A two-dimensional approach to flexibility degree of XOR numbers with application to group decision making

Fang Liu, Ya-Ru Chen and Da-Hai Zhou

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 207, issue C, 267-287

Abstract: Uncertainty is an inevitable challenge in the process of complex decision-making. The “exclusive-or” (XOR) logic is a novel tool to model some uncertainty. An uncertain quantity always exhibits flexibility degree (FD), which has been defined for fuzzy numbers. In this paper, we extend the concept of FD to XOR numbers, report the method for computing the FD of XOR pairwise comparison matrices (XOR-PCMs) and develop a group decision making (GDM) model. First, the comparability between the linguistic term “or”, the XOR logic and pairwise comparisons of alternatives is investigated. It is pointed out the linguistic term “or” may be non-exclusive. Second, the two-dimensional method of computing the FD of XOR numbers is proposed, and some properties are studied. Third, the method for computing FD of XOR-PCMs is proposed, and the FD-driven aggregation operator is developed to aggregate individual XOR-PCMs. The more importance is offered to the decision maker (DM) with the less FD of the provided XOR-PCM. Finally, the proposed model is illustrated by carrying out a case study, where the sensitivity of attitudes and weights of DMs to the optimal solution is analyzed.

Keywords: XOR number; Flexibility degree (FD); Two-dimensional approach; XOR pairwise comparison matrix (XOR-PCM); Group decision making (GDM) (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:207:y:2023:i:c:p:267-287

DOI: 10.1016/j.matcom.2022.12.030

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