Browse > Article

Mathematics of Uncertainty: Probability and Possibility  

Koh, Young-Mee (Department of Mathematics, The University of Suwon)
Ree, Sang-Wook (Department of Mathematics, The University of Suwon)
Publication Information
Journal for History of Mathematics / v.25, no.1, 2012 , pp. 1-13 More about this Journal
Abstract
Possibility theory is a kind of mathematics of uncertainty for handling incomplete information. In this paper, we discuss vagueness and randomness as some causes of uncertainty and we introduce the possibility theory as a way of dealing with uncertainty, comparing it with the probability theory.
Keywords
uncertainty; vagueness; randomness; fuzzy sets; possibility; probability;
Citations & Related Records
연도 인용수 순위
  • Reference
1 박창균, 퍼지이론의 배경과 수학사적 의의, 한국수학사학회지 7 (1992), no. 1, pp. 61-70.
2 박창균, 수학에서의 포스트모던 경향-퍼지논리를 중심으로, 한국수학사학회지 12 (1992), no. 2, pp. 135-141.
3 박창균, 비트겐슈타인의 철학과 퍼지논리-언어 사용을 중심으로, 한국수학사학회지 13 (2000), no. 2, pp. 145-150.
4 박창균, 수학적 대상으로서 '애매모호' 에 대한 고찰, 한국수학사학회지, 14 (2001), no. 2, pp. 93-100.
5 이승온, 김진태, 퍼지 논리의 시조 Zadeh, 한국수학사학회지 21 (2008), no. 1, pp. 29-44.
6 Dubois, D., Ostasiewicz, W., & Prade, H., Fuzzy sets: History and basic notions, The handbook of fuzzy set series (7 volumes), Kluwer Academic Pub., 2000.
7 Dubois, D., Prade, H., Possibility Theory, Plenum Press, New York, 1988.
8 Dubois, D., Prade, H., Fuzzy sets and probability: Misunderstandings, bridges and gaps, Proceedings of IEEE conference, 1993.
9 Dubois, D., Prade, H., Possibility theory and its applications: Where do we stand? http://www.irit.fr/-Didier.Dubois/Papers1208/possibility-EUSFLAT-Mag.pdf, 2011.
10 Kikuchi S., Chakroborty, P.,"Place of possibility theory in transportation analysis", Transfortation Research Part B 40 (2006), pp. 595-615.   DOI   ScienceOn
11 Kosko, B.,"Fuzziness vs. Probability", Int. J. general systems 17 (1990), pp. 211-240.   DOI   ScienceOn
12 Nguyen, H. & Walker, E., A first course in Fuzzy logic, Chapman & Hall, 2000.
13 Raufaste, E., Neves, R. & Marine, C.,"Testing the descriptive validity of possibility theory in human judgements of uncertainty", Artificial Intelligence 148 (2003), pp. 197-218.   DOI   ScienceOn
14 Wierman, M., An introduction to the mathematics of uncertainty, Center for the mathematics of uncertainty, Creighton University. 2010.
15 Zadeh, L. A.,"Fuzzy sets", Information Control 8 (1965), pp. 338-353.   DOI
16 Zadeh, L. A.,"Fuzzy sets as a basis for a theory of possibility", Fuzzy sets and systems, 1, pp. 3-28, 1978.   DOI   ScienceOn
17 Zadeh, L. A.,"Possibility theory and soft data analysis", from Selected papers by Lofti A. Zadeh, 1981.
18 Zalila, Z., Cuquemelle, J., Penet, C., Chikh, A., Lorentz, B., Deschamps, D., & Assemat, C., Fuzzy logic and fuzzy inference systems, v1.2-02/2007, intellitech, 2007.
19 http://en.wikipedia.org/wiki/Fuzzy_logic
20 http://en.wikipedia.org/wiki/Uncertainty
21 http://en.wikipedia.org/wiki/Vagueness