On the Roots of Fuzzy Sets - Fuzzy Logic: An Introductory Course for Engineering Students - page 1

Chapter 1
On the Roots of Fuzzy Sets
As fuzzy sets were introduced by Zadeh in 1965, they were born closely linked with
imprecise predicates, that is, with names of non-precisely defined classes of objects.
Even more, most of the applications of Zadeh's ideas are made with properties
the objects do verify in some degree between the two classical extremes 0 and 1,
respectively. Because of that, it is not at all odd to introduce fuzzy sets from some
considerations on how predicates are used in language. We will follow Wittgenstein's
statement “The meaning of a word is its use in language”.
1.1 A Genesis of Fuzzy Sets
Usually, isolated words mean nothing. To mean something, words are to be used
in a given context and in a known way. Words do serve to describe perceptions, to
translate reasoning, and to show the reasons for judgements.
For example, what it is meant by the predicate unleaty ? It is impossible to answer
this question, since nobody has never heard something like “this is unleaty”, “such
is leaty”, etc. Neither unleaty, nor leaty, are English words, nobody has used them
and they don't appear in English dictionaries. Meaning is inherited by predicates P
only after being used, in some ground, by means of elemental statements ' x is P '.
By now, unleaty has no meaning.
Words are introduced in a language by using them in concrete ways. For example,
the Spanish word 'madre' comes from the latin 'mater' that, at its turn, came from one
in older indo-european languages, but always used to name someone's mother. Later
on, the word could take, by analogy, new meanings as it is, for example, 'mother
country', 'goodmother', 'mother in law', 'mother of all wars', 'mother Nature',
'mother-of-pearl', etc. The predicate leaty neither appears in English, nor in Spanish,
French, German, …, because it was never before used to name a property of the
elements in some class, like it is with tall, young, middle-aged , with people, high
with buildings or mountains, or heavy with metals, for example. It is only through
its use that predicates do acquire 'meaning'.