 The standard set of truth-values for fuzzy logics is the real unit interval \([0,1]\) with its natural ordering \(\leq\), ranging from total falsity (represented by \(0\)) to total truth (represented by \(1\)) through a continuum of intermediate degrees of truth (see Sections  5  and  7  for alternative interpretations of truth constants and alternative sets of truth-values). A fundamental assumption of (mainstream) mathematical fuzzy logic is that connectives are to be interpreted truth-functionally over the set of degrees of truth. Such truth-functions are assumed, in the standard setting, to behave classically on the extremal values \(0\) and \(1\). A very natural behavior of conjunction, disjunction, and negation is achieved by imposing \(x \land y = \min\{x,y\}\), \(x \lor y = \max\{x,y\}\), and \(\neg x = 1 - x\) for each \(x,y \in [0,1]\).