Possibility Of Information Research Articles

CD-BFT: Canonical Decomposition-Based Belief Functions Transformation in Possibility Theory.

Based on subjective possibilistic semantics, an agent's subjective probability mass function is dominated by a qualitative Possibility Mass Function (PossMF), which can also be transformed into a unique consonant mass function. However, the existing transformation method cannot maintain the consistency of combination rules, i.e., fusing PossMFs and consonant mass functions with same information content, respectively, the results no longer maintain the reversible transformation. To address the above issue, a novel belief functions transformation is proposed, which can be interpreted based on both Smets' canonical decomposition and Pichon's canonical decomposition. The proposed method is validated based on consistency of combination rules, the least commitment principle, and its application in the fusion of information. In addition, based on the two canonical decompositions, we extend the transformation to possibilistic belief structure, and offer a new perspective of relationship between possibilistic information and evidential information.

A Possibilistic Information Fusion-Based Unsupervised Feature Selection Method Using Information Quality Measures

The main goal of most information quality (IQ)-based measures is to combine data provided by multiple information sources to enhance the quality of information essential for decision makers to perform their tasks. However, there is few work to fuse multi-source information from the perspective of possibility distribution (PD) and use IQ as the evaluation criteria for feature selection. The PD is one of important concepts in possibility theory, which is a generally acknowledged method for describing a kind of uncertain knowledge. In this paper, we propose a novel representation model of possibility distributions based on fuzzy multisets, namely, a possibility distribution information system (PDIS). Then, several IQ measures are defined in the PDIS, including Gini entropy, compatibility, conflict, credibility and separability degrees. In view of this, a minimal-separability-minimal-uncertainty-based unsupervised feature selection algorithm (UmSMU) is designed. The proposed UmSMU can sufficiently fuse multiple possibilistic information. Meanwhile, the selected features maintain as much information as possible while minimizing the uncertainty of information. The experimental results show that the proposed algorithm performs well, especially when it comes to selecting fewer features and improving performance.

A fuzzy/possibility approach for area coverage in wireless sensor networks

The literature approaches, devoted to sensor improve network coverage, are deterministic in terms of deployment environment and node configuration parameters. Nevertheless, this type of approaches has not proven to be very successful in uncertain deployment environments. This paper aims to deal with this issue using theories of uncertainty. We consider deployment environment’s imperfections and the characteristics of the sensor nodes. The selection of a minimum number of nodes for a minimum number of clusters to guarantee coverage in wireless sensor networks (WSNs) is uncertain. As a consequence, this paper proposes a hybrid Fuzzy-Possibilistic model to Schedule the Active/Passive State of Sensor nodes Strategy (FP-3SNS). This model helps to plan the scheduling of node states (Active/Passive) based on possibilistic information fusion to make a possibilistic decision for the node activation at each period. We evaluated our model (FP-3SNS) with (a) a running example (that shows the best choice of the active node with a probability of 0.81215); (b) a statistical evaluation (calculation of the confidence interface), where the average coverage reliability at 95% of FP-3SNS use is between (92.94, 96.27); and (c) a comparison with maximum sensing coverage region problem (MSCR), coverage maximization with sleep scheduling (CMSS), Spider Canvas Strategy, Semi-Random Deployment Strategy (SRDP), Probing Environment and Adaptive Sleeping with Location Information Protocol (PEAS-LI), and Variable Length Particle Swarm Optimization Algorithm with a Weighted Sum Fitness Function (WS-VLPSO). The simulation results highlight the benefits of using the fuzzy and possibility theories for treating the area coverage problem and the proposed model maintained a coverage between 99.99 and 90.00% for a significant period of time.

Designing Possibilistic Information Fusion—The Importance of Associativity, Consistency, and Redundancy

One of the main challenges in designing information fusion systems is to decide on the structure and order in which information is aggregated. The key criteria by which topologies are constructed include the associativity of fusion rules as well as the consistency and redundancy of information sources. Fusion topologies regarding these criteria are flexible in design, produce maximal specific information, and are robust against unreliable or defective sources. In this article, an automated data-driven design approach for possibilistic information fusion topologies is detailed that explicitly considers associativity, consistency, and redundancy. The proposed design is intended to handle epistemic uncertainty—that is, to result in robust topologies even in the case of lacking training data. The fusion design approach is evaluated on selected publicly available real-world datasets obtained from technical systems. Epistemic uncertainty is simulated by withholding parts of the training data. It is shown that, in this context, consistency as the sole design criterion results in topologies that are not robust. Including a redundancy metric leads to an improved robustness in the case of epistemic uncertainty.

