Research On Metric Of Interval-valued Fuzzy Sets

Distance and similarity are important tools in the process of fuzzy reasoning and pattern recognition,and interval-valued fuzzy sets and intuitionistic fuzzy sets are more advantageous than fuzzy sets in the fuzziness and uncertainty of processing information.Therefore,distance and similarity of interval-valued fuzzy sets are studied.The main contents and innovation points of this paper are as follows:In the second chapter,we propose a new distance metric between intervalvalued fuzzy sets,and construct four kinds of interval-valued fuzzy metric spaces based on four spacial interval-valued residuated implication operations.Moreover,we analyze in detail space structures of four intervalvalued fuzzy metric spaces.It is prove that interval-valued ?ukasiewicz metric space and interval-valued Goguen metric space are more suitable for fuzzy reasoning.In the third chapter,based on left-continuous t-norms and its corresponding residuated implications,distance metric between interval-valued fuzzy sets is given.And we discuss the robustness of interval-valued fuzzy reasoning triple I algorithms.It shows that interval-valued fuzzy reasoning algorithms based on G?del implication,?ukasiewicz implication and Goguen implication are robust.In the forth chapter,we propose a new similarity between intuitionistic fuzzy sets for drawbacks of Nguyen's similarity.The proposed similarity is applied to the pattern recognition problem,it shows that the proposed similarity on dealing with pattern recognition problem than some existing similarity is more reasonable and reliable.