Abstract
In this paper, we give some basic principle of possibility models and its applications. We briefly review possibility analysis based on the max-min operator and explain possibility analysis based on exponential possibility distributions in contrast to statistical analysis. Using possibility analysis, we show an identification method of possibility distributions and fuzzy data analysis such as regression analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
G. Alefed and J. Herzberger, Introduction to Interval Computations, Academic Press, New York (1983).
L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems 1 (1978) 3–28.
D. Dubois and H. Prade, Possibility Theory, Plenum Press, New York and London (1988).
H.-J. Zimmermann, “Fuzzy programming and linear programming with several objective functions,” Fuzzy Sets and Systems 1 (1978) 45–56.
H. Tanaka and K. Asai, “Fuzzy linear programming problems with fuzzy numbers,” Fuzzy Sets and Systems 13 (1984) 1–10.
M. Inuiguchi, H. Ichihashi and H. Tanaka, “Fuzzy programming: A survey of recent development,” in: Stochastic versus Fuzzy Approaches to Multiple-Objective Mathematical Programming under Uncertainty, ed. by R. Slowinski and J. Teghem, Kluwer Academic Publishers, Netherlands (1990) 45–68.
W. Lipski, “On semantic issues connected to incomplete information in databases,” ACM Trans. on Database Systems 4 (1979) 262–296.
Z. Pawlak, “Rough classification,” Man-Machine Studies 20 (1984) 469–483.
L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning (I),” Inform. Sci. 8 (1975) 199–249.
H. Tanaka and H. Ishibuchi, “Evidence theory of exponential possibility distributions,” Int. J. of Approximate Reasoning 8 (1993) 123–140.
H. Tanaka and H. Ishibuchi, “Possibility analysis by exponential possibility distributions,” Fuzz-IEEE’93, San Francisco, Proc. II (1993) 1119–1124.
H. Tanaka, S. Uejima and K. Asai, “Linear regression analysis with fuzzy model,” IEEE Trans. SMC 12 (1982) 903–907.
H. Tanaka, “Fuzzy data analysis by possibilistic linear models,” Fuzzy Sets and Systems 24 (1987) 363–375.
H. Tanaka and J. Watada, “Possibilistic linear systems and their applications to the linear regression model,” Fuzzy Sets and Systems 27 (1988) 275–289.
H. Tanaka, I. Hayshi and J. Watada, “Possibilistic linear regression analysis for fuzzy data,” European J. Oper. Res. 40 (1989) 389–396.
J. Kacprzyk and M. Fedrizzi (Ed.), Fuzzy Regression Analysis, Omnitech Press, Warsaw (1992).
H. Tanaka and H. Ishibuchi, “Possibilistic regression analysis based on linear programming,” in: Fuzzy Regression Analysis, ed. by J. Kacprzyk and M. Fedrizzi, Omnitech Press, Warsaw (1992) 47–60.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Tanaka, H. (1996). Possibility Model and its Applications. In: Ruan, D. (eds) Fuzzy Logic Foundations and Industrial Applications. International Series in Intelligent Technologies, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1441-7_5
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1441-7_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8627-1
Online ISBN: 978-1-4613-1441-7
eBook Packages: Springer Book Archive