Type 2 uncertainty in knowledge representation and reasoning

Type 2 fuzziness exists both in knowledge representation and approximate reasoning. First, it has been shown that acquisition of membership functions, whether (1) they are obtained by subjective measurement experiments, such as direct or reverse rating procedures or else (2) they are obtained with the application of fuzzy clustering methods, we can capture Type 2 membership functions. Type 2 fuzziness can be represented either with interval-valued Type 2 or with "full" Type 2 membership functions, which specify gradations between the upper and lower bounds of the interval of its variation. Secondly, it has been shown that the combination of linguistic values with linguistic operators, "AND", "OR", "IMP", etc., as opposed to crisp connectives that are known as t-norms and t-conorms and standard negation, lead to the generation of Fuzzy Disjunctive and Conjunctive Canonical Forms, FDCF and FCCF, respectively. In this paper, we discuss how one captures Type 2 representation and how one executes Type 2 reasoning that rests on Type 1 representation. This entails interval-valued Type 2 consequences. Furthermore we demonstrate some of its consequences.