Imprecision,Uncertainty & Vagueness: a reply

Kamil Murat EKSIOGLU (eksioglk@se.bel.alcatel.be)
Fri, 3 Sep 1999 12:46:53 +0200 (MET DST)

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"Peter Rijnbeek" wrote:
>Can anyone explain to me the difference between imprecision,
uncertainty,
>and vagueness, because this is very confusing to me.

>From the first section of my Ph.D. thesis (translated form French, sorry
for errors, if any):

"[..]
Imprecision of the human systems is due to the imperfection of knowledge
that humain receives (observation) from the external world. Imperfection
leads to a doubt about the value of a variable, a decision to be taken
or a conclusion to be drawn for the actual system. The sources of
uncertainty can be stochasticity (the case of
intrinsic imperfection where a typical and single value does not exist),
incomplete knowledge (ignorance of the
totality, limited view on a system because of its complexity) or the
acquisition errors (intrinsically imperfect observations, the
quantitative errors in measures). Some even add conceptual imprecision,
lexical vagueness and linguistic inexactitude. In spite of the multitude
of definitions, these can be gathered in a category of imperfections of
knowledge, quantifiable in various ways which depend, actually, of the
choosen knowledge representation.

Probability (called sometimes the objective probability) process
uncertainty of random type (stochastic) introduced by the chance.
Uncertainty of the chance is clarified by the time or by events'
occurence. The probability is thus connected to the frequency of the
events' occurrence. [..]

[..]

The vagueness which constitutes another form of uncertainty is the
character of which with contours
or limits lacking precision, clearness. Bertrand Russel was the first
to have discussed of them in
the ancient paradox of bald person; at the beginning, man is not bald.
Then he loses his hair one by one; at the end, he is a bald person.
Therefore it should be a hair whose loss converted the man into a bald
person. This is of course absurd. In truth the concept of bald person is
vague. There are men certainly bald, others not, and between them, there
are men for whom this is not completely true to define them like bald or
not.

While Russel philosophically discusses the existence of vagueness, Black
is the first to give more concrete definitions. [ ..]. For each vague
category, there is an area so that it is doubtful to talk that objects
belong totally or not to that area. The aspect of vagueness is
descriptive for a given category. Certain objects belong to this
category; others are straightforwardly excluded from it. For certain
objects, the fact to be in or out of a category is difficult to
mention. Rather, it is possible to express a partial or gradual
membership. [...].

Why vagueness does exist? [..] Some people support that it is completely
linguistic, and it is an inaccuracy related to the language. Others such
as Wallsten and Zwick, claim that vagueness is completely intrinsic
within the natural language. This assertion is reasonable, by taking
into account of the descriptive nature of vagueness on the conceptual
classes. Goguen affirms that the human capability to express himself
vague, enables him to better define the objects of the external world.
[..] Sowa claims that the external world is a continuum while the
linguistic concepts are discrete. The vague assists to better express
himself because of the existence of a universal paradox between the
external reality and its mental projection at human's cognitive
structure. Regarding Wallsten, vagueness is a state of the mental system
(even soul) according to the information available.

[..]"

Some related articles :
---------------

[] Dreyfuss, G. R., Kochen, M., Robinson, J., Badre, A. N., "On the
psycholinguistic reality of fuzzy sets", in Functionalism, 1975, p.
135-149, (Eds.) R. E. Grossman, L. J. San, T. J. Vance.

[] Dubois, D., Prade, H., "Quantifying vagueness and possibility: new
trends in knowledge representation" in Acting under uncertainty:
multidisciplinary conceptions, 1990, p. 399-422, Kluwer Academic
Publishers, Norwell, Mass, USA.

[] Farreny, H., Prade, H., "Dealing with the vagueness of natural
languages in man-machine communication", Applications of Fuzzy Set
Theory in Human Factors, 1986, p. 71-85, (Eds.) W. Karwowski et A.
Mital, Elsevier Science Publishers, Amsterdam, NL.

[] Gazdar, G., "Speech act assignment", Elements of Discourse
Understanding, 1981, p. 64-83, (Eds.) A. K. Joshi, B. L. Webber, I. A.
Sag, Cambridge University Press, Mass., USA.

[] Goguen, J., "Fuzzy sets and the social nature of truth", Advances in
Fuzzy Set Theory and Applications, 1979, p. 49-67, (Eds.) M. M. Gupta,
R. K. Ragade, R. R. Yager, North-Holland Publishing Company.

[] Goldman, N. M., "The boundaries of language generation", Theoretical
Issues in Natural Language Processing: An Interdisciplinary Workshop in
Computational Linguistics, Psychology, Linguistics, Artificial
Intelligence, 1975, June 10-13, p. 84-88, Cambridge, Massachusetts, USA.