Plant Leaf Disease Detection using Mean Possibilistic Fuzzy Local Information C-Means and Reweighted Linear Program Boost Classification Algorithms on Image Processing

Plant Leaf Disease Detection using Mean Possibilistic Fuzzy Local Information C-Means and Reweighted Linear Program Boost Classification Algorithms on Image Processing

A Redundancy Metric Set within Possibility Theory for Multi-Sensor Systems.

In intelligent technical multi-sensor systems, information is often at least partly redundant—either by design or inherently due to the dynamic processes of the observed system. If sensors are known to be redundant, (i) information processing can be engineered to be more robust against sensor failures, (ii) failures themselves can be detected more easily, and (iii) computational costs can be reduced. This contribution proposes a metric which quantifies the degree of redundancy between sensors. It is set within the possibility theory. Information coming from sensors in technical and cyber–physical systems are often imprecise, incomplete, biased, or affected by noise. Relations between information of sensors are often only spurious. In short, sensors are not fully reliable. The proposed metric adopts the ability of possibility theory to model incompleteness and imprecision exceptionally well. The focus is on avoiding the detection of spurious redundancy. This article defines redundancy in the context of possibilistic information, specifies requirements towards a redundancy metric, details the information processing, and evaluates the metric qualitatively on information coming from three technical datasets.

A universal approach to imprecise probabilities in possibility theory

Possibility theory is a computationally efficient framework for reasoning with imprecise probabilities. Before performing any possibilistic analysis, however, the (imprecise) probabilistic information about the experiment needs to be expressed in the form of a possibility distribution. In this paper, we propose a novel Imprecise Probability-to-Possibility Transformation. This method unifies many results in quantitative possibility theory concerning information modeling, data analysis, and the construction of joint distributions. Furthermore, we show how it enables new results about possibilistic information aggregation and how it may refine frequentist inference in (im-)precise statistical models. The approach is characterized by a clear distinction between the elementary events' well-known objective possibilities from quantitative possibility theory and the elementary events' subjective plausibilities, a reimagination of qualitative possibility measures, which helps overcome several non-uniqueness issues.

An intelligent quality-based approach to fusing multi-source possibilistic information

Recently, Yager and Petry were proposing a quality-based methodology to combine data provided by multiple probabilistic sources to improve the quality of information for decision-makers. This paper offers a sort of companion paper that adapts this methodology to possibilistic sources. Possibility theory is particularly well suited to cope with incomplete information from poor-data sources. The methodology and algorithms used for the probabilistic approach are adapted for the possibilistic case. Both approaches are then compared by the means of a numerical example and four experimental benchmark datasets: one, the IRIS data set, being data-poorer than the three other ones (Diabetes dataset, Glass dataset and Liver-disorder dataset). A vector representation is introduced for a possibility distribution as in the probabilistic case and, the Gini's formulation of entropy is being used. However, the Gini's entropy has to be used differently than with the probabilistic case. This has an impact on the selection of subsets. A fusion scheme is designed to select the best-quality subsets according to two information quality factors: quantity of information and source credibility. Results obtained from comparison of both approaches on the four experimental benchmarks confirm the superiority of the possibilistic approach in the presence of information scarcity or incompleteness.

Introduction of Local Spatial Constraints and Local Similarity Estimation in Possibilistic c-Means Algorithm for Remotely Sensed Imagery

This paper presents a unique Possibilistic c-Means with constraints (PCM-S) with Adaptive Possibilistic Local Information c-Means (ADPLICM) in a supervised way by incorporating local information through local spatial constraints and local similarity measures in Possibilistic c-Means Algorithm. PCM-S with ADPLICM overcome the limitations of the known Possibilistic c-Means (PCM) and Possibilistic c-Means with constraints (PCM-S) algorithms. The major contribution of proposed algorithm to ensure the noise resistance in the presence of random salt & pepper noise. The effectiveness of proposed algorithm has been analysed on random “salt and pepper” noise added on original dataset and Root Mean Square Error (RMSE) has been calculated between original dataset and noisy dataset. It has been observed that PCM-S with ADPLICM is effective in minimizing noise during supervised classification by introducing local convolution.

An Extension of Fuzzy Linguistic Summarization Considering Probabilistic Uncertainty

Linguistic summarization provides to express large volumes of quantitative data in easy understandable natural language based forms. While various methods have been recommended for linguistic summarization, there is not any approach for linguistic summarization where possibilistic and probabilistic uncertainties exist together in data. In this study, we establish a tie between Z-number concept and type-I and type-II quantified sentences in order to calculate the truth degree of a linguistic summary covering possibilistic and probabilistic information. The proposed approach employs copulas to obtain a joint probability distribution of the variables included in type-II quantified sentence.

