The Study For The Smallest Uninorm Logic Systems And Robustness Of Interval-valued Triple I Algorithms

As a generalization of t-norms and t-conorms,uninorms have become a hot topic in recent years.So far,Uninorm Logic and its extension have been present,and have been used to fuzzy reasoning.This dissertation is a study of construction of the the smallest uninorm based fuzzy logic sys-tem,and robustness of interval-valued fuzzy reasoning triple I algorithms.The main research contents of this thesis are outlined as follows:First,axiomatic characterizations is given by studying the character-istics of the smallest uninorm,then the corresponding fuzzy logic system SUL is constructed.Moreover,canonically complete theorem of the fuzzy logic system SUL is proved.Second,the smallest uninorm is revised as a left-continuous and con-junctive uninorm based on the ordinal sum theorem of semigroup and or-dinal representation of uninorm.Then construct the revised uninorm based fuzzy logic system RSUL and prove the standard completeness theorem of RSUL.Then,aggregation operators for decision making based on uninorm-s in L~*-fuzzy set theory is constructed.The practicability of the proposed method is illustrated by some examples.Last,sensitivity of interval-valued Schweizer-Sklar t-norms and resid-ual operators are studied based on normalized Minkowski distance in Haus-dorff metrics,robustness of interval-valued fuzzy reasoning triple I algo-rithms based on the Schweizer-Sklar operators are investigated.