CONSTRUCTION OF POSSIBILITY DISTRIBUTIONS FOR RELIABILITY ANALYSIS BASED ON POSSIBILITY THEORY

2004 ◽  
Author(s):  
XIN TONG ◽  
HONG-ZHONG HUANG ◽  
MING J. ZUO
Keyword(s):  
Reliability Analysis ◽  
Possibility Theory ◽  
Possibility Distributions

POSSIBILISTIC SONAR DATA MODELING FOR MOBILE ROBOTS

1999 ◽  
Vol 07 (02) ◽  
pp. 173-198 ◽  
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.

scholarly journals Characterizing and extending answer set semantics using possibility theory

2014 ◽  
Vol 15 (1) ◽  
pp. 79-116 ◽  
Author(s):  
KIM BAUTERS ◽  
STEVEN SCHOCKAERT ◽  
MARTINE DE COCK ◽  
DIRK VERMEIR
Keyword(s):  
Possibility Theory ◽  
Combinatorial Problems ◽  
The Body ◽  
Uncertain Information ◽  
Possibilistic Logic ◽  
Possibility Distributions ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractAnswer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.

scholarly journals ESTIMATIONS OF EXPECTEDNESS AND POTENTIAL SURPRISE IN POSSIBILITY THEORY

1994 ◽  
Vol 02 (04) ◽  
pp. 417-428 ◽  
Author(s):  
HENRI PRADE ◽  
RONALD R. YAGER
Keyword(s):  
Possibility Theory ◽  
Point Of View ◽  
Possibility Distribution ◽  
Owa Operators ◽  
Set Functions ◽  
Basic Set ◽  
Potential Applications ◽  
Possibility Distributions

This note investigates how various ideas of "expectedness" can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying "I would not be surprised that…" before an event takes place, or by saying "I knew it" after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of possibility of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined.

APPLICATION OF POSSIBILITY THEORY TO ROBUST COURNOT EQUILIBRIUM IN THE ELECTRICITY MARKET

2005 ◽  
Vol 19 (4) ◽  
pp. 519-531 ◽  
Author(s):  
F. A. Campos ◽  
J. Villar ◽  
J. Barquín
Keyword(s):  
Electricity Market ◽  
Imperfect Information ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Possibility Theory ◽  
Cournot Equilibrium ◽  
Theoretical Approaches ◽  
Cournot Game ◽  
Residual Demand ◽  
Possibility Distributions

It is known that Cournot game theory has been one of the theoretical approaches used more often to model electricity market behavior. Nevertheless, this approach is highly influenced by the residual demand curves of the market agents, which are usually not precisely known. This imperfect information has normally been studied with probability theory, but possibility theory might sometimes be more helpful in modeling not only uncertainty but also imprecision and vagueness. In this paper, two dual approaches are proposed to compute a robust Cournot equilibrium, when the residual demand uncertainty is modeled with possibility distributions. Additionally, it is shown that these two approaches can be combined into a bicriteria programming model, which can be solved with an iterative algorithm. Some interesting results for a real-size electricity system show the robustness of the proposed methodology.

scholarly journals RELIABILITY ANALYSIS OF EXISTING REINFORCED CONCRETE BEAMS ON NORMAL CRACK LENGTH CRITERION

2017 ◽  
Vol 13 (2) ◽  
pp. 56-63 ◽  
Author(s):  
Vladimir S. Utkin ◽  
Sergey A. Solovyev
Keyword(s):  
Reinforced Concrete ◽  
Crack Length ◽  
Reliability Analysis ◽  
Concrete Beams ◽  
Limit State ◽  
Possibility Theory ◽  
Technical Condition ◽  
Reinforced Concrete Beams ◽  
Numerical Examples ◽  
Tensile Zone

The article discusses a problem of the crack length influence on the reliability (safety) of reinforced concrete beams under conditions of limited statistical information about controlled parameters in the design mathematical models of limit state. Numerical examples revealed the possibility of practical application of the reliability analysis methods for inspections and determining the category of the technical condition of buildings and structures. The article offers the methods for reliability (probability of non-failure) analysis and the residual resource of reinforced concrete beams according to the criterion of the normal crack length in the tensile zone of reinforced concrete beams. The methods of reliability analysis constructed on the basis of possibility theory and fuzzy set theory. The algorithms of reliability analysis of reinforced concrete beams are presented on numerical examples of reliability analysis.

scholarly journals An Iterative Approach to Managing Uncertain Mappings in Dataspace Support Platforms

2014 ◽  
Vol 24 (04) ◽  
pp. 635-652 ◽  
Author(s):  
Nathalie Cindy Kuicheu ◽  
Ning Wang ◽  
Gile Narcisse Fanzou Tchuissang ◽  
De Xu ◽  
Guojun Dai ◽  
...  
Keyword(s):  
Possibility Theory ◽  
Experimental Results ◽  
Iterative Approach ◽  
Schema Mappings ◽  
Mapping Approach ◽  
Possibility Degree ◽  
Degree Function ◽  
Possibility Distributions