[] Hayes, P., "Aristotelian and Platonic views of knowledge
representation", Conceptual Structures: Current Practices, Lecture Notes
in Artificial Intelligence, 1994, vol. 835, p. 1-10, (Eds.), W. M.
Tepfenhart, J. P. Dick, J. F. Sowa, Springer-Verlag, Germany.

[] Kochen, M., "Applications of fuzzy sets in psychology", Fuzzy Sets
and Their Applications to Cognitive and Decision Process, 1975, p.
395-408, (Eds.) L. A. Zadeh, K. S. Fu, K. Tanaka, M. Shimura, Academic
Press Inc.

[] Lakoff, G., "Hedges: a study in meaning criteria and the logic of
fuzzy concepts", Proc. 8th Regional Meeting, Chicago Linguistic Society,
1972, p. 340-350.

[] Norvich, A. M., Turksen I. B., "Stochastic fuzziness", Approximate
Reasoning in Decision Analysis, 1982, p. 13-22, (Eds.) M. M. Gupta, E.
Sanchez, North-Holland Publishing Company.

[] Oden, G. C., "Fuzzy propositional approach to psycholinguistic
problems: an application of fuzzy set theory in cognitive science",
Advances in Fuzzy Set Theory and Applications, 1979, p. 409-420, (Eds.)
M. M. Gupta, R. K. Ragade, R. R. Yager, North Holland Publishing
Company.

[] Osgood, C. E., Tzeng, O. C. S., Language, Meaning and Culture: the
Selected Papers of C. E. Osgood, 1990, Praeger, New York, USA.

[] Robinson, A. E., Appelt, D. E., Grozs, B. J., Hendrix, G. G.,
Robinson, J., Interpreting natural-language utterances in dialogs about
tasks, 1980, SRI Project no: 5844, Technical Note 210, SRI
International, California, USA.

[] Russell, C. S., "Accounting for perception in possibility
distributions: an algorithmic approach to solving the problem How tall
is Dan?", Proc. Third IEEE Conference on Fuzzy Systems, 1994, vol. 3, p.
1939-1949.

[] Schefe P., "On foundations of reasoning with uncertain facts and
vague concepts", Int. J. Man-Machine Studies, 1980, vol. 12, p. 35-62.

[] Schmidt, C. H., "Understanding human action", Theoretical Issues in
Natural Language Processing: An Interdisciplinary Workshop in
Computational Linguistics, Psychology, Linguistics, Artificial
Intelligence, 1975, June 10-13, p. 215-219, Cambridge, Massachusetts,
USA.

[] Sowa, J. F., Conceptual Structures, Information Processing in Mind
and Machine, 1984, Addison Wesley Publishing Company, NY, USA.

[] Staggers, N., Norcio, A. F., "Mental models: concepts for
human-computer interaction research", Int. J. Man-Machine Studies, 1993,
vol. 38, p. 587-605.

[] Suter, G. W. II, "Uncertainty in environmental risk assessment",
Acting under Uncertainty: Multidisciplinary Conceptions, 1990, p.
203-230, (Eds.) G. M. Furstenberg, Kluwer Academic Publishers, Norwell,
Mass., USA.

[] Wallsten, T. S., "Measuring vague uncertainties and understanding
their use in decision making", Acting Under Uncertainty:
Multidisciplinary Conceptions, 1990, p. 377-398 (Eds.) G. M.
Furstenberg, Kluwer Academic Publishers, Norwell, Mass., USA.

[] Zadeh, L. A., "The concept of a linguistic variable and its
application to approximate reasoning I", Information Sciences, 1975,
vol. 8, p. 199-249.

[] Zeleny, M., "The role of fuzziness in the construction of knowledge",
dans The Interface Between Artificial Intelligence and Operations
Research in Fuzzy Environment, 1989, p 233-252, (Eds.) Delgado M.,
Verlage TUV, Rheinland, Germany.

[] Zhang, l., "Structural and functional quantization of vagueness",
Fuzzy Sets and Systems, 1993, vol. 55, p. 51-60.

[] Zwick, R., "Combining stochastic uncertainty and linguistic
inexactness: theory and experimental evaluation of four fuzzy
probability models", Int. J. Man-Machine Studies, 1989, vol. 30, p.
69-111.

