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Fig. 18.1 Tentative membership functions for denoting the linguistic values young, fairly
young, middle-aged, fairly old and old in the context of age (horizontal axis)
constraints are not specified, and they are a matter of perception rather than mea-
surement. In addition, we apply informal and approximate reasoning in this context.
The FLe stems from Zadeh's previous theories on information granulation, pre-
cisiated language and computing with words, as well as on the theory of perceptions
[21],[22-27]. His ideas mean that we can apply both traditional bivalent-based and
novel approximate validity, definitions, axioms, theories and explanations, inter alia.
The well-known syllogism, the fuzzified Modus Ponens, is an example of his ap-
proximate reasoning. Hence, instead of the traditional Modus Ponens,
A
If A ,then B
Thus, B
in the fuzzified version the first premise need not to be identical with the antecedent
of the second premise, and thus we use the fuzzified Modus Ponens in a form
A 1
If A ,then B
Thus, B 1
For example,
John is 22 years old.
If John is 20 years old, then he is young.
Thus, John is approximately young
The FLe opens several prospects for conduct of inquiry [11-14],[16]. Below we
apply its ideas to statistical reasoning and modeling.
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