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Since the left-derivative is left continuous, we can find such that (for ): (3.55).
Then can be regarded as functions on which satisfy (i) is nondecreasing and left continuous; (ii) is nonincreasing and left continuous; (iii). . is nondecreasing and left continuous; is nonincreasing and left continuous;.
Since, and are positive fuzzy numbers, from Theorem 2.1 we have that,, and,, are left continues and so from (3.17), we get that are left continuous as well.
Let : is continuous at, left continuous at and exists, and is continuously differentiable at, and exist,.
(KM-4) is left continuous, for all.
Since, are left continuous from (3.17) and working inductively, we get that,, are also left continuous.
Similar(10)
This is well-defined only if the t-norm is left-continuous.
And T is ((d,g,alpha -left-continuous if it is ((d,alpha -left-continuousus at every point of X.
FA4.: (F x,A,cdot): [ 0,infty [, rightarrow [ 0,1 ] ) is a left-continuous function.
Under the assumptions of Proposition 3.1, the map (lambdarightarrow c_{lambda}) is nonincreasing and left-continuous.
Next we prove that E λ, F is left-continuous in λ ∈ ( 0, 1 ).
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