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LINGUISTIC VARIABLES by hcj

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									                    LINGUISTIC VARIABLES
A linguistic variable is a variable whose values are not numbers but
words or sentences in a natural or artificial language (Zadeh, 1975a, p.
201).
A fuzzy restriction on the base variable, e.g. long, is characterized by a
compatibility function that associates with each value of the base
variable a number in the interval [0, 1].
This value represents the variable's compatibility with the fuzzy
restriction.
The notion of compatibility is distinct from that of probability: The
subject should be interpreted as a subjective indication of the extent to
which a particular value or expression fits one's conception of the base
variable. Zadeh (1981) has extended this idea in the form of a
possibility theory.
Fundamentals:     -- Semantic and syntactic rules
                  -- The use of connectives such as: AND
                                                     OR
                                                     NEITHER
                  -- and hedges such as: VERY
                                         QUITE
                                         MORE_OR_LESS
More formally, a linguistic variable is characterized by a quintuple, say
[, T(), U, G, M], in which stands for the name of the variable, T()
denotes the the term set of , with each value being a fuzzy variable
denoted generically by X, and ranging over a universe of discourse U
that is associated with the variable u. G is a syntactic rule (usually a
grammar) for generating names, X, of values of , and M is a semantic
rule for associating with each X its meaning, M(X), which is a fuzzy
subset of U (Zadeh, 1975b, 314)
A fuzzy subset of A of a universe of discourse U is characterized by a
membership function A: U  [0, 1], with A(u) representing the
grade of membership of u in A. For a more formal definition see
Bellman and Zadeh (1970, 5).

The support of A is the set of points in U at which A is positive, the
height of A is the supremum of A over U, and a crossover point of A
is a point in U whose membership in A is 0.5 (Zadeh 1975a, 219)
Example:
"Arrive in Pittsburgh at approximately 6 pm," can be represented as

      c(x) = (1 + a | x - 6 | m)-1;    a = 2-1, m = 1,
            = 1 / (1 + a | x - R | m)




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                     DUQUESNE UNIVERSITY

    GRADUATE SCHOOL OF BUSINESS ADMINISTRATION

                           Exercise 642: 1



One of the problems in the battle between human and model (machine)
is the problem of LOGIC. Models tend to embrace a form of logic
called Boolean; where a variable takes on a precise value only: say 73
for age, 432 miles for distance, and 6 foot 2 for height. A person
reasoning about these variables most likely would say "quite old,"
       "about 400 miles," and "tall" or "very tall."

Construct a model in LOTUS, SYMPHONY, QUATTRO, EXCEL (or
another spreadsheet) that can convert numerical information about a
concept given by a person into a linguistic variable. Also, include an
option to apply a hedge on the variable.

								
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