In the article we present in the Mizar system ,  the catalogue of triangular norms and conorms, used especially in the theory of fuzzy sets . The name triangular emphasizes the fact that in the framework of probabilistic metric spaces they generalize triangle inequality .
After defining corresponding Mizar mode using four attributes, we introduced the following t-norms:
minimum t-norm minnorm (Def. 6),
product t-norm prodnorm (Def. 8),
Łukasiewicz t-norm Lukasiewicz_norm (Def. 10),
drastic t-norm drastic_norm (Def. 11),
nilpotent minimum nilmin_norm (Def. 12),
Hamacher product Hamacher_norm (Def. 13),
and corresponding t-conorms:
maximum t-conorm maxnorm (Def. 7),
probabilistic sum probsum_conorm (Def. 9),
bounded sum BoundedSum_conorm (Def. 19),
drastic t-conorm drastic_conorm (Def. 14),
nilpotent maximum nilmax_conorm (Def. 18),
Hamacher t-conorm Hamacher_conorm (Def. 17).
Their basic properties and duality are shown; we also proved the predicate of the ordering of norms , . It was proven formally that drastic-norm is the pointwise smallest t-norm and minnorm is the pointwise largest t-norm (maxnorm is the pointwise smallest t-conorm and drastic-conorm is the pointwise largest t-conorm).
This work is a continuation of the development of fuzzy sets in Mizar  started in  and ; it could be used to give a variety of more general operations on fuzzy sets. Our formalization is much closer to the set theory used within the Mizar Mathematical Library than the development of rough sets , the approach which was chosen allows however for merging both theories , .
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