A New Framework of Frequent Uncertain Subgraph Mining

Nowadays, frequent graph mining approaches are very popular in several applications and big data domains. However, some problems are still not solved and need more attention from researchers such as inexact subgraph matching when similarity among subgraphs is not totally proved. Furthermore, many research works dealt with structural graph matching, but a little attention was paid to semantic graph matching when graph vertices and/or edges are attributed and typed. Therefore, this paper proposes a new possibilistic flexible graph mining approach to discover similar subgraphs, by applying possibilistic similarity rather than using hard structural exact similarity. This novel approach is hybrid and uses two similarity measures. An approximate structural similarity function of graph edit distance function and a semantic vertices similarity function based on possibilistic information affinity function. Experimental evaluation was conducted on real datasets borrowed from various domains and tests have shown a highly superiority of our hybrid frequent subgraph mining approach by achieving a good time processing performance and simultaneously discovering more similar subgraphs.

Spatial Possibilistic Fuzzy C-Mean Segmentation Algorithm Integrated with Brain Mid-sagittal Surface Information

A normal human brain holds a high level of bilateral reflection symmetry. On the sagittal view, the brain can be separated into the left and the right hemispheres with approximately identical anatomical properties, so that symmetric mirror pixels have similar properties. As a result, the symmetry information can be used to enhance results of brain segmentation methods. In this paper, we introduced a new version of the Fuzzy C-Mean segmentation method, Symmetry Spatial Possibilistic FCM. SymSPFCM integrates symmetry information with SPFCM which is an extension of PFCM on 3D MR images, and uses the spatial information to calculate possibilistic values and fuzzy membership values. We added spatial and possibilistic information in order to solve the noise sensibility defect of FCM. To integrate the symmetry information, we first extracted the mid-sagittal surface using our proposed method. According to this method, inside each axial slice, a thin-plate spline surface was constructed and local optima were applied to fit this TPS surface to the brain data. Then, the symmetry degree of each symmetry pair was calculated. Finally, the membership values in SPFCM were updated based on the corresponding symmetric values. The efficiency of the proposed method, SymSPFCM, was evaluated using both simulated and real magnetic resonance images and was compared to the state-of-the-art methods. Our results showed images with different degrees of intensity non-uniformity and different levels of noise were segmented efficiently by the SymSPFCM.

Possibilities determine the combinatorial structure of probability polytopes

We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, given by linear equations together with non-negativity constraints on the variables.

The Information Principle

The conventional wisdom is that the concept of information is closely related to the concept of probability. In Shannon’s information theory, information is equated to a reduction in entropy—a probabilistic concept. In this paper, a different view of information is put on the table. Information is equated to restriction. More concretely, a restriction is a limitation on the values which a variable can take. The concept of a restriction is more general than the concept of a constraint and the concept of a probability distribution. There are three principal kinds of restrictions: possibilistic, probabilistic and bimodal. A bimodal restriction is a combination of possibilistic and probabilistic restrictions.Underlying the restriction-centered approach to information is what may be called the Information Principle. Briefly stated, the Information Principle has three parts. (a) Information=restriction. (b) There are three principal types of information: possibilistic information, probabilistic information and bimodal information. Bimodal information is a combination of possibilistic information and probabilistic information. (c) Possibilistic information and probabilistic information are underivable (orthogonal), in the sense that neither is derivable from the other.Information is all around us. And yet, there is widespread unawareness of the existence of the Information Principle. In particular, what is not recognized is that possibilistic information and probabilistic information are underivable (orthogonal). An important empirical observation is that propositions in a natural language are carriers of predominantly fuzzy possibilistic information (FPI) and fuzzy bimodal information (FBI). Existing systems of reasoning and computation—other than fuzzy logic—do not have the capability to reason and compute with fuzzy bimodal information.

Joint exploration of regional importance of possibilistic and probabilistic uncertainty in stability analysis

Stability analysis generally relies on the estimate of failure probability P. When information is scarce, incomplete, imprecise or vague, this estimate is imprecise. To represent epistemic uncertainty, possibility distributions have shown to be a more flexible tool than probability distributions. The joint propagation of possibilistic and probabilistic information can rely on more advanced techniques such as the classical random sampling of the cumulative probability distribution F and of the intervals from the possibility distributions π. The imprecise probability P is then associated with a random interval, which can be summarized by a pair of indicators bounding it. In the present paper, we propose a graphical tool to explore the sensitivity on these indicators. This is conducted by means of the contribution to sample probability of failure plot based on the ordering of the randomly generated levels of confidence associated with the quantiles of F and to the α-cuts of π. This presents several advantages: (1) the contribution of both types of uncertainty, aleatoric and epistemic, can be compared in a unique setting; (2) the analysis is conducted in a post-processing step, i.e. at no extra computational cost; (3) it allows highlighting the regions of the quantiles and of the nested intervals which contribute the most to the bounds of P. The method is applied on two case studies (a mine pillar and a steep slope stability analysis) to investigate the necessity for extra data acquisition on parameters whose imprecision can hardly be modelled by probabilities due to the scarcity of the available information (respectively the extraction ratio and the cliff geometry).

