ABSTRACT

Consider a piece of information of the form “If (x is A and y is not B), then (z is C or z is D)”. An approach to the translation of this type of knowledge is to model it as fuzzy sets. To translate completely the sentence above, we need to model the connectives “and”, “or”, and “not”, as well as the conditional “If...then...”. This combining of evidence, or “data fusion”, is essential in building expert systems or in synthesizing controllers. But the connectives experts use are domain dependentthey vary from field to field. The connectives used in data fusion in medical science are different from those in geophysics. So there are many ways to model these connectives. The search for appropriate models for “and” has led to a class of connectives called “t-norms”. Similarly, for modeling “or” there is a class called “t-conorms”. In this chapter we will investigate ways for modeling basic connectives used in combining knowledge that comes in the form of fuzzy sets. These models may be viewed as extensions of the analogous connectives in classical two-valued logic. A model is obtained for each choice of such extensions, and one concern is with isomorphisms between the algebraic systems that arise.