Research On The Unified Form And Property Of The SIS Methods For Intuitionistic Fuzzy Reasoning

Intuitionistic fuzzy sets,viewed as a generalization of fuzzy sets,introduce the concept of real membership and false membership,which could widely explain the uncertainty of things or phenomena.And similar to the research methods of fuzzy reasoning,the key point of intuitionistic fuzzy reasoning is to solve the problems of Intuitionistic Fuzzy Modus Ponens(IFMP)and Intuitionistic Fuzzy Modus Tollens(IFMT).So far,the CRI method and the triple I method of fuzzy reasoning have been successfully extended to the intuitionistic fuzzy reasoning,but compared to the CRI and the triple I methods,the SIS method for fuzzy reasoning has the advantage of unconditional reducibility.In this paper,the SIS method of fuzzy reasoning has been extended to the framework of intuitionistic fuzzy reasoning and the corresponding properties of the algorithm have been studied.The paper mainly includes three parts.Under the framework of residual intuitionistic implication operators,the unified expression for solving IFMP and IFMT is given firstly based on SIS algorithms in the present paper.Importantly,it has been proved that SIS algorithms for IFMP and IFMT are unconditionally reversible.At the same time,the solution of SIS algorithm is studied.Secondly,the continuity of the SIS method for the intuitionistic fuzzy reasoning is studied,it is proved that the SIS method for Lukasiewicz intuitionistic fuzzy reasoning are continuous with respect to two kinds of intuitionistic fuzzy natural distances.Finally,the robustness of the SIS algorithm for solving Lukasiewicz intuitionistic fuzzy reasoning on two kinds of intuitionistic fuzzy natural distance is studied.