Fuzzy sets : X = {0.2/a, 0.4/b, 1/c , 0.8/d, 0/e} Y = {0/a, 0.9/b, 0.3/c, 0.2/d, 0.1/e} - Draw the Fuzzy Graph of X and Y - Core, Cardinality, and Complement (X and Y respectively) - Union & Intersection of X and Y - the new set Z (alpha cut $X_{0.5}$)
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Fuzzy Graph of X and Y: The fuzzy graph of X and Y can be drawn on a graph where the x-axis represents the elements (a, b, c, d, e) and the y-axis represents the membership degree (ranging from 0 to 1). Each point on the graph represents the membership degree Show more…
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The sum of two fuzzy sets $A$ and $B$ is the fuzzy set $A \oplus B,$ where $d_{A \oplus B}(x)=$ 1$\wedge\left|d_{A}(x)+d_{B}(x)\right|$ itheir difference is the fuzzy set $A-B,$ where $d_{A-B}(x)=$ $0 \vee\left[d_{A}(x)-d_{B}(x)\right] ;$ and their eartesian produet is the fuzzy set $A \times B$ where $d_{A \times B}(x, y)=d_{A}(x) \wedge d_{B}(x) .$ Use the fuzzy sets $A=\{\text { Angelo } 0.4, \text { Bart }$ $0.7,$ Cathy 0.6$\}$ and $B=\{\operatorname{Dan} 0.3, \text { Elsie } 0.8, \text { Frank } 0.4\}$ to find each fuzzy set. $$ A \cup B^{\prime} $$
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The sum of two fuzzy sets $A$ and $B$ is the fuzzy set $A \oplus B,$ where $d_{A \oplus B}(x)=$ 1$\wedge\left|d_{A}(x)+d_{B}(x)\right|$ itheir difference is the fuzzy set $A-B,$ where $d_{A-B}(x)=$ $0 \vee\left[d_{A}(x)-d_{B}(x)\right] ;$ and their eartesian produet is the fuzzy set $A \times B$ where $d_{A \times B}(x, y)=d_{A}(x) \wedge d_{B}(x) .$ Use the fuzzy sets $A=\{\text { Angelo } 0.4, \text { Bart }$ $0.7,$ Cathy 0.6$\}$ and $B=\{\operatorname{Dan} 0.3, \text { Elsie } 0.8, \text { Frank } 0.4\}$ to find each fuzzy set. $$ A \cup B $$
The sum of two fuzzy sets $A$ and $B$ is the fuzzy set $A \oplus B,$ where $d_{A \oplus B}(x)=$ 1$\wedge\left|d_{A}(x)+d_{B}(x)\right|$ itheir difference is the fuzzy set $A-B,$ where $d_{A-B}(x)=$ $0 \vee\left[d_{A}(x)-d_{B}(x)\right] ;$ and their eartesian produet is the fuzzy set $A \times B$ where $d_{A \times B}(x, y)=d_{A}(x) \wedge d_{B}(x) .$ Use the fuzzy sets $A=\{\text { Angelo } 0.4, \text { Bart }$ $0.7,$ Cathy 0.6$\}$ and $B=\{\operatorname{Dan} 0.3, \text { Elsie } 0.8, \text { Frank } 0.4\}$ to find each fuzzy set. $$ A \cap B $$
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