Multiple Criteria Decision Making Based on Weighted Archimedean Power Partitioned Bonferroni Aggregation Operators of Generalised Orthopair Membership Grades

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Abstract

In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are respectively demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers.
Original languageEnglish
JournalSoft Computing
Publication statusAccepted/In press - 1 Jan 2020

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Multiple Criteria Decision Making
Bonferroni
Aggregation Operators
Agglomeration
Decision making
Operator Mean
Operator
Fuzzy sets
T-conorms
Mathematical operators
T-norm
Demonstrations
Fuzzy Sets
Biased
Aggregation
Flexibility
Benchmark
Numerical Examples

Cite this

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title = "Multiple Criteria Decision Making Based on Weighted Archimedean Power Partitioned Bonferroni Aggregation Operators of Generalised Orthopair Membership Grades",
abstract = "In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are respectively demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers.",
keywords = "Multiple criteria decision making, Aggregation operator, Generalised orthopair fuzzy set, Bonferroni mean, Geometric Bonferroni mean, Archimedean T-norm and T-conorm",
author = "Yuchu Qin and Qunfen Qi and Paul Scott and Jane Jiang",
year = "2020",
month = "1",
day = "1",
language = "English",
journal = "Soft Computing",
issn = "1432-7643",
publisher = "Springer Verlag",

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TY - JOUR

T1 - Multiple Criteria Decision Making Based on Weighted Archimedean Power Partitioned Bonferroni Aggregation Operators of Generalised Orthopair Membership Grades

AU - Qin, Yuchu

AU - Qi, Qunfen

AU - Scott, Paul

AU - Jiang, Jane

PY - 2020/1/1

Y1 - 2020/1/1

N2 - In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are respectively demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers.

AB - In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are respectively demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers.

KW - Multiple criteria decision making

KW - Aggregation operator

KW - Generalised orthopair fuzzy set

KW - Bonferroni mean

KW - Geometric Bonferroni mean

KW - Archimedean T-norm and T-conorm

M3 - Article

JO - Soft Computing

JF - Soft Computing

SN - 1432-7643

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