Applications of Possibility Theory to Ocean Surveillance Correlation

Abstract This paper compares probabilistic and possibility-based methods for design against catastrophic failure under uncertainty. It studies the effect of the amount of information on the effectiveness of each method. The study is confined to problems where the boundary between survival and failure is sharp. First, the paper examines the theoretical foundations of probability and possibility. It also compares the two methods when they are used to assess the risk of a system. Finally, it compares the two methods on two design problems. A major difference between probability and possibility is in the axioms about the union of events. Because of this difference, probability and possibility calculi are fundamentally different and one cannot simulate possibility calculus using probabilistic models. It is shown that possibility-based methods can be less conservative than probability-based methods in systems with many failure modes. On the other hand, possibility-based methods tend to be more conservative than probability-based methods in systems that fail only if many unfavorable events occur simultaneously. Probabilistic methods are better than possibility-based methods if sufficient information is available. However, the latter can be better if little information is available. A principal reason is that it is easier to identify the most conservative possibilistic model than the most conservative probabilistic model that is consistent with the available information.

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New Semantics for Quantitative Possibility Theory

Lecture Notes in Computer Science - Symbolic and Quantitative Approaches to Reasoning with Uncertainty ◽

10.1007/3-540-44652-4_36 ◽

2001 ◽

pp. 410-421 ◽

Cited By ~ 26

Author(s):

Didier Dubois ◽

Henri Prade ◽

Philippe Smets

Keyword(s):

Possibility Theory

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Possibility theory in hydrology and water management

Journal of Hydrology and Hydromechanics ◽

10.2478/v10098-010-0008-y ◽

2010 ◽

Vol 58 (2) ◽

Cited By ~ 1

Author(s):

Karel Nacházel ◽

Pavel Fošumpaur

Keyword(s):

Water Management ◽

Possibility Theory

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POSSIBILISTIC SONAR DATA MODELING FOR MOBILE ROBOTS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488599000118 ◽

1999 ◽

Vol 07 (02) ◽

pp. 173-198 ◽

Cited By ~ 2

Author(s):

K. DEMIRLI ◽

M. MOLHIM ◽

A. BULGAK

Keyword(s):

Probability Theory ◽

Mobile Robots ◽

Data Modeling ◽

Possibility Theory ◽

Sensor Design ◽

Map Building ◽

Sonar Sensors ◽

New Models ◽

Possibility Distributions ◽

Target Characteristics

Sonar sensors are widely used in mobile robots applications such as navigation, map building, and localization. The performance of these sensors is affected by the environmental phenomena, sensor design, and target characteristics. Therefore, the readings obtained from these sensors are uncertain. This uncertainity is often modeled by using Probability Theory. However, the probablistic approach is valid when the available knowledge is precise which is not the case in sonar readings. In this paper, the behavior of sonar readings reflected from walls and corners are studied, then new models of angular uncertainty and radial imprecision for sonar readings obtained from corners and walls are proposed. These models are represented by using Possibility Theory, mainly possibility distributions.

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