The Construction of Fuzziness - Fuzziness and Medicine - page 10

2.2.2 What Does “Fuzzy Logic” Mean?

The term “fuzzy logic” has become ambiguous in the meantime. It is used to denote
at least three different things. According to Lotfi Zadeh ([14] p. 2), it is appropriate
to distinguish between:

• Fuzzy logic in the narrow sense, FLn for short, and

• Fuzzy logic in the wider sense, FLw for short.

Fuzzy logic in the narrow sense, FLn, is the logical, more or less formal system that
deals with inexact, vague, or approximate reasoning concerned with rules of fuzzy
inference such as the compositional rule of inference and others. In this sense, FLn
is a particular extension of many-valued logic.
FLn is one of the branches of fuzzy logic in the wider sense, FLw, a subset of
FLw, so to speak. FLw comprises, in addition to FLn, (i) fuzzy set theory; (ii) the
theory of linguistic variables; (iii) the theory of fuzzy if-then rules; (iv) possibility
theory; and (v) the theory of computing with words ([14] p. 2). FLw and fuzzy
mathematics jointly yield what may be called Fuzzy Theory, or more appropriately,
the theory of fuzziness. In what follows, by the term “fuzzy logic”

I shall mean

FLw.
A third variant that has emerged recently, in addition to FLn and FLw, is the
mathematical fuzzy logic that is trying to develop a completely mathematical, ax-
iomatized framework in the style of traditional, formal logic. It is in fact a math-
ematical, infinite-valued logic with truth values in the real, unit interval (see, e.g.,
[1]; [2]; [3], [4]; [5]; [9]). Lotfi Zadeh does not consider this approach a fuzzy logic
at all (personal communication, 2005).
Now, turning to our original question:

2.2.3 What Kind of Science Is Fuzzy Logic?

We can observe that FLn is a pure science, whereas FLw is a mixed science. It is
partly a pure science, namely FLn; partly an applied science; and partly a practical
science. I would like to give a few examples:

• We have seen that FLn is a pure science;

• The theory of linguistic variables is an applied theory in that it is developed by

analyzing a particular characteristic of natural languages such as English, Span-
ish, and German. Its goal is to investigate fuzzy set-theoretical correspondences
and associations between qualitative and quantitative terms;

• Fuzzy control is a practical science in that it deals with fuzzy if-then rules of

action to find out in what fuzzy circumstances C 1 ,..., A n

are to be performed to control real processes in the world out there, be they
machines, biological processes, or others;

C m what actions A 1 ,...,

• The concern of your institute, i.e., Soft Computing , is partly a pure science,

partly an applied science, and partly a practical science.

It is thus a mixed

science.