PROPERTY ANALYSIS OF TRIPLE IMPLICATION METHOD FOR APPROXIMATE REASONING ON ATANASSOVS INTUITIONISTIC FUZZY SETS

Abstract

Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitionistic fuzzy modus ponens has both continuity and approximation property with respect to these two kinds of natural distances based on {L}ukasiewicz 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.