Abstract. This paper applies an order relation on intervals, called the lower– weighted midpoint order (LWMα ), and studies interval-valued equilibrium problems. The proposed order combines the midpoint and the lower bound of an interval through a fixed parameter α \in (0, 1), providing a comparison rule that lies strictly between the classical LU-order and the midpoint–width (MW) order. Based on this order, we introduce a new interval equilibrium problem for interval-valued bifunctions. We show that the interval-valued equilibrium problem can be equivalently reduced to a scalar equilibrium problem involving a single real-valued bifunction, which allows the direct use of standard tools from equilibrium theory and nonlinear analysis. In particular, existence results can be established under mild continuity and generaliezed convexity assumptions by means of KKM arguments.