I hope this helps,
Kamil Murat Eksioglu

--
-----------------------------------------------------------------------
Kamil Murat Eksioglu                         eksioglk@se.bel.alcatel.be
ALCATEL, Software Design Engineer, Intelligent Networks, SRD Group, R&D
1. Esensehir,  Ataturk Caddesi  Y.Dudullu,  Istanbul,  81260,  Turkey
Phones: +90 (216) 420 7500 #2707                Fax: +90 (216) 420 7584
-----------------------------------------------------------------------

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<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> "Peter Rijnbeek" wrote:
>Can anyone explain to me the difference between imprecision, uncertainty,
>and vagueness, because this is very confusing to me.

From the first section of my Ph.D. thesis (translated form French, sorry for errors, if any):

"[..]
Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for the actual system. The sources of uncertainty can be stochasticity (the case of
intrinsic imperfection where a typical and single value does not exist), incomplete knowledge (ignorance of the
totality, limited view on a system because of its complexity) or the acquisition errors (intrinsically imperfect observations, the quantitative errors in measures). Some even add conceptual imprecision, lexical vagueness and linguistic inexactitude. In spite of the multitude of definitions, these can be gathered in a category of imperfections of knowledge, quantifiable in various ways which depend, actually, of the choosen knowledge representation.

Probability (called sometimes the objective probability) process uncertainty of random type (stochastic) introduced by the chance. Uncertainty of the chance is clarified by the time or by events' occurence. The probability is thus connected to the frequency of the events' occurrence. [..]

[..]

The vagueness which constitutes another form of uncertainty is the character of which with contours
 or limits lacking precision, clearness. Bertrand Russel was the first to have discussed of them in
 the ancient paradox of bald person; at the beginning, man is not bald. Then he loses his hair one by one; at the end, he is a bald person. Therefore it should be a hair whose loss converted the man into a bald person. This is of course absurd. In truth the concept of bald person is vague. There are men certainly bald, others not, and between them, there are men for whom this is not completely true to define them like bald or not.

While Russel philosophically discusses the existence of vagueness, Black is the first to give more concrete definitions. [ ..]. For each vague category, there is an area so that it is doubtful to talk that objects belong totally or not to that area. The aspect of vagueness is descriptive for a given category. Certain objects belong to this category; others are straightforwardly excluded from it. For certain objects, the fact to be in or out of a category  is difficult to mention.  Rather, it is possible to express a partial or gradual membership. [...].

Why vagueness does exist? [..] Some people support that it is completely linguistic, and it is an inaccuracy related to the language. Others such as Wallsten and Zwick, claim that vagueness is completely intrinsic within the natural language. This assertion is reasonable, by taking into account of the descriptive nature of vagueness on the conceptual classes. Goguen affirms that the human capability to express himself vague, enables him to better define the objects of the external world. [..] Sowa claims that the external world is a continuum while the linguistic concepts are discrete. The vague assists to better express himself because of the existence of a universal paradox between the external reality and its mental projection at human's cognitive structure. Regarding Wallsten, vagueness is a state of the mental system (even soul) according to the information available.

[..]"
 

Some related articles :
---------------

[] Dreyfuss, G. R., Kochen, M., Robinson, J., Badre, A. N., "On the psycholinguistic reality of fuzzy sets", in Functionalism, 1975, p. 135-149, (Eds.) R. E. Grossman, L. J. San, T. J. Vance.

[] Dubois, D., Prade, H., "Quantifying vagueness and possibility: new trends in knowledge representation" in Acting under uncertainty: multidisciplinary conceptions, 1990, p. 399-422, Kluwer Academic Publishers, Norwell, Mass, USA.

[] Farreny, H., Prade, H., "Dealing with the vagueness of natural languages in man-machine communication", Applications of Fuzzy Set Theory in Human Factors, 1986, p. 71-85, (Eds.) W. Karwowski et A. Mital, Elsevier Science Publishers, Amsterdam, NL.

[] Gazdar, G., "Speech act assignment", Elements of Discourse Understanding, 1981, p. 64-83, (Eds.) A. K. Joshi, B. L. Webber, I. A. Sag, Cambridge University Press, Mass., USA.

[] Goguen, J., "Fuzzy sets and the social nature of truth", Advances in Fuzzy Set Theory and Applications, 1979, p. 49-67, (Eds.) M. M. Gupta, R. K. Ragade, R. R. Yager, North-Holland Publishing Company.

[] Goldman, N. M., "The boundaries of language generation", Theoretical Issues in Natural Language Processing: An Interdisciplinary Workshop in Computational Linguistics, Psychology, Linguistics, Artificial Intelligence, 1975, June 10-13, p. 84-88, Cambridge, Massachusetts, USA.

