Research On Several Models And Properties Of Fuzzy Inference Systems

Fuzzy reasoning technology is an indispensable theoretical basis for the development of artificial intelligence.It is increasingly widely used in the fields of artificial intelligence,pattern recognition,fuzzy control and robotics.As a generalization of fuzzy sets,interval-valued fuzzy sets and intuitionistic fuzzy sets,interval-valued intuitionistic fuzzy sets(IVIFSs)are more profound in describing uncertain information and more consistent with human thinking.Therefore,they have been widely used in many fields such as intelligent prediction,multi-attribute decision making,image processing and pattern recognition.By combining fuzzy reasoning technique with IVIFSs,the algorithms of interval-valued intuitionistic fuzzy inference and its properties studied not only enriched and developed the theory of fuzzy sets,and also provided a new mathematical tool to cope with uncertainty problems.This thesis studies the inference algorithm under the interval-valued intuitionistic fuzzy environment,and the conclusions are as follows:(1)Interval-valued intuitionistic fuzzy logical operators researchIt is first given that expressions of the interval-valued intuitionistic fuzzy t-norms and t-conorms generated by the left-continuous t-norms,and their related properties are studied.Secondly,on the basis of co-residual lattices,the algebraic properties and structural properties of residual interval-valued intuitionistic fuzzy implication operators associated with left-continuous interval-valued intuitionistic fuzzy t-norms are studied.By introducing fuzzy difference operators,the unified expression of residual interval-valued intuitionistic fuzzy implications is given,the internal relations between it and ordinary fuzzy operators are revealed and the corresponding expressions of residual interval-valued intuitionistic fuzzy implication operators generated by four different left-continuous t-norms are given respectively.Finally,the algebraic properties and structural properties of residual interval-valued intuitionistic fuzzy difference operators associated with right-continuous interval-valued intuitionistic fuzzy t-conorms are studied similarly,the unified expression of that is given.Moreover,the internal relations between it and ordinary fuzzy operators are revealed,and the specific expressions of residual interval-valued intuitionistic fuzzy difference operators generated by four different left-continuous t-norms are given respectively.(2)Triple I Principle for interval valued intuitionistic fuzzy inferenceTriple Implication Principles(TIPs)of both interval-valued intuitionistic fuzzy modus ponens(IVIFMP)and fuzzy modus tollens(IVIFMT)based on residual interval-valued intuitionistic fuzzy implications are presented and analyzed.It is shown that the TIP solution of IVIFMP is recoverable and the TIP solution of IVIFMT is only weakly local recoverable.Meanwhile,α-(1,2,1)type TIP solutions of IVIFMP and IVIFMT are provided respectively.In order to improve the reductivity of the TIP solution of IVIFMT,the dual TIP for IVIFMT problem is proposed based on the residual interval-valued intuitionistic fuzzy difference operator and dual TIP solution of IVIFMT proved is reductive.Similarly,the dual TIP for FMP is given,its solution is reductive under certain condition and it is proved that dual TIP solution of FMP is equivalent TIP solution of FMP if the residual implication ’→’ satisfies contrapositive symmetry.Then,the dual TIP for FMP is extended to the IVIFSs,the expression of the dual TIP solution of the IVIFMP is also presented and the TIP solution of IVIFMP also is only weakly local recoverable.Finally,the α-(1,2,1)type dual TIP solutions of IVIFMP and IVIFMT are also given.(3)The Quintuple Implication Principles(QIP)of IVIFMP and IVIFMT and its application in medical diagnosisIt sees by an illustrated example that the TIP method sometimes makes the computed solutions for IVIFMP and IVIFMT meaningless or misleading.To avoid the above shortcoming and enhance the recovery property of the TIP solution of IVIFMT,QIP andα-QIP for IVIFMP and IVIFMT are investigated and the corresponding expressions of solutions of them are also given respectively.It is shown that the QIP solutions for IVIFMP and IVIFMT are recoverable and more sound.So it can be regarded as an effective improvement and replacement of TIP method for IVIFMP and IVIFMT.In addition,QIP solutions of IVIFMP for multiple fuzzy rules are investigated under two strategies:one is First Infer Then Aggregate(FITA)and the other is First Aggregate Then Infer(FATI),and an example for medical diagnosis to illustrate it’s application is presented and the feasibility and effectiveness of the method in medical diagnosis are verified by utilizing residual interval-valued intuitionistic fuzzy implication operators induced by four different left-continuous t-norms respectively.(4)Robustness of TIP and QIP solutions for IVIFMP and IVIFMTOn the basis of residual interval-valued intuitionistic fuzzy implications,the concept and formula of interval-valued intuitionistic double residual operator are given.A generalized interval-valued intuitionistic similarity formula is constructed through this operator and its related properties are studied.Moreover,the robustness of the TIP and QIP solutions of IVIFMP and IVIFMT are studied by using this similarity formula.