Possibilistic Information Flow Control for Workflow Management Systems

In workflows and business processes, there are often security requirements on both the data, i.e. confidentiality and integrity, and the process, e.g. separation of duty. Graphical notations exist for specifying both workflows and associated security requirements. We present an approach for formally verifying that a workflow satisfies such security requirements. For this purpose, we define the semantics of a workflow as a state-event system and formalise security properties in a trace-based way, i.e. on an abstract level without depending on details of enforcement mechanisms such as Role-Based Access Control (RBAC). This formal model then allows us to build upon well-known verification techniques for information flow control. We describe how a compositional verification methodology for possibilistic information flow can be adapted to verify that a specification of a distributed workflow management system satisfies security requirements on both data and processes.

Approaches to multistage one-shot decision making

In this research, multistage one-shot decision making under uncertainty is studied. In such a decision problem, a decision maker has one and only one chance to make a decision at each stage with possibilistic information. Based on the one-shot decision theory, approaches to multistage one-shot decision making are proposed. In the proposed approach, a decision maker chooses one state amongst all the states according to his/her attitude about satisfaction and possibility at each stage. The payoff at each stage is associated with the focus points at the succeeding stages. Based on the selected states (focus points), the sequence of optimal decisions is determined by dynamic programming. The proposed method is a fundamental alternative for multistage decision making under uncertainty because it is scenario-based instead of lottery-based as in the other existing methods. The one-shot optimal stopping problem is analyzed where a decision maker has only one chance to determine stopping or continuing at each stage. The theoretical results have been obtained.

Variable consistency and variable precision models for dominance-based fuzzy rough set analysis of possibilistic information systems

The dominance-based fuzzy rough set approach (DFRSA) is a theoretical framework that can deal with multi-criteria decision analysis of possibilistic information systems. While a set of comprehensive decision rules can be induced from a possibilistic information system by using DFRSA, generation of several intuitively justified rules is sometimes blocked by objects that only partially satisfy the antecedents of the rules. In this paper, we use the variable consistency models and variable precision models of DFRSA to cope with the problem. The models admit rules that are not satisfied by all objects. It is only required that the proportion of objects satisfying the rules must be above a threshold called a consistency level or a precision level. In the presented models, the proportion of objects is represented as a relative cardinality of a fuzzy set with respect to another fuzzy set. We investigate three types of models based on different definitions of fuzzy cardinalities including -counts, possibilistic cardinalities, and probabilistic cardinalities; and the consistency levels or precision levels corresponding to the three types of models are, respectively, scalars, fuzzy numbers, and random variables.

Importance identification for fault trees based on possibilistic information measurements

Subjective factors and nonlinear characteristics, inherent in the importance identification for a fault tree in the reliability and risk analysis, make it necessary for fuzzy or possibilistic approaches to accommodate the quantificational assessment of epistemic uncertainty in a practical problem when data and information are very limited. After investigating the intuitive interpretations, possibilistic information semantics, measure-theoretic terms and entropy-like models, a new axiomatic index of importance measure for fault trees is proposed based upon possibilistic information entropy, which adopts the possibilistic assumption in place of the probabilistic one. An example of the fault tree is provided along with the concordance analysis and other discussions. The more conservative numerical results of importance rankings that involve more choices could be viewed as “soft” fault identification under a certain expected value. Finally, possible extension to the evidence space and further research directions are discussed.

Uniqueness of reconstruction for Yager's t-norm combination of probabilistic and possibilistic knowledge

Often, about the same real-life system, we have both measurement-related probabilistic information expressed by a probability measure P(S) and expert-related possibilistic information expressed by a possibility measure M(S). To get the most adequate idea about the system, we must combine these two pieces of information. For this combination, R. Yager—borrowing an idea from fuzzy logic—proposed to use a t-norm f&(a,b) such as the product f&(a,b)=a· b, i.e., to consider a set function f(S)=f&(P(S),M(S)). A natural question is: can we uniquely reconstruct the two parts of knowledge from this function f(S)? In our previous paper, we showed that such a unique reconstruction is possible for the product t-norm; in this paper, we extend this result to a general class of t-norms. © 2011 Wiley Periodicals, Inc.