GFRGGlass Fiber Reinforced Gypsum
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where [[mu].sub.GFRG] is the optimal GFRG value of predicted mean, [GFRG.sub.m] is the total mean of grey-fuzzy reasoning grade, [GFRG.sub.o] is the optimal mean grey-fuzzy reasoning grade for each level of factor, and q is the number of significant parameters affecting the grey-fuzzy reasoning grade.
Subsequently, the grey relational coefficients (GRCs) would be imported into fuzzy logic system to achieve a grey-fuzzy reasoning grade (GFRG) through (12)-(14).
As mentioned in Section 3, the nine fuzzy subsets were used for GRC of displacement, the three fuzzy subsets for GRC of frequency, and the nine fuzzy subsets for the output GFRG. The 27 fuzzy rules were then established in a matrix form for this study, as given in Table 7.
The last column gave the defuzzified grey-fuzzy reasoning grade (GFRG).
To sum up, Table 8 provides the difference sequences, grey relational coefficients, and GFRG for two responses.
The response graph for average GFRG at parameter level was plotted as in Figure 10.
The optimal results were corresponding to the 9th experiment with a highest GFRG of 0.625 (see Tables 6 and 8).
The estimated mean of the GFRG was determined by (15), and then 95% confidence interval of confirmation experiments ([CI.sub.CE]) was calculated using (16).
The confirmation value [[mu].sub.confirmation] of the GFRG should fall within the range as follows:
The experimental results of Table 11 revealed that the confirmation GFRG results fall within 95% of the [CI.sub.CE] (see (17)).
The GRCs were then imported into fuzzy logic system to achieve a grey-fuzzy reasoning grade (GFRG).
Caption: Figure 8: Membership function of output (GFRG).