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Among the various extensions to the common [0,1]-valued truth degrees of “traditional” fuzzy set theory, closed intervals of[0,1] stand out as a particularly appealing and promising choice for representing imperfect information, nicely accommodating and combining the facets of vagueness and uncertainty without paying too much in terms of computational complexity. From a logical point of view, due to the failure of the omnipresent prelinearity condition, the underlying algebraic structure L^I falls outside the mainstream of the research on formal fuzzy logics (including MV-, BL- and MTL-algebras), and consequently so far has received only marginal attention. This comparative lack of interest for interval-valued fuzzy logic has been further strengthened, perhaps, by taking for granted that its algebraic operations amount to a twofold application of corresponding operations on the unit interval. Abandoning that simplifying …