Second thoughts on linguistic variables

Linguistic variables, as defined by L.A. Zadeh (1987), play a central role in the modelling of approximate reasoning by fuzzy sets. Graduate predicates habitually form bipolar linguistic variables by means of a predicate P and its antonym predicate aP, and, hence, in order to manage a linguistic variable V, both the principal term P (or a predicate generating the variable) and its antonym aP are essential. The knowledge of the membership functions of the fuzzy sets, respectively labelled P and aP, allow one, by means of linguistic modifiers and logical connectives, to obtain the membership functions of all the required terms of V. The antonym relation between predicates remains for all linguistic terms of the linguistic variable. For example, "cold" and "hot" are antonyms, but so are "very cold" and "very hot" or "cool" and "warm". The problem is, of course, the fuzzy modelling of all the terms of V. This paper is focused on obtaining a linguistic variable model where all linguistic terms maintain the basic antonym relation that exists between two bipolar predicates, allowing the use of linguistic modifiers, and on the special case in which the interesting terms of V classify the common universe X in some adequate way.