Some Kinds Of Special Fiters And Fuzzy Filters

Since 1998, P.Hajek has proposed a new fuzzy propositional deductive system called the bisic logic BL and the corresponding algebraic structure called BL-algebra on the basis of t-norm in his work "Metamathematics of Fuzzy Logic". A lot of research related to it comes one after another. Thereafter under the influence of this book, F.Esteva and L. Godo has put forward another new fuzzy propositional deductive system called the monoidal t-norm based logic MTL and the relative algebraic system called MTL-algebra in the literature [3]. In recent years, there were more and more studis on MTL logic system and MTL-algebra, make some abundant research results at the same time. In the fuzzy deductive research, the corresponding algebra system of it is one important direction to study the nonclassics logic system. Furthermore the filter of a algebra is a kind of important tool to study its algebra system, the special ones play a very important role under study for action. In this paper, we discuss some kinds of special filters and congruence relation in fuzzy algebraic system MTL which is used extensively. The conceptions of the special filter are fuzzified in terms of the fuzzy set of Zadeh's theories and further study them by way of logic algebra of n-value.Now introduce the structure herein and main content.Chapter one: Provide the simple introduction to basic conceptions and properties used in the article about MTL-algebra; prove the set of all the filters form a complete distribution lattice in MTL-algebra; Discussion some property characteristics of Boolean filter, at the same time introduce the conceptions of positive implicative filter and obstinate filter, receive some properties of them, discuss the relation between the important filters and their equivalent condition.Chapter two: Utilize fuzzy set thought that L.A.Zadeh put forward, make MTL-algebra's filter conception fuzzified, provide the conceptions and properties of fuzzy filter, obtain the structure of all fuzzy, filters, prove that the set of all fuzzy filters forms a complete distribution lattice; Provide several fuzzy Boolean filter's equivalent forms, introduce fuzzy positive implicative filter, fuzzy obstinate filter and fuzzy ultra filter, discuss some property characteristics and terms that transform each other under certain terms to obtain them.Chapter three: Define fuzzy congruence relation of MTL-algebra, prove that fuzzy fiter and fuzzy congruence relation is a bijective function in MTL-algebra, quotient algebra induced by congruence relation still forms a MTL-algebra; Introduce the relation between some kinds of fiters and fuzzy filters maitained above in IMTL-algebra,i.e. BR₀ algebra, which is a MTL-algebra satisfied inversely odering and involutive relation.