Interval order relationships based on automorphisms and their application to interval optimization

Costa, Tiago Mendonça da; Chalco-Cano, Y.; Osuna-Gómez, R.; Lodwick, Weldon A.

doi:10.1016/j.ins.2022.10.020

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…Therefore, interval ordering can transform uncertain evaluation information into quantifiable interval evaluation information and improve the scientificity and rationality of decision-making results. The earliest interval ordering was a set of integer intervals, and it has been widely used in various situations, such as interval optimization [39], pattern recognition [40], and project scheduling [41]. Gonzalez-Pachon et al [42] used the interval goal programming model to aggregate preference ranking information to obtain the ranking results of the schemes.…”

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confidence: 99%

Probabilistic Interval Ordering Prioritized Averaging Operator and Its Application in Bank Investment Decision Making

Ruan,

Gong,

Chen

2023

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Probabilistic interval ordering, as a helpful tool for expressing positive and negative information, can effectively address multi-attribute decision-making (MADM) problems in reality. However, when dealing with a significant number of decision-makers and decision attributes, the priority relationships between different attributes and their relative importance are often neglected, resulting in deviations in decision outcomes. Therefore, this paper combines probability interval ordering, the prioritized aggregation (PA) operator, and the Gauss–Legendre algorithm to address the MADM problem with prioritized attributes. First, considering the significance of interval priority ordering and the distribution characteristics of attribute priority, the paper introduces probability interval ordering elements that incorporate attribute priority, and it proposes the probabilistic interval ordering prioritized averaging (PIOPA) operator. Then, the probabilistic interval ordering Gauss–Legendre prioritized averaging operator (PIOGPA) is defined based on the Gauss–Legendre algorithm, and various excellent properties of this operator are explored. This operator considers the priority relationships between attributes and their importance level, making it more capable of handling uncertainty. Finally, a new MADM method is constructed based on the PIOGPA operator using probability intervals and employs the arithmetic–geometric mean (AGM) algorithm to compute the weight of each attribute. The feasibility and soundness of the proposed method are confirmed through a numerical example and comparative analysis. The MADM method introduced in this paper assigns higher weights to higher-priority attributes to establish fixed attribute weights, and it reduces the impact of other attributes on decision-making results. It also utilizes the Gauss AGM algorithm to streamline the computational complexity and enhance the decision-making effectiveness.

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