Integral similarity degree and distance in S-implication fuzzy logic

It was different from the usual similarity degree is defined based on truth degree, this paper put forward the integral similarity degree by use of S- implication operator in S-implication fuzzy logic system, thus the relevant calculation and proof became concise. Then the paper discussed the properties of the integral similarity degree, gave the pseudo-distance corresponding to the integral similarity degree. Finally, the continuity of the logical operators about limit operation in pseudo-metric space was proved.