Possibilistic linear systems and their application to the linear regression model.

*(English)*Zbl 0662.93066The authors regard certain fuzzy equations as possibilistic equations. They illustrate that a possibility model is a new interpretation of fuzzy equations and deals with linear regression analysis formulated by possibilistic linear systems. It is shown that a possibilistic model is governed by a possibility measure in the same way as a probability model is governed by a probability measure. The main concerns of the authors are on properties of possibilistic linear systems and a new formulation of fuzzy linear regression analysis in the case of fuzzy data.

The possibilistic linear model can be used in the framework of interval analysis, whether the data are fuzzy or not.

The proposed theoretical results are illustrated by the example of the Yen rate exchange to the dollar.

The possibilistic linear model can be used in the framework of interval analysis, whether the data are fuzzy or not.

The proposed theoretical results are illustrated by the example of the Yen rate exchange to the dollar.

Reviewer: R.Vachnadze

##### MSC:

93E03 | Stochastic systems in control theory (general) |

62J05 | Linear regression; mixed models |

94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |

##### Keywords:

fuzzy numbers; possibilistic linear systems; possibility measure; fuzzy linear regression analysis
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\textit{H. Tanaka} and \textit{J. Watada}, Fuzzy Sets Syst. 27, No. 3, 275--289 (1988; Zbl 0662.93066)

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