Property Analysis Of The Triple ? Method For Lukasiewicz Intuitionistic Fuzzy Reasoning Based On Several Distances

Intuitionistic fuzzy set is the generalization of the concept of fuzzy set,because it uses the membership and non-membership degrees to describe the ambiguity of things,so the three states of “support”,“neutral” and “objection” in fuzzy phenomenon can be expressed at the same time and therefore it is widely used in many fields such as pattern recognition,machine learning and image processing and so on.As the generalization of fuzzy reasoning,the core problem of intuitionistic fuzzy reasoning is to solve the problems of intuitionistic fuzzy modus ponens(IFMP in brief)and intuitionistic fuzzy modus tollens(IFMT in brief).Whether some inference algorithm can be applied in practice depends on the quality of the reasoning algorithm.In this paper,the related properties of the triple ? algorithm for intuitionistic fuzzy reasoning are studied,the main contents in this paper are as follows:(1)In the case of the finite universe,the Hamming distance between intuitionistic fuzzy sets is defined by the Hamming distance of the fuzzy sets.As to the infinite universe,two kinds of natural distances between intuitionistic fuzzy sets are defined by the natural distance between fuzzy sets,therefore the intuitionistic fuzzy metric space both on the finite and infinite domains are established.(2)The continuity and approximation of the triple ? method for Lukasiewicz intuitionistic fuzzy reasoning are studied in intuitionistic fuzzy metric space.(3)The robustness of the triple ? method for Lukasiewicz intuitionistic fuzzy reasoning is studied in intuitionistic fuzzy metric space.