Proportional Conflict Redistribution Research Articles

Fusion of Identification Information from ESM Sensors and Radars Using Dezert–Smarandache Theory Rules

This paper presents a method of fusion of identification (attribute) information provided by two types of sensors: combined primary and secondary (IFF) surveillance radars and ESMs (electronic support measures). In the first section, the basic taxonomy of attribute identification is adopted in accordance with the standards of STANAG 1241 ed. 5 and STANAG 1241 ed. 6 (draft). These standards provide the following basic values of the attribute identifications: FRIEND; HOSTILE; NEUTRAL; UNKNOWN; and additional values, namely ASSUMED FRIEND and SUSPECT. The basis of theoretical considerations is Dezert–Smarandache theory (DSmT) of inference. This paper presents and uses in practice six information-fusion rules proposed by DSmT, i.e., the proportional conflict redistribution rules (PCR1, PCR2, PCR3, PCR4, PCR5, and PCR6), for combining identification information from different ESM sensors and radars. This paper demonstrates the rules of determining attribute information by an ESM sensor equipped with the database of radar emitters. It is proposed that each signal vector sent by the ESM sensor contains an extension specifying a randomized identification declaration (hypothesis)—a basic belief assignment (BBA). This paper also presents a model for determining the basic belief assignment for a combined primary and secondary radar. Results of the PCR rules of sensor information combining for different scenarios of a radio electronic situation (deterministic and Monte Carlo) are presented in the final part of this paper. They confirm the legitimacy of the use of Dezert–Smarandache theory in information fusion for primary radars, secondary radars, and ESM sensors.

Fusing Landsat-8, Sentinel-1, and Sentinel-2 Data for River Water Mapping Using Multidimensional Weighted Fusion Method

River water extent is critical for understanding river discharge or its hydrological conditions. Although numerous methods have been proposed to map river water from either optical or synthetic aperture radar (SAR) remotely sensed images, uncertainties still exist broadly. In this study, we developed an image fusion method that integrates Landsat-8, Sentinel-1 and Sentinel-2 images simultaneously for river water mapping with two major steps. Firstly, a posterior probability support vector machine model was adopted to generate water probability maps from each individual image; and second, a Multi-dimensional Weighted Fusion Method (MDWFM) was developed to fuse these probability maps. Four reaches with different characteristics were selected as case study sites. High resolution aerial images were acquired and used as the reference to evaluate our results. We found the fusion process not only improves the quality of river water mapping, but also excludes the cloud interference. The fused river water maps become more reliable after the conflicts from difference images being solved by the proposed MDWFM method that contains a proportional conflict redistribution rule. The weighted root mean square difference was reduced to 0.066, and the Area Under the ROC curve reached up to 0.984. The Critical Success Index, Kappa Coefficient, and F-measure reached up to 0.810, 0.836 and 0.895, respectively. These stable and accurate river extent mapping results obtained through fusing multiple images with high spatial resolution (10 m) and short revisit interval (0.4~4.4 days) are of great significance for enriching the data and methodology of hydrological studies.

An ECR-PCR rule for fusion of evidences defined on a non-exclusive framework of discernment

In the research of uncertain information processing, Dempster-Shafer Theory (DST) provides a framework for dealing with uncertain information, where evidence is defined on a Frame of Discernment (FOD) consisting of mutually exclusive elements. However, the requirement of exclusiveness on FOD sometimes is not satisfied, as shown in Dezert-Smarandache Theory(DSmT), a derivative of DST. In DSmT, the non-exclusiveness is expressed by propositions’ intersection and the fusion of evidence is realized through a Proportional Conflict Redistribution (PCR) rule. In order to handle non-exclusive FODs, a new framework called D Number Theory (DNT) has been proposed recently, which quantifies the non-exclusive degree between propositions different from DSmT. In previous studies, an Exclusive Conflict Redistribution (ECR) rule has been designed in DNT to implement the fusion of evidence defined on a non-exclusive FOD, but there are some deficiencies in the ECR rule. In this paper, a new rule called ECR-PCR rule is proposed by combining the ECR and PCR rules to better implement the fusion of evidence defined on a non-exclusive FOD. Within the proposed rule, the definition of conflict utilizes the idea of ECR’s exclusive conflict, and the disposal of conflict is following the idea of PCR’s proportional redistribution. Properties of the ECR-PCR rule are presented. The effectiveness of the proposed new rule is verified through numerical examples and applications, in comparison with other fusion methods.

