UGC NET CSE | June 2025 | Part 2 | Question: 37

Question

Which of the followings is not a valid property over two fuzzy relations $\tilde{R}$ and $\tilde{S}$ which must be obeyed for performing $\lambda$-cut defuzzifications?

• A. $(\tilde{R} \cup \tilde{S})_{\lambda}=\tilde{R}_{\lambda} \cup \tilde{S}_{\lambda}$
• B. $(\tilde{R} \cap \tilde{S})_{\lambda}=\tilde{R}_{\lambda} \cap \tilde{S}_{\lambda}$
• C. $(\bar{\widetilde{R}})_{\lambda} \neq \bar{R}_{\lambda}$ except when $\lambda=1$
• D. For any $\lambda \leq \beta$, where $0 \leq \beta \leq 1$, it is true that $R_{\beta} \subseteq R_{\lambda}$