Multi-attribute group decision making algorithm based on (<i>p</i>, <i>q</i>)-rung interval-valued orthopair fuzzy set and weight optimization model

Mengmeng Wang; Xiangzhi Kong; Mengmeng Wang; Xiangzhi Kong

doi:10.3934/math.20231224

AIMS Mathematics

2023, Volume 8, Issue 10: 23997-24024. doi: 10.3934/math.20231224

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Research article

Multi-attribute group decision making algorithm based on (p, q)-rung interval-valued orthopair fuzzy set and weight optimization model

Mengmeng Wang ,
Xiangzhi Kong ^,

School of Science, Jiangnan University, Wuxi, Jiangsu, China

Received: 05 June 2023 Revised: 19 July 2023 Accepted: 25 July 2023 Published: 07 August 2023
MSC : 03B52, 03E72

With the aim of addressing the complexity of decision environments, uncertainty of decision information and weight determination of mutual influence between decision makers, a (p, q)-rung interval-valued orthopair fuzzy multi-attribute group decision making algorithm based on weight optimization is proposed. First, in order to improve the ability of decision makers to capture their judgment in a wider space, the concept of a (p, q)-rung interval-valued orthopair fuzzy set is proposed, and its related definition and properties are studied. Second, considering the mutual influence between decision makers and the relationship between attributes, the analytic network process (ANP) and entropy method are employed to determine the subjective and objective weights, respectively. Considering the influence of subjective and objective weights on the combination weights, the deviation degree and dispersion degree of the subjective and objective weights are taken as objective functions, and the optimal solution of the combination weights is iteratively solved by genetic algorithm. Then, based on the (p, q)-rung interval-valued orthopair fuzzy set and weight optimization model, an improved (p, q)-rung interval-valued orthopair fuzzy ELECTRE method is proposed. Finally, in order to verify the accuracy and robustness of the algorithm, the algorithm is applied to the example analysis of investment enterprise evaluation, and the results demonstrate that the algorithm has definite theoretical and application value.
- (p, q)-rung interval-valued orthopair fuzzy sets,
- multi-attribute group decision making,
- ANP,
- entropy method,
- genetic algorithm,
- ELECTRE method
Citation: Mengmeng Wang, Xiangzhi Kong. Multi-attribute group decision making algorithm based on (p, q)-rung interval-valued orthopair fuzzy set and weight optimization model[J]. AIMS Mathematics, 2023, 8(10): 23997-24024. doi: 10.3934/math.20231224

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Abstract

With the aim of addressing the complexity of decision environments, uncertainty of decision information and weight determination of mutual influence between decision makers, a (p, q)-rung interval-valued orthopair fuzzy multi-attribute group decision making algorithm based on weight optimization is proposed. First, in order to improve the ability of decision makers to capture their judgment in a wider space, the concept of a (p, q)-rung interval-valued orthopair fuzzy set is proposed, and its related definition and properties are studied. Second, considering the mutual influence between decision makers and the relationship between attributes, the analytic network process (ANP) and entropy method are employed to determine the subjective and objective weights, respectively. Considering the influence of subjective and objective weights on the combination weights, the deviation degree and dispersion degree of the subjective and objective weights are taken as objective functions, and the optimal solution of the combination weights is iteratively solved by genetic algorithm. Then, based on the (p, q)-rung interval-valued orthopair fuzzy set and weight optimization model, an improved (p, q)-rung interval-valued orthopair fuzzy ELECTRE method is proposed. Finally, in order to verify the accuracy and robustness of the algorithm, the algorithm is applied to the example analysis of investment enterprise evaluation, and the results demonstrate that the algorithm has definite theoretical and application value.

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