Multi-featured collective perception with Evidence Theory: tackling spatial correlations

Collective perception allows sparsely distributed agents to form a global view on a common spatially distributed problem without any direct access to global knowledge and only based on a combination of locally perceived information. However, the evidence gathered from the environment is often subject to spatial correlations and depends on the movements of the agents. The latter is not always easy to control and the main question is how to share and to combine the estimated information to achieve the most precise global estimate in the least possible time. The current article aims at answering this question with the help of evidence theory, also known as Dempster–Shafer theory, applied to the collective perception scenario as a collective decision-making problem. We study eight most common belief combination operators to address the arising conflict between different sources of evidence in a highly dynamic multi-agent setting, driven by modulation of positive feedback. In comparison with existing approaches, such as voter models, the presented framework operates on quantitative belief assignments of the agents based on the observation time of the options according to the agents’ opinions. The evaluated results on an extended benchmark set for multiple options (n>2) indicate that the proportional conflict redistribution (PCR) principle allows a collective of small size (N=20), occupying 3.5% of the surface, to successfully resolve the conflict between clustered areas of features and reach a consensus with almost 100% certainty up to n=5.

A Study on Human Learning Ability during Classification of Motion and Colour Visual Cues and Their Combination

Abstract The paper presents a study on the human learning process during the classification of stimuli, defined by motion and color visual cues and their combination. Because the classification dimension and the features that define each category are uncertain, we model the learning curves using Bayesian inference and more precisely the Normalized Conjunctive Consensus rule, and also on the base of the more efficient probabilistic Proportional Conflict Redistribution rule No 5 (pPCR5) defined within Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning. Our goal is to study how these rules succeed to model consistently both: human individual and group behaviour during the learning of the associations between the stimuli and the responses in categorization tasks varying by the amount of relevant stimulus information. The effect of age on this process is also evaluated.

A new approach to the application of conflict redistribution rule in Satellite Image Classification

Nowadays solution of different scientific problems using satellite images, generally includes a classification procedure. Classification is one of the most important procedures used in remote sensing, because it involves a lot of mathematical operations and data preprocessing. The processing of information and combining of conflicting data is a very difficult problem in classification tasks. Nowadays many classification methods are applied in remote sensing. Classification of conflicting data has been a key problem, both from a theoretical and practical point of view. But a lot of known classification methods can not deal with highly conflicted data and uncertainty. The main purpose of this article is to apply proportional conflict redistribution rule (PRC5) for satellite image classification in conditions of uncertainty, when conflicting sources of evidence give incomplete and vague information. This rule can process conflicting data and combine conflicting bodies of evidence (spectral bands). Proportional conflict redistribution rule can redistribute the partial conflicting mass proportionally on non-empty sets involved in the conflict. It was noticed, that this rule can provide a construction of aggregated estimate under conflict. It calculates all partial conflicting masses separately. It was also shown, that proportional conflict redistribution rule is the most mathematically exact redistribution of conflicting mass to non-empty set. But this rule consists of difficult calculation procedures. The more hypotheses and more masses are involved in the fusion, the more difficult is to implement proportional conflict redistribution rule, therefore special computer software should be used. It was considered an example of practical use of the proposed conflict redistribution rule. It also was noticed, that this new approach to the application of conflict redistribution rule in satellite image classification can be applied for analysis of satellite images, solving practical and ecological tasks, assessment of agricultural lands, classification of forests, in searching for oil and gas.

