INF

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References in periodicals archive ?
The interval solution is obtained by setting the supremum and infimum values of the previous solution, which are
(iii) The number [??] [member of] (0, [infinity]) attains the second infimum in (41).
Under Assumptions 1, 7, and 8, for any given [zeta] > 0, there exists a pair [mathematical expression not reproducible] which attains the infimum in (39).
Under Assumption 8, for any given [zeta] > 0, there exists a unique [??] = [[??].sub.[zeta]] [member of] B which attains the infimum in (68).
By Algorithm 7, the infimums of a1 and the average transmission intervals [bar.T] for different sampling period h are obtained and are listed in Table 1.
By Algorithm 7, the infimums 0.3561 and 0.3565 of [[sigma].sub.1] and [[sigma].sub.2] are obtained, respectively.
Often in the course of interval arithmetic, operations like multiplication and division produce infimum and supremum which are overestimations of the actual bounds of the interval extension.
Since abovementioned sets have been posets, we only need to prove that supremum and infimum of x, y exist.
Thereby, s, t are, respectively, supremum and infimum of x, y with respect to R[a] in A [a].
Thus x [[disjunction].sub.b] y is supremum with respect to [R.sup.(a)] of x, y in [A.sup.(a)] Analogously we can prove that infimum exists in [A.sup.(a)] too.
The fuzzy number valued outer measure for the fuzzy subset [mu] is defined as m*([mu]) = (0, [??]) where K = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the infimum is taken over all countable collection ([A.sub.n]) in [Omega] which cover X.
If [mu] is fuzzy set on X then m*([mu]) = (0, K), where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the infimum is taken over all sequences ([A.sub.n]) of sets in [[Omega].sub.1] such that X = [??] [A.sub.n].
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