By Bernhard Heinemann (auth.), Hector Geffner, Rui Prada, Isabel Machado Alexandre, Nuno David (eds.)

ISBN-10: 3540883088

ISBN-13: 9783540883081

ISBN-10: 3540883096

ISBN-13: 9783540883098

This publication constitutes the refereed complaints of the eleventh Ibero-American convention on synthetic Intelligence, IBERAMIA 2008, held in Lisbon, Portugal, in October 2008.

The forty six papers provided have been conscientiously reviewed and chosen from 147 submissions. The papers are prepared in topical sections on wisdom illustration; making plans and Scheduling; Constraint pride and Optimization; Probabilistic Reasoning; computer studying; Multiagent platforms; traditional Language Processing; clever info structures and NLP; Robotics; and functions.

**Read or Download Advances in Artificial Intelligence – IBERAMIA 2008: 11th Ibero-American Conference on AI, Lisbon, Portugal, October 14-17, 2008. Proceedings PDF**

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**Additional resources for Advances in Artificial Intelligence – IBERAMIA 2008: 11th Ibero-American Conference on AI, Lisbon, Portugal, October 14-17, 2008. Proceedings**

**Example text**

We now present some examples which show up the expressiveness of our logic and the applicability of the previous properties. Example 2. We continue with the Example 1, by assuming now that the time required by tasks (a), (b) and (c) are positive small, medium and large numbers, respectively. This means that: A Propositional Dynamic Logic Approach for Order of Magnitude Reasoning 17 Table 1. Deﬁnability of Properties PROPERTY DEFINED BY 0 + Eq = Eq 0 → [+Eq ]Eq pl + (ps ∪ pm ∪ pl) ⊆ pl pl? [+ps ∪ +pm ∪ +pm ]pl (pl + nm) ⊆ (ps ∪ pm ∪ pl) pl?

The membership function of a fuzzy number can be interpreted as a possibility distribution on the real numbers. This allows to deﬁne its expected value [10], given for a TFN N by E[N ] = 14 (n1 + 2n2 + n3 ). It coincides with the neutral A Study of Schedule Robustness for Job Shop with Uncertainty 33 scalar substitute of a fuzzy interval and the centre of gravity of its mean value [3]. It induces a total ordering ≤E in the set of fuzzy numbers [8], where for any two fuzzy numbers M, N M ≤E N if and only if E[M ] ≤ E[N ].

In this setting, it is impossible to predict what the exact time-schedule will be, because it depends on the realisation of the task’s durations, which is not known yet. Each fuzzy schedule 36 I. Gonz´ alez-Rodr´ıguez et al. corresponds to a crisp ordering of tasks and it is not until tasks are executed according to this ordering that we know their real duration and, hence, know the exact schedule, the a-posteriori solution with crisp job completion times and makespan. The practical interest of a solution to the fuzzy job shop would lie in the ordering of tasks that it provides a priori using the available incomplete information, which should yield good schedules in the moment of its practical use.

### Advances in Artificial Intelligence – IBERAMIA 2008: 11th Ibero-American Conference on AI, Lisbon, Portugal, October 14-17, 2008. Proceedings by Bernhard Heinemann (auth.), Hector Geffner, Rui Prada, Isabel Machado Alexandre, Nuno David (eds.)

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