SYNTESIS OF GROUP DECISIONS IN THE PROBLEM OF ANALYSIS OF THE TECHNICAL CONDITION OF MILITARY-CIVILIAN OBJECTS

Context. Quite often, experts are involved in the process of diagnosis and monitoring the technical condition of buildings and structures, and in this case, situations might arise when expert data is generated under some specific types of uncertainty, and their possible combinations. This, in turn, necessitates the development of new approaches aimed at solving the problems of structuring and analytical processing of inaccurate, uncertain, fuzzy expert knowledge. Objective. The methodology for choosing the category of technical condition of construction objects, including buildings and structures, and ranking the corresponding construction objects within the given category of the technical condition according to their degree of danger (expected damage in the event of an emergency) has been proposed in this paper. The proposed approach is based on the expert assessment methods and the mathematical apparatus of the evidence theory, which allows operating correctly with data generated under uncertainty, incompleteness, and inaccuracy. In order to improve the quality of combination results, it is proposed to use one of the proportional conflict redistribution rules and determine the optimal evidence combination order based on metrics in evidence theory. Results. The paper proposes a methodology for the synthesis of group solutions for assessing the technical condition of civil, industrial and military-technical construction objects, and determining objects that primarily need maintenance or overhaul under complex forms of uncertainty and multi-alternatives. Application of the proposed methodology will allow rational distribution of available resources when planning preventive measures and carrying out repair work (overhaul, reconstruction, etc.) to increase the efficiency of their trouble-free operation. Conclusions. The methodology proposed in this study constitutes the theoretical basis for the design of decision support systems for monitoring the technical condition of residential and/or non-residential real estate (buildings, structures) for various purposes.

DSmT-Based Group DEMATEL Method with Reaching Consensus

The decision-making trial and evaluation laboratory (DEMATEL) method employs expert assessments expressed by crisp values to construct a group initial direct-relation (IDR) matrix. However, it tends to be a low-precision expression, especially in complex practical problems. Although significant efforts have been made to improve the DEMATEL method, these improvements tend to neglect individual characteristics and group consensus, resulting in unconvincing decision results. This study provides a Dezert–Smarandache theory-based group DEMATEL method with reaching consensus. In order to reasonably determine the group IDR matrix, basic belief assignment function is employed to extract expert assessments and the proportional conflict redistribution rule no.5 of DSmT is employed to make fusion to derive the temporary group IDR matrix. Moreover, the consensus measures at both expert level and pair-factors level are calculated to determine whether the acceptable consensus level has been reached or not. If the required consensus level is not reached, a feedback mechanism will be activated to help experts reach a consensus. A consensus group IDR matrix for the group DEMATEL can be obtained with the help of feedback mechanism, based on which an algorithm is summarized for the proposed method to identify major factors in a complex system. Finally, numerical comparison and discussion are introduced to verify the effectiveness and applicability of the proposed method and algorithm.

Secure multimodal biometric system based on diffused graphs and optimal score fusion

Biometric authentication systems offer potential advantages over traditional knowledge-based methods. However, most of the biometric systems which are extensively used lack template security and robustness. In order to address these issues, in this study, the authors have proposed a multimodal biometric system based on the combination of multiple modalities and optimal score level fusion. In addition, key features are introduced for each modality for generating cancellable biometric features. Features from individual traits are combined with corresponding key features to provide feature transformation. A robust template is generated by diffusion of individual transformed matrices using graph-based random walk cross-diffusion. In addition, individual classifier score is optimally fused using proposed multistage score level fusion model. Optimal belief masses for individual classifier are determined using cuckoo search optimisation. Wherein, optimal classifier beliefs are fused using DSmT based proportional conflict redistribution (PCR-6) rules. Experimental results demonstrate that optimal score fusion applied on cross-diffused features produce better results than existing state-of-the-art multimodal fusion schemes. On average of the outcome, equal error rate and accuracy achieved using the proposed method on four chimeric benchmarked datasets, are 2.32 and 98.316%.

Enhance the Performance of Back Propagation Algorithm Using Proportional Conflict Redistribution Rule for the Diagnosis of Hypertension

Enhance the Performance of Back Propagation Algorithm Using Proportional Conflict Redistribution Rule for the Diagnosis of Hypertension

Robust multimodal biometric system based on optimal score level fusion model

Multimodal biometric systems fuse information from multiple modalities to overcome limitations of individual classifiers. Score level fusion of multiple classifiers can effectively combine information from different modalities. However, most of the multimodal biometric systems are impaired by conflicting classifier scores under dynamic environment, which results in degradation in system's robustness and reliability. To address this, we propose a multimodal biometric system based on an optimal score level fusion model. The key idea of this work is to optimally integrate three complementary biometric traits namely iris, finger vein and fingerprint. For this, individual classifier performance is optimized using evolutionary Backtracking Search Optimization Algorithm (BSA). In addition, conflicting beliefs from individual classifiers are resolved using proportional conflict redistribution rules (PCR-6) to obtain a concurrent solution. The system exhibits optimal behaviour under dynamic environment through boosting or suppression of concurrent classifiers and resolving conflicts among discordant classifiers. The proposed biometric system is evaluated over chimeric multimodal datasets created from benchmark images. On an average, we achieve an accuracy of 98.43% and an EER of 1.57%. The proposed biometric system not only outperforms state-of-the-art techniques but also shows directions towards development of an expert multimodal biometric system.

