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The group membership equation (Eq. 11) could be modeled with the logistic distribution.
In particular, we use binary logit specifications of a union membership equation in our imputation model based on the complete data set for the years 1985 and 1989.
Results from the model show that the estimated coefficient of correlation between the cooperative membership equation and the consumption expenditure function is negative and significantly different from 0 for nonmembers of agricultural cooperatives.
As indicated before, if the correlations between the components and the group membership equation are zero (mathcal {M}_{3}) is identical to (mathcal {M}_{2}) and as a result the latter will provide very good starting values for the former.
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Therefore, using conventional sigmoidal membership function of Equations 13 and 14) to depict UD will be an appropriate choice.
Step 2: Calculate the linear membership functions in equations (10) and (11) for (DM_{11}) and (DM_{2f}), (forall f).
For ICM we use the probabilistic memberships p z| i) (equation 8 in Methods) and for HMoF we simply have the binary assignments.
Atomic sentences are equations or membership statements, and they are only well-formed if they take one of the forms xn = yn or xn ∈ yn+1.
Since this is a gradually changed procedure, we select commonly used Gaussian membership function defined in Equations 15 and 16 to model MC.
Finally, expert opinions were combined using Fuzzy Logic Theory for each relationship using the standard procedure aforementioned (i.e., membership functions specified by equations 1 to 5, Mamdani algorithm, sum method of aggregation, and centroid for defuzzification).
While the aim is to minimise the same error function E as in Equation 7, memberships are defined as μ ij = 1 ∀ x i ∈ c j ̲ 1 ∑ l = 1 C | | x i − m j | | | | x i − m l | | ) 2 / ( α − 1 ) ∀ x i ∈ c j b. (12).
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