Fuzzy disjunctive and conjunctive canonical forms: a foundation for interval-valued fuzzy techniques

Fuzzy disjunctive and conjunctive canonical forms, FDCF, and FCCF, respectively, should be used as a foundation for interval-valued approximate reasoning. It has been shown that in the combination of linguistic concepts, membership values generated by linguistic operators, "AND", "OR", "IMP", etc., as opposed to crisp connectives that are known as t-norms and t-conorms and standard negation, are computed with fuzzy disjunctive and conjunctive canonical forms, FDCF and FCCF, respectively. Approximate reasoning computed with these forms reveals the information content available in information granules, as well as exposing the uncertainty and risk represented with the gradation between the lower and the upper membership degrees.