Online Object Tracking via Novel Adaptive Multicue Based Particle Filter Framework for Video Surveillance

Multicue based object tracking frameworks have been extensively explored due to their numerous applications in the field of computer vision. However, the online adaptive fusion of multicue under scale and illumination variations, partial or full occlusion, background clutters and object deformation remains an open challenge problem. In order to address this, we propose an online visual tracking algorithm using adaptive integration of multicue in a particle filter framework. The particle level fusion process is modelled as Shafer’s model with a power set defined over two focal elements. Partial conflicting masses and conjunctive consensus among three cues are estimated for each evaluated particle. Partial conflicts among cues are redistributed using Dezert-Smarandache Theory (DSmT) based proportional conflict redistribution rules (PCR-6). Additionally, context sensitive transductive cues reliabilities are used for discounting the particle likelihoods for quick adaptation of tracker. In the proposed model, automatic boosting of good particles and suppression of low performing particles not only improves resampling process but also enhances tracker accuracy. Experimental validation over benchmarked video sequences reveals that the proposed multicue tracking framework outperforms state-of-the-art trackers under various dynamic environmental challenges.

A New PCR Combination Rule for Dynamic Frame Fusion

Dynamic frame fusion which is based on hybrid DSm model is an important problem in information fusion. But the traditional combination rules are mainly under fixed discernment frame (Shafer model and free DSm model) responding to static model. A new method for dynamic proportional conflict redistribution rules (dynamic PCR rules) based on hybrid DSm model is proposed for the shortness of classical dynamic PCR rules. In the new dynamic PCR rule, combination involved with empty set is defined as one kind to obtain more reasonable results. For the redistribution weight, the conjunction Basic belief assignment (BBA) and conflict redistribution BBA are both taken into account to raise the fusion precision. The effectiveness of revised dynamic PCR rule is studied and simulated in both aspect of fusion accuracy and calculation.

A fast combination method in DSmT and its application to recommender system.

In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs) to subjective probabilities (called Bayesian BBAs). This necessity occurs if one needs to embed the fusion result in a system based on the probabilistic framework and Bayesian inference (e.g. tracking systems), or if one needs to make a decision in the decision making problems. In this paper, we present a new fast combination method, called modified rigid coarsening (MRC), to obtain the final Bayesian BBAs based on hierarchical decomposition (coarsening) of the frame of discernment. Regarding this method, focal elements with probabilities are coarsened efficiently to reduce computational complexity in the process of combination by using disagreement vector and a simple dichotomous approach. In order to prove the practicality of our approach, this new approach is applied to combine users’ soft preferences in recommender systems (RSs). Additionally, in order to make a comprehensive performance comparison, the proportional conflict redistribution rule #6 (PCR6) is regarded as a baseline in a range of experiments. According to the results of experiments, MRC is more effective in accuracy of recommendations compared to original Rigid Coarsening (RC) method and comparable in computational time.

Online Signature Verification: To What Extent Should a Classifier be Trusted in?

To select the best features to model the signatures is one of the major challenges in the field of online signature verification. To combine different feature sets, selected by different criteria, is a useful technique to address this problem. In this line, the analysis of different features and their discriminative power has been researchers’ main concern, paying less attention to the way in which the different kind of features are combined. Moreover, the fact that conflicting results may appear when several classifiers are being used, has rarely been taken into account. In this paper, a score level fusion scheme is proposed to combine three different and meaningful feature sets, viz., an automatically selected feature set, a feature set relevant to Forensic Handwriting Experts (FHEs), and a global feature set. The score level fusion is performed within the framework of the Belief Function Theory (BFT), in order to address the problem of the conflicting results appearing when multiple classifiers are being used. Two different models, namely, the Denoeux and the Appriou models, are used to embed the problem within this framework, where the fusion is performed resorting to two well-known combination rules, namely, the Dempster-Shafer (DS) and the Proportional Conflict Redistribution (PCR5) one. In order to analyze the robustness of the proposed score level fusion approach, the combination is performed for the same verification system using two different classification techniques, namely, Ramdon Forests (RF) and Support Vector Machines (SVM). Experimental results, on a publicly available database, show that the proposed score level fusion approach allows the system to have a very good trade-off between verification results and reliability.

