Integral Filters And(Positive)Implicative Pseudo Valuations On Hoop Algebras

In order to prove the completeness of fuzzy logic systems,various logical algebras have been proposed as the semantical systems of fuzzy logic systems,for example,MV-algebras,BL-algebras,MTL-algebras,R0-algebras,residuated lattices and Hoop algebras.Among these logical algebras,Hoop algebras are the most fundamental and important logical algebras.In this thesis,we introduce the concepts of integral filters and(positive)implicative pseudo valuations on Hoop algebras.Through the study of integral filters,we find a new class of Hoop algebras,that is,integral Hoop algebras.Through the study of pseudo valuations,we study the quotient structure of Hoop algebras.The main results are as follows:(1)We discuss the relation between integral filters and types of filters of Hoop algebras and prove that an integral filter is a primary filter.(2)We introduce integral Hoop algebras via integral filters and obtain that a filter F is an integral filter if and only if H/F is an integral Hoop algebra.(3)We study the(positive)implicative pseudo valuations on/Hoop algebras.The conditions for a pseudo valuation to be a(positive)implicative pseudo are given.And we obtain that a pseudo valuation is an implicative pseudo valuation if and only if ?(x?y)=?(x?(x?y));a pseudo valuation is a positive implicative pseudo valuations if and only if ?(x)= ?((x?y)?x).(4)We define a binary relation ??,via pseudo valuations and prove that it is a congruence on Hoop algebras.(5)We obtain that if H1 and H2 are two Hoop algebras and f:H1?H2 is an epimorphism and ? is a pseudo valuation on H2,then H1/(?of)(?)H2/?.