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I have given $\alpha$ in the interval $[0,1]$ and the $\beta$ interval $[0,1]$ and the condition is $\bigcap \alpha: \alpha\lt\beta [μ]\alpha = [μ]\beta$ How do I evaluate this condition to check for the condition? $μ$ is the membership function of the fuzzy set. Any help would be appreciated.

Additional info: my function is $\alpha = [1-\sqrt{\ln(\frac 1 {\alpha})}, 1+\sqrt{\ln(\frac 1 {\alpha})}]$ if $\alpha\gt0 = \mathbb{R}$ , if $\alpha = 0$ I have considered values from $0.1$ to $0.9$ and obtained different intervals for the above function but cannot validate the condition. In a way, I do not understand how to evaluate the intersection condition. Additionally, this is a representation theorem for the system of sets for alpha cuts. Hope this information is sufficient.

user12986714
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ranjir
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  • Would you like to share what you have tried/thought of so far? – user12986714 May 05 '20 at 19:09
  • So basically, my function is Aα = [1-√ln(1/α), 1+√ln(1/α)] if α >0 = ℝ , if α = 0 I have considered values from 0.1 to 0.9 and obtained different intervals for the above function but cannot validate the condition. In a way, I do not understand how to evaluate the intersection condition. Additionally, this is a representation theorem for the system of sets for alpha cuts. Hope this information is sufficient. – ranjir May 05 '20 at 19:18
  • Would you like to edit the question body to include that information? People usually vote to close questions before reading the comments. – user12986714 May 05 '20 at 19:19
  • Hope this helps, I'm new to this community. – ranjir May 05 '20 at 19:21

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