<p>The picture fuzzy set, as a direct extension of the intuitionistic fuzzy set, characterizes information through the degree of positive membership, the degree of neutral membership and the degree of negative membership. Although several distances between picture fuzzy sets have been proposed in previous papers, some of these distances fail to exhibit satisfactory differentiation capabilities when dealing with highly similar picture fuzzy sets, resulting in outcomes that do not align with the actual situation. In this paper, we introduce a novel distance between picture fuzzy sets based on a matrix norm and a binary monotone function. Furthermore, we use the proposed distance to solve the problems of multiple attribute decision-making and pattern recognition. The experimental results demonstrate that the proposed distance cannot only address some issues that some existing distance fail to handle effectively, but also possesses high degrees of confidence.</p>