On the Roots of Fuzzy Sets - Fuzzy Logic: An Introductory Course for Engineering Students - page 28

It is the evolution of the use of P in different universes that produces the
descriptions of P that are found in dictionaries. Such current meaning, or mean-
ings, always never can be described by a 'if and only if' definition like in the case of
P odd in the set of positive integers, but just by some more or less clear descrip-

tion, as it is with the same word 'odd' when applied either to social situations, or to
people. Most of the words appearing in dictionaries are imprecise and, hence, not
definable by precise terms. For this kind of reasons, dictionaries contain several short
descriptions for most of the words in them.
The current meaning of P is also influenced with the simultaneous use of its
synonyms and antonyms, as well as by the more or less different uses of P some
groups of people did, for saying nothing of the influences coming from other natural
languages. Of course, there are some words that evanish since their universe of
application disappears; words are 'born' when applied to concrete universes, and
are 'dying' when these universes disappear, as it happened, for instance, with some
old words that were use in the wide middle age's world of cavalry. Language is a
dynamical system, and their dynamicity implies that it cannot be well studied by
only employing the methods that are typical of classical logic. Fuzzy logic could be
a mathematical and practical tool for that study in the cases where ambiguity can be
left aside.

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1.5 Linguistic Variables

Linguistic variables are basic tools in most application of fuzzy sets in the technol-
ogy's field. They do mainly appear when linguistically describing the behavior of the
physical variables of a system. A linguistic variable explicits a concept by (linguis-
tically) granulating some elemental components of it, by showing the perceptually
distinguishable shades that are relevant for the corresponding application.
A linguistic variable LV is formed after considering

1. Its principal predicate, P
2. One of the opposites of P , aP
3. Some linguistic modifiers m 1 ,...,

m n ,

and by adding:
4. Its negate ( not P ), or the middle-predicate ( MP ), or P and Q ,or not m 1 P ,or P
and m 2 aP ,...

Then LV, is called the linguistic variable generated by P , and reflects the linguistic
granulation perceived for the concept. For example,

• LV = Age, is Age ={ young, old, middle-aged, not old, not very young, … }

• LV = Truth, is Truth ={ true, false, very false, not very true, … }

• LV = Temperature, is Temperature ={ cold, hot, warm, not cold, not very hot, … }

• LV = Size, is Size ={ large, small, medium, very large, … }

• LV = Height, is