Abstract
The raw value of the normal yield of rice is estimated by a multiple regression of the actual yield on the year effect and damage rate. The final normal yield is determined from the raw value taking in opinions of experts concerned. However, there are several theoretical problems in the present estimation procedure. We propose that the estimation of the normal yield should be based on the base yield defined as the sum of the actual yield and the amount of damage. The base yield is the yield that could be obtained if there were no damage. It is expected to vary smoothly. However, it does not always so in the actual data. We set up the hypothesis H1 that the trend of base yield changes at some year in accordance with some qualitative change in the cultivation method, varieties, and so on, and the hypothesis H1' that there exists the systematic error in estimating of the degree of damage against the null hypothesis H0 that the trend varies smoothly. We applied a fuzzy model with fuzzy rules taking the form that if ~ then ~. The best fitted hypothesis (number of rules) to data was assessed by AIC. This procedure was applied to the yearly data from 1970 to 1989 in all Japan, Hokkaido and Kouchi Pref. The hypothesis H1' with two fuzzy rules was adopted in the case of all Japan and Hokkaido. The different trend of the base yield was apparent between the cases where the degree of damage was `small' and `large'. On the other hand, H1 with two non-fuzzy rules was adopted in the case of Kouchi Pref. It was shown that the trend of the base yield may change at 1976. When H1 is adopted, we propose that the estimation of the normal yield is obtained by subtracting normal values of the amount of damage under respective rules from the trend of the base yield. On the other hand, when H1' is adopted, we assume that there exists the systematic error in estimating of the degree of damage in the case where the degree of damage is `large'. We propose that the estimation of the normal yield is obtained by subtracting the normal value of the amount of damage revised on the systematic error from the trend of the base yield revised on the systematic error.
