And that we derive the decreasing function or upper

And that we derive the decreasing function or upper ?-cut of the division of symmetric trapezoidal fuzzy random variables derived as follows
((“?” _”1″ “+” “?” _”1″ )/(“?” _”2″ “-” “?” _”2″ )-“X” )/(((“?” _”2″ -“?” _”2″ /”2″ )(“?” _”1″ ” + ” “?” _”1″ )-?”(?” ?_”2″ -“?” _”2″ “)(” “?” _”1″ ” + ” “?” _”1″ /”2″ “)” )/(?”(?” ?_”2″ -“?” _”2″ /”2″ “)(” “?” _”2″ -“?” _”2″ “)” )) ” ? ?”
(“?” _”1″ “+” “?” _”1″ )/(“?” _”2″ “-” “?” _”2″ )-“X ? ? ” ((“?” _”2″ -“?” _”2″ /”2″ )(“?” _”1″ ” + ” “?” _”1″ )-?”(?” ?_”2″ -“?” _”2″ “)(” “?” _”1″ ” + ” “?” _”1″ /”2″ “)” )/(?”(?” ?_”2″ -“?” _”2″ /”2″ “)(” “?” _”2″ -“?” _”2″ “)” )

(“?” _”1″ “+” “?” _”1″ )/(“?” _”2″ “-” “?” _”2″ )-“X ? ? ” (“( ” “?” _”1″ “?” _”2″ ” + ” “?” _”2″ “?” _”1″ “)” )/(?”(2?” ?_”2″ -“?” _”2″ “)(” “?” _”2″ -“?” _”2″ “)” )
– “X ? ” (“?” (” ” “?” _”1″ “?” _”2″ “+ ” “?” _”2″ “?” _”1″ )-?”(?” ?_”1″ “+” “?” _”1″ “)” ?”(2?” ?_”2″ -“?” _”2″ “)” )/(?”(2?” ?_”2″ -“?” _”2″ “)(” “?” _”2″ -“?” _”2″ “)” )
“P{((” ?”(X/Y)” ?_”?” ^”U” ” + ” (“(” “?” _”1″ “?” _”2″ (“? + 1″ )” + ” “?” _”2″ “?” _”1″ (“?” -“2” )-“2” “?” _”1″ “?” _”2″ ” + ” “?” _”1″ “?” _”2″ “)” )/(“(2” “?” _”2″ -“?” _”2″ “)(” “?” _”2″ -“?” _”2″ “)” ) ” ? 0}”
Which is the required decreasing function or upper ?- cut of the symmetric trapezoidal fuzzy random variable. Therefore, the membership function of division of two symmetric trapezoidal fuzzy random variable “(X/Y) ” is
“P{(” ?”(X/Y)” ?_”?” ^”L” -(“(” “?” _”1″ “?” _”2″ (“? + 1″ )” + ” “?” _”2″ “?” _”1″ (“?” -“2″ )” + 2″ “?” _”1″ “?” _”2″ -“?” _”1″ “?” _”2″ “)” )/(“(2” “?” _”2″ ” + ” “?” _”2″ “)(” “?” _”2″ ” + ” “?” _”2″ “)” ) ” ? 0″

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“? (” ?”(X/Y)” ?_”?” ^”U” ” + ” (“(” “?” _”1″ “?” _”2″ (“? + 1″ )” + ” “?” _”2″ “?” _”1″ (“?” -“2” )-“2” “?” _”1″ “?” _”2″ ” + ” “?” _”1″ “?” _”2″ “)” )/(“(2” “?” _”2″ -“?” _”2″ “)(” “?” _”2″ -“?” _”2″ “)” ) ” ? 0}”
The result of division of two symmetric trapezoidal fuzzy random variable is not a symmetric.
Hence, the proof.

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