A DataSpace Support Platform (DSSP) is a self-sustained and self-managed system which needs to support uncertainty among its mediated schemas and its schema mappings. Some approaches for managing such uncertainty by assigning probabilities and reliability degrees to schema mappings have been proposed. Unfortunately, the number of mappings self-generated by a DSSP is usually too large and among those possible mappings, some might be totally correct and others partially correct. Therefore, providing probabilities or reliability degrees to the mappings is necessary but not sufficient to resolve uncertainty among them. This paper proposes a stepper-based approach called pos-mapping to managing reliable mappings using possibility theory. Instead of choosing a threshold for managing the reliable mappings, pos-mapping approach orders and divides the set of reliable mappings into subsets of possibility distributions and assigns to each of these subsets a recursive possibility degree function. The recursiveness of the possibility degree function leads to an incremental management of the possibility distributions. Experimental results show that our system is more efficient than the existing systems and the accuracy of the results increases with the number of reliable schemas in the DSSP.

Aggregation of Epistemic Uncertainty in Forms of Possibility and Certainty Factors

2020 ◽  
Vol 24 (1) ◽  
pp. 83-94
Author(s):  
Koichi Yamada ◽  
Keyword(s):  
Epistemic Uncertainty ◽  
Information Source ◽  
Possibility Theory ◽  
Source Model ◽  
New Combination ◽  
Combination Rule ◽  
Combination Rules ◽  
Possibility Distributions ◽  
New Interpretation ◽  
Sound Theoretical Basis

Uncertainty aggregation is an important reasoning for making decisions in the real world, which is full of uncertainty. The paper proposes an information source model for aggregating epistemic uncertainties about truth and discusses uncertainty aggregation in the form of possibility distributions. A new combination rule of possibilities for truth is proposed. Then, this paper proceeds to discussion about a traditional but seemingly forgotten representation of uncertainty (i.e., certainty factors (CFs)) and proposes a new interpretation based on possibility theory. CFs have been criticized because of their lack of sound mathematical interpretation from the viewpoint of probability. Thus, this paper first establishes a theory for a sound interpretation using possibility theory. Then it examines aggregation of CFs based on the interpretation and some combination rules of possibility distributions. The paper proposes several combination rules for CFs having sound theoretical basis, one of which is exactly the same as the oft-criticized combination.

scholarly journals A Possibilistic Portfolio Model with Fuzzy Liquidity Constraint

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Yunyun Sui ◽  
Jiangshan Hu ◽  
Fang Ma
Keyword(s):  
Turnover Rate ◽  
Possibility Theory ◽  
Expected Return ◽  
Asset Return ◽  
Liquidity Constraint ◽  
Fuzzy Variables ◽  
Asset Liquidity ◽  
Possibility Distributions ◽  
Investment Portfolios ◽  
Portfolio Selection Model

Investors are concerned about the reliability and safety of their capital, especially its liquidity, when investing. This paper sets up a possibilistic portfolio selection model with liquidity constraint. In this model, the asset return and liquidity are fuzzy variables which follow the normal possibility distributions. Liquidity is measured as the turnover rate of the asset. On the basis of possibility theory, we transform the model into a quadratic programming problem to obtain its solution. We illustrate that, in the process of investment, investors can make better use of capital by choosing their investment portfolios according to their expected return and asset liquidity.

Reliability Analysis of Crane Structure Based on Possibilistic Theory

2013 ◽  
Vol 321-324 ◽  
pp. 1784-1787
Author(s):  
Li Hong Gao ◽  
Shen Quan Liu ◽  
Jing Huang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Statistical Data ◽  
Possibility Theory ◽  
Structural Safety ◽  
Computational Error ◽  
Sample Collection ◽  
Reliability Method ◽  
Probability Methods ◽  
The Impact

With the increasing for crane in the industrial production, its structural reliability has now been an important concept to guarantee stable performances. The structural safety for the traditional stochastic and probabilistic reliability method is both measured with the viewpoint of probability. But large crane structure with low fault rate is often unable to get necessary statistic data. The new developing crane also has not large amount of statistical data due to no precedent of use. Aiming to these problems, the reliability analysis based on possibility theory is supplied. The method abandons two value state hypotheses, and can avoid a large number of sample collection and the impact of human factors. Compared with the probability methods applied to the crane structure, the possibility reliability method is not only feasible, but also reduces the computational error.

Rendering optimal design under various uncertainties

2019 ◽  
Vol 37 (1) ◽  
pp. 345-367
Author(s):  
Hui Lü ◽  
Kun Yang ◽  
Wen-bin Shangguan ◽  
Hui Yin ◽  
DJ Yu
Keyword(s):  
Reliability Analysis ◽  
Optimization Design ◽  
Design Method ◽  
Possibility Theory ◽  
Response Analysis ◽  
Analysis Method ◽  
Unified Framework ◽  
Central Difference ◽  
Content Type ◽  
Uncertain Variables

Purpose The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework. Design/methodology/approach Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases. Findings The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method. Originality/value Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

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