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

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.