Abstract :
Firstly, two kinds of natural distances between intuitionistic fuzzy
sets are generated by the classical natural distance between fuzzy sets un-
der a unied framework of residual intuitionistic implication operators. Sec-
ondly, the continuity and approximation property of a method for solving
intuitionistic fuzzy reasoning are dened. It is proved that the triple impli-
cation method for intuitionistic fuzzy modus ponens has both continuity and
approximation property with respect to these two kinds of natural distances
based on Lukasiewicz implication, meanwhile the triple implication method
for intuitionistic fuzzy modus tollens possesses unconditional continuity and
conditional approximation property. Finally, some robustness results about
the triple implication method of intuitionistic fuzzy reasoning are given.
Keywords :
Robustness , Intuitionistic fuzzy reasoning , Triple implication method , Approximation property , Continuity
