Uncertainty in Soft Temporal Constraint Problems:A General Framework and Controllability Algorithms for the Fuzzy Case

TL;DR

This paper introduces a formal framework for handling uncertainty and preferences in temporal constraints, extending classical controllability notions to fuzzy preferences and providing efficient algorithms for controllability testing and plan execution.

Contribution

It generalizes controllability concepts to include fuzzy preferences in uncertain temporal problems and offers polynomial algorithms for testing and executing optimal plans.

Findings

Controllability testing complexity remains unchanged with fuzzy preferences.

Algorithms for checking controllability are efficient and tractable.

Optimal temporal plans can be generated under uncertainty with fuzzy preferences.

Abstract

In real-life temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (that is, strong, weak, and dynamic), which have been developed for uncertain temporal problems, can be generalized to handle preferences as well. After defining this general framework, we focus on problems where preferences follow the fuzzy approach, and with properties that assure tractability. For such problems, we propose algorithms to check the presence of the controllability properties. In particular, we show that in such a setting dealing simultaneously with preferences and uncertainty does not increase the complexity of controllability testing. We also develop a dynamic execution algorithm, of polynomial complexity, that produces temporal plans under uncertainty that are optimal with respect to fuzzy preferences.