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This article is a contribution to papers applying two kinds of fuzzy arithmetics to analyze fuzzy queues characteristics, namely, fuzzy arithmetic based on Zadeh's extension principle and fuzzy arithmetic based on alpha-cuts and intervals arithmetic. The two arithmetics being compatible, the paper shows that without reference to arithmetic based on Zadeh's extension principle, fuzzy queues characteristics can be analyzed normally by an other technique called flexible $\alpha-cuts$ method following which all calculations are based only on alpha-cuts approach. To accomplish this task, the paper brings out all mathematical optimization programs contained in intervals arithmetic, which is one of ineluctable tools of $\alpha-cuts$ approach, and shows how these programs are solved progressively. To illustrate this approach, the expected customer waiting time and the expected customers number in a single server fuzzy retrial queue are computed at steady state through an example in the next to last section. |
