Residuated lattice; EQ-algebra; mathematical fuzzy logic; fuzzy type theory; evaluative linguistic expressions; intermediate quantifiers

In this paper, we deal with the fuzzy type theory (FTT) --- a higher-order fuzzy logic. There are several kinds of this logic depending on the chosen structure of truth values. Higher-order (fuzzy) logic is still not fully appreciated despite its high explicative power. Our goal is to point out several great virtues of it to convince the reader that this logic is worth of studying and has a potential for many applications. After brief presentation of the main algebraic structures of truth values convenient for FTT, we discuss several virtues of the latter, namely: (1) FTT has a simple and highly uniform syntax, (2) Semantics of FTT is based on a small collection of well-established ideas, (3) FTT is a highly expressive logic and (4) There are practical extensions of FTT that can be effectively implemented.