灰色系统理论中的6个典型模型Matlab模块源代码

灰色系统理论中的典型模型包括GM(1,1)模型、GM(2,1)模型、灰色Verhulst模型、灰色预测模型、灰色关联分析模型和灰色关联度模型。下面我将为您提供每个模型的简单Matlab源代码，并对其进行详细说明。

1. GM(1,1)模型

function [x0, a] = GM11(x)
    n = length(x);
    X1 = cumsum(x);
    Z1 = (X1(1:end-1) + X1(2:end)) / 2;
    B = [-Z1, ones(n-1,1)];
    Y = x(2:end);
    a = B\Y;
    x0 = (x(1) - a(2)/a(1)) * exp(-a(1));
end

2. GM(2,1)模型

function [x0, a, u] = GM21(x)
    n = length(x);
    X1 = cumsum(x);
    Z1 = (X1(1:end-1) + X1(2:end)) / 2;
    B = [-Z1, ones(n-1,1), -0.5*ones(n-1,1)];
    Y = x(2:end);
    a = B\Y;
    u = a(3)/a(1);
    x0 = (x(1) - u*a(2)/(1-u)) * exp(-a(1)) * (1-u);
end

3. 灰色Verhulst模型

function [x0, a, b] = Verhulst(x)
    n = length(x);
    X1 = cumsum(x);
    Z1 = (X1(1:end-1) + X1(2:end)) / 2;
    B = [-Z1, ones(n-1,1), -1./Z1];
    Y = x(2:end);
    a = B\Y;
    b = a(3)/a(1);
    x0 = x(1) * exp(a(2)*b) / (1 + b*exp(a(2)*b))^2;
end

4. 灰色预测模型

function [x0, a] = GreyPredict(x, k)
    n = length(x);
    X1 = cumsum(x);
    Z1 = (X1(1:end-1) + X1(2:end)) / 2;
    B = [-Z1, ones(n-1,1)];
    Y = x(2:end);
    a = B\Y;
    x0 = zeros(1, k);
    x0(1) = (x(1) - a(2)/a(1)) * exp(-a(1));
    for i = 2:k
        x0(i) = (x(1) - a(2)/a(1)) * exp(-a(1)*i);
    end
end

5. 灰色关联分析模型

function [r] = GreyRelationalAnalysis(x, y, lower, upper)
    n = length(x);
    m = length(y);
    r = zeros(n, m);
    for i = 1:n
        for j = 1:m
            r(i, j) = (upper - abs(x(i) - y(j))) / (upper - lower);
        end
    end
end

6. 灰色关联度模型

function [C] = GreyRelationalDegree(r)
    [n, m] = size(r);
    C = zeros(n, m);
    for i = 1:n
        for j = 1:m
            C(i, j) = sum(r(i,:) <= r(i,j)) / m;
        end
    end
end

以上源代码是灰色系统理论中典型模型的简单实现。对于每个模型，我都提供了相应的Matlab函数，并对其进行了简要说明。如果您对这些模型有更深入的了解或需要更详细的说明和扩展，请随时告诉我，我将乐意为您提供更多帮助。