Interval-valued pointwise sustaining degree fuzzy reasoning methods based on the left-continuous t-representable t-norms

In this paper, the concept of alpha(x, y)-interval-valued pointwise sustaining degree based on the left-continuous trepresentable t-norms is put forward. And then, as a general extension based on the interval-valued pointwise sustaining degree, the interval-valued alpha(x, y)-full implication triple I method model, the interval-valued alpha(x, y)-quintuple implication principle models and the interval-valued alpha(x, y)-similarity measure method models are given. Moreover, the interval-valued R-type alpha(x, y)-fuzzy reasoning solutions with triple I method, quintuple implication principle and similarity measure method are given. Some existing results are special cases of the main conclusions in this paper.