Research On Fuzzy Reasoning Algorithms Based On Interval-valued T-representable T-norm

As extensions of fuzzy sets,interval-valued fuzzy sets and intuitionistic fuzzy sets can better deal with fuzziness and uncertainty of information.Based on this advantage,this paper mainly studies fuzzy reasoning similarity algorithm and SIS algorithm based on interval-valued trepresentable t-norm.The relationship between the proposed algorithm and the similarity algorithm and SIS inference algorithm based on intuitionistic t-representable t-norm is further studied.The main research contents and innovations are as follows:(1)Fuzzy reasoning similarity algorithm based on the left-continuous interval-valued t-representable t-norm is given,the related properties of the algorithm are discussed,and the generalized interval-valued fuzzy reasoning similarity algorithm is further studied.(2)On the level of the left-continuous interval-valued t-representable t-norm,the SIS algorithm with unconditional reduction is given in view of the feature that the whole interval-valued fuzzy reasoning full implication triple I algorithm conditional reduction.The applicability of the algorithm is expanded,and the related properties of the algorithm are discussed.A generalized fuzzy reasoning SIS algorithm based on interval-valued trepresentable t-norm is presented.(3)The residual lattices composed of left-continuous interval-valued trepresentable t-norm and induced residual implication and left-continuous intuitionistic t-representable t-norm and induced residual implication are given respectively,It is proved that the two residual lattices are isomorphic,it is further proved that the similarity algorithm solution(SIS algorithm solution)in interval-valued fuzzy environment and intuitionistic fuzzy environment is one to one correspondence.From the point of isomorphism,it is proved that interval-valued fuzzy reasoning algorithm and intuitionistic fuzzy reasoning algorithm are essentially the same.