Abstract
In this paper we examine important research carried out on vagueness, haziness, and fuzziness in 20th century philosophy, logic, and science. Whereas vagueness was avidly discussed in the fields of logic and philosophy during the first decades of the century – particularly in Vienna and at Cambridge – haziness and fuzziness were concepts of interest in mathematics and engineering during the second half of the 1900s. Our logico-philosophical history covers the work of Bertrand Russell, Max Black, and Ludwig Wittgenstein. The mathematical-technical history deals with the theories founded by Karl Menger and Lotfi Zadeh. We note interesting connections between these two protagonists and their findings as well as their preparatory work for the establishment of human-friendly technology.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Zadeh, L.A.: From Circuit Theory to System Theory. In: Proceedings of the IRE, vol. 50(5), pp. 856–865 (1962)
Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)
Zadeh, L.A.: Fuzzy Sets and Systems. In: Fox, Jerome (eds.) System Theory. Microwave Res. Inst. Symp. Ser., vol. XV, pp. 29–37. Polytechnic Press, Brooklyn (1965)
Seising, R.: 40 years ago: ‘Fuzzy Sets’ is going to be published. In: Proceedings of the 2004 IEEE International Joint Conference on Neural Networks / International Conference on Fuzzy Systems (FUZZ-IEEE 2004), July 25-29, 2004, Budapest, Hungary, CD (2004)
Seising, R.: 1965 – ‘Fuzzy Sets’ appear – A Contribution to the 40th Anniversary. In: Proceedings of the Conference FUZZ-IEEE 2005, Reno, Nevada, May 22-25, CD (2005)
Seising, R.: The 40th Anniversary of Fuzzy Sets – A New View on System Theory. In: Ying, H., Filev, D. (eds.) Proceedings of the Annual Conference of the North American Fuzzy Information Processing Society Soft Computing for Real World Applications (NAFIPS), Ann Arbor, Michigan, USA, June 22-25, pp. 92–97 (2005)
Frege, G.: Grundgesetze der Arithmetik, vol. 2. Hermann Pohle, Jena (1893-1903)
Russell, B.: Vagueness. The Austral. J. Psych. and Phil. 1, 84–92 (1923)
Black, M.: Vagueness. An exercise in logical analysis. Philosophy of Science 4, 427–455 (1937)
Black, M.: Reasoning with loose concepts. Dialogue 2, 1–12 (1963)
Menger, K.: Statistical Metrics. Proc. Nat. Acad. of Sci. 28, 535–537 (1942)
Menger, K.: Probabilistic Theories of Relations. Proc. Nat. Acad. of Sci. 37, 178–180 (1951)
Menger, K.: «Ensembles flous et fonctions aléatoires». Comptes Rendus Académie des sciences 37, 2001–2003 (1951)
Menger, K.: Geometry and Positivism. A Probabilistic Microgeometry, Selected Papers in Logic and Foundations, Didactics, Economics. In: Menger, K. (ed.) Vienna Circle Collection, vol. 10, pp. 225–234. D. Reidel Publ. Comp., Dordrecht (1979)
Mach, E.: Die Prinzipien der Wärmelehre. Historisch-kritisch entwickelt. Leipzig, Verlag von Johann Ambrosius Barth (1896)
Zadeh, L.A.: Some Basic Problems in communication of information. The New York Academy of Sciences, March 1952, Series II, vol. 14(5), pp. 201–204 (1952)
Zadeh, L.A.: Theory of filtering. J. Soc. Ind. Appl. Math. 1, 35–51 (1953)
Seising, R., Bradley, J.: Are Soft Computing and Its Applications in Technology and Medicine Human-Friendly? In: Gabrys, B., Howlett, R.J., Jain, L.C. (eds.) KES 2006. LNCS, vol. 4253. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Seising, R., Bradley, J. (2006). From Vague or Loose Concepts to Hazy and Fuzzy Sets – Human Understanding Versus Exact Science. In: Gabrys, B., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2006. Lecture Notes in Computer Science(), vol 4253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893011_48
Download citation
DOI: https://doi.org/10.1007/11893011_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46542-3
Online ISBN: 978-3-540-46544-7
eBook Packages: Computer ScienceComputer Science (R0)