zbMATH — the first resource for mathematics

Exponential possibility regression analysis. (English) Zbl 0842.62062
Summary: This paper aims at giving the application of possibility theory based on exponential distributions to regression analysis. A general outline of the possibility theory is illustrated by exponential possibility distributions. It is shown that possibility analysis is well corresponding to statistical analysis. Using exponential possibility analysis, we propose possibility regression analysis which is suitable for rough phenomena arising from social and economic systems. The spread of the given data can be directly transferred into the exponential possibility distribution of coefficients in the regression model by the proposed method.

62J99 Linear inference, regression
62J02 General nonlinear regression
62J05 Linear regression; mixed models
Full Text: DOI
[1] Bandemer, H., Evaluating explicit functional relationship from fuzzy observations, Fuzzy sets and systems, 16, 41-52, (1985) · Zbl 0582.62066
[2] Celmins, A., Least squares model Fitting to fuzzy vector data, Fuzzy sets and systems, 22, 245-269, (1987) · Zbl 0636.62111
[3] Celmins, A., Multidimensional least-squares Fitting of fuzzy models, Math. modelling, 9, 669-689, (1987) · Zbl 0636.62111
[4] Diamond, P., Least squares Fitting of several fuzzy variables, (), 329-331
[5] Diamond, P., Fuzzy least squares, Inform. sci., 46, 141-157, (1988) · Zbl 0663.65150
[6] Dubios, D.; Prade, H., Possibility theory, (1988), Plenum New York
[7] Schemerling, S.; Bandemer, H., Transformation of fuzzy interval data into the parameter region of an explicit functional relationship, Freiberger forschungshefte, 91-100, (1985) · Zbl 0587.62145
[8] Tanaka, H., Fuzzy data analysis by possibilistic linear models, Fuzzy sets and systems, 24, 363-375, (1987) · Zbl 0633.93060
[9] Tanaka, H.; Hayashi, I.; Watada, J., Possibilistic linear regression analysis for fuzzy data, European J. oper. res., 40, 389-396, (1989) · Zbl 0669.62054
[10] Tanaka, H.; Ishibuchi, H., Identification of possibilistic linear systems by quadratic membership functions, Fuzzy sets and systems, 41, 145-160, (1991) · Zbl 0734.62072
[11] Tanaka, H.; Ishibuchi, H., Possibilistic regression analysis based on linear programming, (), 47-60
[12] Tanaka, H.; Ishibuchi, H., Evidence theory of normal possibility distributions, Approximate reasoning, 8, 123-140, (1993) · Zbl 0778.68083
[13] Tanaka, H.; Uejima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE trans. SMC, 12, 903-907, (1982) · Zbl 0501.90060
[14] Tanaka, H.; Watada, J., Possibilistic linear systems and their application to the linear regression model, Fuzzy sets and systems, 27, 275-289, (1988) · Zbl 0662.93066
[15] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning I, Inform. sci., 8, 199-249, (1975) · Zbl 0397.68071
[16] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1977) · Zbl 0377.04002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.