d. *Membership function of ψ*~ð Þ *x*

The membership function of the fuzzy function *ψ*~ð Þ *x* is defined by:

$$\eta\_{\check{\boldsymbol{\nu}}(\boldsymbol{x})} = \begin{cases} \left(\check{\boldsymbol{\nu}}^{\boldsymbol{L}}\right)^{-1}(\boldsymbol{x}, \boldsymbol{\xi}\_{\boldsymbol{x}}) & \text{if } \check{\boldsymbol{\nu}}^{\boldsymbol{L}}(\boldsymbol{x}, \mathbf{0}) \leq \boldsymbol{\xi}\_{\mathbf{x}} \leq \check{\boldsymbol{\nu}}^{\boldsymbol{L}}(\boldsymbol{x}, \mathbf{1}) \\\\ \left(\check{\boldsymbol{\nu}}^{\boldsymbol{U}}\right)^{-1}(\boldsymbol{x}, \boldsymbol{\xi}\_{\mathbf{x}}) & \text{if } \check{\boldsymbol{\nu}}^{\boldsymbol{U}}(\boldsymbol{x}, \mathbf{1}) \leq \boldsymbol{\xi}\_{\mathbf{x}} \leq \check{\boldsymbol{\nu}}^{\boldsymbol{L}}(\boldsymbol{x}, \mathbf{0}) \\\ 0 & \text{otherwise} \end{cases} \tag{26}$$

$$\eta\_{\check{\boldsymbol{\nu}}(\boldsymbol{\varkappa})} = \begin{cases} \frac{\boldsymbol{\xi}\_{\boldsymbol{\varkappa}} - \bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, \cdot)}{\bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, 1) - \bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, 0)} & \text{if } \bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, 0) \leq \boldsymbol{\xi}\_{\boldsymbol{\varkappa}} \leq \bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, 1) \\\ \frac{\bar{\boldsymbol{\nu}}^{U}(\boldsymbol{\varkappa}, 0) - \boldsymbol{\xi}\_{\boldsymbol{\varkappa}}}{\bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, 0) - \bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, 1)} & \text{if } \bar{\boldsymbol{\nu}}^{U}(\boldsymbol{\varkappa}, 1) \leq \boldsymbol{\xi}\_{\boldsymbol{\varkappa}} \leq \bar{\boldsymbol{\nu}}^{L}(\boldsymbol{\varkappa}, 0) \\\ 0 & \text{otherwise} \end{cases} \tag{27}$$
