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Note that is an continuous increasing function for, and (2.32).
(i there exist ordered topological space, increasing operator, and increasing operator such that ; (ii) is an continuous operator; (iii) is a demicontinuous MMC-operator; (iv),.
where is fuzzy coefficient, is the set of all upper semicontinuously convex fuzzy numbers on with, and are nonlinear regular fuzzy functions, is a nonlinear continuous function, is an continuous matrix such that is continuous for and with,, is a control function, is an initial value and are bounded functions,, where and represent the left and right limits of at, respectively.
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