Docstoc

LINGUISTIC VARIABLES

Document Sample
LINGUISTIC VARIABLES Powered By Docstoc
					                    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)




REFERENCES:
AbdelRahman M. (1991) Artificial Intelligence Expands Sensor
     Applications, EC&M, December, 20-23

Bandler W., Kohout L.J. (1985) Probabilistic Versus Fuzzy Production
     Rules in Expert Systems, International Journal of Man-
     Machine Studies, 22:3, 347-353

Bellman R.E., Zadeh L.A. (1970) Decision-Making in a Fuzzy
     Environment, Management Science, 17:4, B-141 - B-164

Brubaker D.I. (1993) Everything You Always Wanted To Know About
     Fuzzy Logic, EDN, March 31, 103-106

Conner D. (1993) Designing a Fuzzy-Logic Control System, EDN,
     March 31, 76-82, 84, 86, 88
Dubois D., Prade H. (1987) Upper and Lower Images of a Fuzzy Set
     Induced by a Fuzzy Relation -A Fresh Look at Fuzzy Inference
     and Diagnosis, Technical Report, No. 265, pp. 36-66, Université
     P. Sabatier, Toulouse, France

Fusaro D. (1993) Why All the Fuss About Fuzzy Logic, Control,
     February, 28-30, 32

Lim M-H., Takefuji Y. (1990) Implementing Fuzzy Rule-Based
     Systems on Silicon Chips, IEEE Computer, 5:1, 31-45

Lundberg C.G. (1988) On the Structuration of Multi-Activity Task
     Environments, Environment and Planning A, 20:12, 1603-1621

Roth E.M., Mervis C.B. (1983) Fuzzy Set Theory and Class Inclusion
     Relations in Semantic Categories, Journal of Verbal Learning
     and Verbal Behavior, 22:5, 509-525

Togai M., Wang P.P. (1985) Analysis of a Fuzzy Dynamic System and
     Synthesis of Its Controller, International Journal of Man-
     Machine Studies, 22:3, 355-363
Zadeh L.A. (1975a) The Concept of a Linguistic Variable and its
     Application to Approximate Reasoning - I, Information
     Sciences, 8:3, 199-249
Zadeh L.A. (1975a) The Concept of a Linguistic Variable and its
     Application to Approximate Reasoning - II, Information
     Sciences, 8:4, 301-357

Zadeh L.A. (1975a) The Concept of a Linguistic Variable and its
     Application to Approximate Reasoning - III, Information
     Sciences, 9:1, 43-80

Zadeh L.A. (1981) Possibility Theory and Soft Data Analysis, in Cobb
     L., Thrall R.M. (Eds.) Mathematical Frontiers of Social and
     Policy Sciences, pp. 69-129, Westview Press, Boulder, CO
Zadeh L.A. (1982) Fuzzy Probabilities and Their Role in Decision
     Analysis, Proceedingsof the Fourth MIT/ONR Workshop on
     Distributed Information and Decision Systems, place and date
     unknown

Zadeh L.A. (1983) A Computational Approach to Fuzzy Quantifiers in
     Natural Languages, Computation and Mathematics with
     Applications, 9:1, 149-184

Zadeh L.A. (1983) Linguistic Variables, Approximate Reasoning and
     Dispositions, Medical Information, 8:3, 173-186
Zadeh L.A. (1983) A Theory of Commonsense Knowledge, Memo-
     randum No. UCB/ERL M83/26, Electronics Research Labora-
     tory, College of Engineering, University of California, Berkeley

Zadeh L.A. (1983) The Role of Fuzzy Logic in the Management of
     Uncertainty in Expert Systems, Fuzzy Sets and Systems, 11, pp.
     199-227
                     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.

				
DOCUMENT INFO
Jun Wang Jun Wang Dr
About Some of Those documents come from internet for research purpose,if you have the copyrights of one of them,tell me by mail vixychina@gmail.com.Thank you!