Some Properties Of Extended Implications And Coimplications Over Algebras Of Truth Values Of Type-2 Fuzzy Sets

In this thesis,we study some properties of extended implications and extended coimplications on truth value algebras of type-2 fuzzy sets.Firstly,the T-conditionality under two kinds of partial orders and generalized Frege law of extended implications are discussed.We then analysis the iterative Boolean-like law,and the relationship between generalized Frege law and iterative Boolean-like law under extended implications.We obtain the relevant properties of extended coimplications.Next,we give the definitions of extended coimplications of overlapping functions and extended implications of grouping functions,we discuss the closure properties,normalities of extended coimplications of overlapping functions and extended implications of grouping functions,and their distributive laws,respectively.Finally,some representations of extended coimplications of overlapping functions and extended implications of grouping functions are given.