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

It is well known that the fuzzy reasoning is a significant part of the theory of fuzzy sets.Fuzzy reasoning has achieved great success as the core of fuzzy control.Interval-valued fuzzy set is a extension of Zadeh’s fuzzy set,which can solve the problem of vagueness and uncertainty,and it can effectively avoid the fuzzy information losing.In this paper,we mainly study the fuzzy reasoning algorithms based on the left-continuous interval-valued t-representable t-norm and apply these methods to pattern recognition problems.The main research contents of this thesis are outlined as follows:（1）The interval-valued fuzzy reasoning triple implication algorithms based on the left-continuous interval-valued t-representable t-norm T_T1,T2are proposed.Furthermore,we discuss the reducibility and study the ro-bustness of the algorithms.Finally,we apply this method to pattern recog-nition problems.（2）The interval-valued fuzzy reasoning quintuple implication algo-rithms based on the left-continuous interval-valued t-representable t-norm T_T1,T2are proposed.Furthermore,we discuss the reducibility and study the robustness of the algorithms.Finally,we apply this method to pattern recognition problems.（3）A new similarity measure between interval-valued fuzzy sets is in-troduced.Meanwhile,fuzzy reasoning algorithms based on similarity mea-sures between interval-valued fuzzy sets for Fuzzy Modus Ponens（FMP for short）and Fuzzy Modus Tollens（FMT for short）are proposed,the reducibility and the robustness of the algorithms are discussed.More-over,[α,β]-type fuzzy reasoning algorithms based on similarity measures between interval-valued fuzzy sets are proposed.Finally,we apply this method to pattern recognition problems.