers

In this article, the gained and lost dominance score (GLDS) method is extended into the 2-tuple linguistic neutrosophic environment, which also combined the power aggregation operator with the evaluation information to deal with the multi-attribute group decision-making problem. Since the power aggregation operator can eliminate the effects of extreme evaluating data from some experts with prejudice, this paper further proposes the 2-tuple linguistic neutrosophic numbers power-weighted average operator and 2-tuple linguistic neutrosophic numbers power-weighted geometric operator to aggregate the decision makers’ evaluation. Moreover, a model based on the score function and distance measure of 2-tuple linguistic neutrosophic numbers (2TLNNs) is developed to get the criteria weights. Combing the GLDS method with 2-tuple linguistic neutrosophic numbers and developing a 2TLNN-GLDS method for multiple attribute group decision making, it can express complex fuzzy information more conveniently in a qualitative environment and also consider the dominance relations between alternatives which can get more effective results in real decision-making problems. Finally, an applicable example of selecting the optimal low-carbon logistics park site is given. The comparing results show that the proposed method outperforms the other existing methods, as it can get more reasonable results than others and it is more convenient and effective to express uncertain information in solving realistic decision-making problems.

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

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488515500129 ◽

2015 ◽

Vol 23 (02) ◽

pp. 285-315 ◽

Cited By ~ 18

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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