Aiming at reduction problem in fuzzy relation decision systems， a fuzzy relation decision system with two universes and its attribute reduction concept were proposed by combining framework of the rough set theory with two universes. Firstly， the binary relations induced by conditional attributes and decision attributes were defined as fuzzy relations according to different universes， leading to introduction of the fuzzy relation decision system with two universes. Secondly， to obtain a deeper understanding of essence of reduction， the concept of approximate reduction in the fuzzy relation decision system with two universes was proposed. Thirdly， based on definition of approximate reduction， an discernibility matrix corresponding to approximate reduction was designed and constructed， and through proof of the discernibility matrix， discernibility matrix-based approximate reduction algorithms — LRFT and URFT were proposed. Finally， the feasibility and effectiveness of the proposed algorithms were further verified through experiments of comparing the classification accuracy metrics of the dataset before and after reduction.