T-norms and t-conorms are basic operators of fuzzy logics. The classifications of these operators are significant problems. Some results of the classifications of fuzzy logics operators for fuzzy sets are known. In 2013, we defined the picture fuzzy sets, and in 2015 some representable t-norms operators and t-conorms operators were defined. In this paper, we investigate the classification of representable picture t-norms and picture t-conorms operators for picture fuzzy sets.