Closures of fuzzy linguistic truth value with regards to the extension principle

摘要

We have studied non-convex or subnormal linguistic truth values that has not been considered so far. The logical operations based on the extension principle are closed into VN, VC and VR and arbitrary intersection of any of these is also closed. There are infinite number of subsets outside of convex truth value, that are classified by the ranks. We have shown that a set of linguistic truth value of a common rank is not closed.