Abstract
In the field of pattern recognition or decision making theory, the following complicated problems have been left unsolved: (1)ambiguity of objects, (2)variety of character, (3)subjectivity of observers, (4)evolution of knowledge or learning. With regard to each problem, however, there are several general theories: many-valued logic, fuzzy set theory (in connection with (1)and(2)), modal logic (in conjunction with (2)and(4)), and subjective probability (in relation to (3)). It seems, however, that there are few carefully thought-out investigations by paying attention to all problems mentioned above. In this paper we would like to give our opinion about these problems and to introduce a new concept called ‘probabilistic sets’.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Birkhoff, Lattice Theory,Am.Math.Soc.Colloq.Publ. (Am.Math.Soc.,Mew York,1969).
[J.G.Brown, A note on Fuzzy sets, Information and Control 18(1971) 32–39.
J.A.Geguen, L-fuzzy sets, J.Math.Anal.Appl. 18(1967) 145–174.
P.R.Halmos, Naive Set Theory(Van Nostrand,New York, 1960).
P.R.Halmos, Measure Theory (Van Nostrand, New York, 1960).
K.Hirota, Kakuritsu-Shugoron to sono Oyourei (Probabilistic sets and its applications), Presented at the Behaviormetric Society of Japan 3rd Conference(1975)(in Japanese).
K.Hirota, Kakuritsu-Shugoron (Probabilistic set theory), in: Fundamental research works of fuzzy system theory and artificial intelligence, Research Reports of Scientific Research fund from the Ministry of Education in Japan(1976) 193–213(in Japanese).
K.Hirota, Concepts of probabilistic sets,IEEE Conf. on Decision and Control (New Orleans)(1977) 1361–1366.
K.Hirota, Extended fuzzy expression of probabilistic sets-Analytical expression of ambiguity and subjectivity in pattern recognition, Presented at Seminar on Applied Functional Analysis(July,1978) 13–18.
K.Hirota er al., A decision making model-A new approach based on the concepts of probabilistic sets, Presented at Int.Conf.on Cybernetics and Society 1978, Tokyo(Nov.1978) 1348–1353.
K.Hirota et al., The bounded variation quantity (B.V.Q) and its application to feature extractions, Presented at the 4th Int.Conf. on Pattern Recognition,Kyoto(Nov.1978) 456–461.
M.Mizumoto and K.Tanaka,Some properties of fuzzy sets of type 2, Information and Control 31(1976) 312–340.
K.Nanba, shugo-ron(Set Theory) (Science-sha Publ., 1975) (in Japanese)
L.A.Zadeh, Fuzzy sets, Information and Control 8 1965) 228–353.
L.A.Zadeh, Probabilistic measure of fuzzy events, J. Math. Ana.. App1.23(1968) 421–427.
L.A.Zadeh et al., Fuzzy Sets and their Applications to Cognitive and Decision Theory (Academic Press, New York,1975).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hirota, K. (1992). Probabilistic Sets Probabilistic Extension of Fuzzy Sets. In: Yager, R.R., Zadeh, L.A. (eds) An Introduction to Fuzzy Logic Applications in Intelligent Systems. The Springer International Series in Engineering and Computer Science, vol 165. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3640-6_16
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3640-6_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6619-5
Online ISBN: 978-1-4615-3640-6
eBook Packages: Springer Book Archive