Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T01:03:46.589Z Has data issue: false hasContentIssue false
  • English
  • Français

Probability, Vague Statements and Fuzzy Sets

Published online by Cambridge University Press:  01 April 2022

A. I. Dale
A. I. Dale*
Affiliation:
University of Natal, Durban
Get access Rights & Permissions [Opens in a new window]

Abstract

The relationship between vague statements and fuzzy sets is examined. It is shown that the probability of vague statements may be defined in a manner analogous to that discussed in Reichenbach's logic of weight.

Type
Research Article
Information
Philosophy of Science , Volume 47 , Issue 1 , March 1980 , pp. 38 - 55
Copyright
Copyright © Philosophy of Science Association 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I am grateful to the referees for the references Lewis (1976) and Bellman & Giertz (1973), and for other helpful comments.

References

Bayes, T., (1763), “An essay towards solving a problem in the doctrine of changes.” Philos. Trans. Roy. Soc. 53: 370–418.Google Scholar
Bellman, R. & Giertz, M., (1973), “On the analytic formalism of the theory of fuzzy sets.” Information Sciences 5: 149–156.10.1016/0020-0255(73)90009-1CrossRefGoogle Scholar
Boole, G., (1854), An Investigation of the Laws of Thought. London: Macmillan.Google Scholar
Goguen, J. A., (1969), “The logic of inexact concepts.” Synthese 19: 325–373.10.1007/BF00485654CrossRefGoogle Scholar
Kaufmann, A., (1975), Introduction to the Theory of Fuzzy Subsets, Vol. I. New York: Academic Press.Google Scholar
Kolmogorov, A. N., (1950), Foundations of the Theory of Probability. New York: Chelsea Publishing Co.Google Scholar
Lewis, D., (1976), “Probabilities of conditionals and conditional probabilities.” Philosophical Review 85, 3: 297–315.10.2307/2184045CrossRefGoogle Scholar
Menges, G., (1973), “Inference and decision,” in Inference and Decision, Selecta Statistica Canadiana Vol. I. Toronto: University Press of Canada.Google Scholar
Menges, G. & Skala, H. J., (1974), “On the problem of vagueness in the social sciences,” in Information, Inference and Decision (ed. Menges, G.), Dordrecht: Reidel.10.1007/978-94-010-2159-3CrossRefGoogle Scholar
Reichenbach, H., (1949), The Theory of Probability. Berkeley: University of California Press.Google Scholar
Zadeh, L. A., (1965), “Fuzzy sets.” Information and Control 8: 338–353.10.1016/S0019-9958(65)90241-XCrossRefGoogle Scholar
Zadeh, L. A., (1968), “Probability measures of fuzzy events.” J. Math. Anal. Appl. 21: 421–427.10.1016/0022-247X(68)90078-4CrossRefGoogle Scholar