[] Hayes, P., "Aristotelian and Platonic views of knowledge representation", Conceptual Structures: Current Practices, Lecture Notes in Artificial Intelligence, 1994, vol. 835, p. 1-10, (Eds.), W. M. Tepfenhart, J. P. Dick, J. F. Sowa, Springer-Verlag, Germany.

[] Kochen, M., "Applications of fuzzy sets in psychology", Fuzzy Sets and Their Applications to Cognitive and Decision Process, 1975, p. 395-408, (Eds.) L. A. Zadeh, K. S. Fu, K. Tanaka, M. Shimura, Academic Press Inc.

[] Lakoff, G., "Hedges: a study in meaning criteria and the logic of fuzzy concepts", Proc. 8th Regional Meeting, Chicago Linguistic Society, 1972, p. 340-350.

[] Norvich, A. M., Turksen I. B., "Stochastic fuzziness", Approximate Reasoning in Decision Analysis, 1982, p. 13-22, (Eds.) M. M. Gupta, E. Sanchez, North-Holland Publishing Company.

[] Oden, G. C., "Fuzzy propositional approach to psycholinguistic problems: an application of fuzzy set theory in cognitive science", Advances in Fuzzy Set Theory and Applications, 1979, p. 409-420, (Eds.) M. M. Gupta, R. K. Ragade, R. R. Yager, North Holland Publishing Company.

[] Osgood, C. E., Tzeng, O. C. S., Language, Meaning and Culture: the Selected Papers of C. E. Osgood, 1990, Praeger, New York, USA.

[] Robinson, A. E., Appelt, D. E., Grozs, B. J., Hendrix, G. G., Robinson, J., Interpreting natural-language utterances in dialogs about tasks, 1980, SRI Project no: 5844, Technical Note 210, SRI International, California, USA.

[] Russell, C. S., "Accounting for perception in possibility distributions: an algorithmic approach to solving the problem How tall is Dan?", Proc. Third IEEE Conference on Fuzzy Systems, 1994, vol. 3, p. 1939-1949.

[] Schefe P., "On foundations of reasoning with uncertain facts and vague concepts", Int. J. Man-Machine Studies, 1980, vol. 12, p. 35-62.

[] Schmidt, C. H., "Understanding human action", Theoretical Issues in Natural Language Processing: An Interdisciplinary Workshop in Computational Linguistics, Psychology, Linguistics, Artificial Intelligence, 1975, June 10-13, p. 215-219, Cambridge, Massachusetts, USA.

[] Sowa, J. F., Conceptual Structures, Information Processing in Mind and Machine, 1984, Addison Wesley Publishing Company, NY, USA.

[] Staggers, N., Norcio, A. F., "Mental models: concepts for human-computer interaction research", Int. J. Man-Machine Studies, 1993, vol. 38, p. 587-605.

[] Suter, G. W. II, "Uncertainty in environmental risk assessment", Acting under Uncertainty: Multidisciplinary Conceptions, 1990, p. 203-230, (Eds.) G. M. Furstenberg, Kluwer Academic Publishers, Norwell, Mass., USA.

[] Wallsten, T. S., "Measuring vague uncertainties and understanding their use in decision making", Acting Under Uncertainty: Multidisciplinary Conceptions, 1990, p. 377-398 (Eds.) G. M. Furstenberg, Kluwer Academic Publishers, Norwell, Mass., USA.

[] Zadeh, L. A., "The concept of a linguistic variable and its application to approximate reasoning I", Information Sciences, 1975, vol. 8, p. 199-249.

[] Zeleny, M., "The role of fuzziness in the construction of knowledge", dans The Interface Between Artificial Intelligence and Operations Research in Fuzzy Environment, 1989, p 233-252, (Eds.) Delgado M., Verlage TUV, Rheinland, Germany.

[] Zhang, l., "Structural and functional quantization of vagueness", Fuzzy Sets and Systems, 1993, vol. 55, p. 51-60.

[] Zwick, R., "Combining stochastic uncertainty and linguistic inexactness: theory and experimental evaluation of four fuzzy probability models", Int. J. Man-Machine Studies, 1989, vol. 30, p. 69-111.
 
 

I hope this helps,
Kamil Murat Eksioglu

-- 
-----------------------------------------------------------------------
Kamil Murat Eksioglu                         eksioglk@se.bel.alcatel.be
ALCATEL, Software Design Engineer, Intelligent Networks, SRD Group, R&D
1. Esensehir,  Ataturk Caddesi  Y.Dudullu,  Istanbul,  81260,  Turkey
Phones: +90 (216) 420 7500 #2707                Fax: +90 (216) 420 7584
-----------------------------------------------------------------------
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