In this paper, a triangle of complex characteristic temperature parameters derived from glass transition temperature Tg is constructed from two perspectives of the glass-forming ability (GFA) in cooling process and glass stability (GS) in heating process. According to two complex characteristic temperature parameters, a GFA & GS criterion is derived and modified from the perspective of balanced contribution of two temperature parameters Tg/Tl and Tx/Tg, and the three temperature parameter (Tx-Tg)/(Tl-Tg) to the evaluation criterion: GTg=Tg/Tl+Tx/Tg+(Tx-Tg)/(Tl-Tg) and GTgm=Tg/Tl+(Tx/Tg)/2+((Tx-Tg)/(Tl-Tg))^0.3. Through a large number of metallic glasses, oxide glasses and cryoprotectants, the reliability and efficiency of the criteria are verified and elaborated from GFA and GS in comparison with the current criteria based on characteristic temperatures. The results show that the new criteria have wide application in the evaluation of GFA & GS, especially the modified criterion has the best performance in the evaluation of GFA & GS of metallic glasses, and can be used as a reliable criterion.