A Novel Decision Support for Composite Sketch Matching using Fusion of Probabilistic Neural Network and Dictionary Matching

Traditional pencil sketches drawn by skilled pencil sketch artists are a product of illustration based on exaggeration; there is always some amount of discrepancy between the description of eye-witnesses and depiction of the offender by the sketch artist. To overcome this difficulty, law enforcement agencies worldwide have started using composite sketches (sketches created using computer). Composite sketches have obviated the need of a skilled sketch artist. Composite sketches can be easily drawn by eyewitnesses using face design system software (SketchCop FACETTE) in a very short time period without any prior specialized software training. Matching composite sketches with photos available in database are still a challenging task. In this paper, a novel technique is proposed to match composite sketches with photos available in database. The key contribution of the proposed system in this paper is an efficient and novel methodology developed to match composite sketches with photos available in databases which could be used by law enforcement agencies. The photos taken from law enforcement agencies databases are passed to face detection module. On the detected faces and composite sketches, feature extraction and classification are performed using Multi-resolution uniform Local Binary Pattern (LBP) and Probabilistic Neural Network (PNN) to generate score 1. Similarly, on detected faces and composite sketches, feature extraction and classification are again performed using Dictionary Matching (DM) to generate score 2. The generated scores are collected using Dempster-Shafer (DS) theory and Proportional Conflict Redistribution rule no. 5 (PCR5). In this study, the authors have performed pilot testing of their technique and results of their analysis are presented to the readers. Keywords: Local binary pattern, probabilistic neural network, dictionary matching, SketchCop FACETTE, dempster-shafer, Proportional Conflict Redistribution.

Static versus Dynamic Data Information Fusion analysis using DDDAS for Cyber Security Trust

Abstract Information fusion includes signals, features, and decision -level analysis over various types of data including imagery, te xt, and cyber security detection. With the maturity of data processing, the e xplosion of big data, and the need fo r user acceptance; the Dynamic Data-Driven Application System (DDDAS) philosophy fosters insights into the usability of information systems solutions. In this paper, we e xp lore a notion of an adaptive adjustment of secure communication trust analysis that seeks a balance between standard static solutions versus dynamic -data driven updates. A use case is provided in determin ing trust for a cyber security scenario exp loring comparisons of Bayesian versus evidential reasoning for dynamic security detection updates. Using the evidential reasoning proportional conflict redistribution (PCR) method, we demonstrate improved trust for dynamically changing detections of denial of service attacks.

An evidence clustering DSmT approximate reasoning method for more than two sources

Due to the huge computation complexity of Dezert–Smarandache Theory (DSmT), its applications especially for multi-source (more than two sources) complex fusion problems have been limited. To get high similar approximate reasoning results with Proportional Conflict Redistribution 6 (PCR6) rule in DSmT framework (DSmT + PCR6) and remain less computation complexity, an Evidence Clustering DSmT approximate reasoning method for more than two sources is proposed. Firstly, the focal elements of multi evidences are clustered to two sets by their mass assignments respectively. Secondly, the convex approximate fusion results are obtained by the new DSmT approximate formula for more than two sources. Thirdly, the final approximate fusion results by the method in this paper are obtained by the normalization step. Analysis of computation complexity show that the method in this paper cost much less computation complexity than DSmT + PCR6. The simulation experiments show that the method in this paper can get very similar approximate fusion results and need much less computing time than DSmT + PCR6, especially, when the numbers of sources and focal elements are large, the superiorities of the method are remarkable.

ADAPTIVE MULTIMODAL BIOMETRIC FUSION ALGORITHM USING PARTICLE SWARM OPTIMIZATION AND BELIEF FUNCTIONS

In this paper, an adaptive multimodal biometric fusion algorithm is proposed. It is based on belief functions and Particle Swarm Optimization (PSO). The fusion is performed at the score level using belief functions such as Dempster Shafer, Yager, Proportional Conflict Redistribution and Dezert-Smarandache hybrid rules. A hybrid PSO is employed to select the best belief function and estimate its parameters. Several experiments have been conducted on BANCA dataset and a comparison between the well established methods has been performed. The preliminary results provide adequate motivation towards future research in the application of optimization techniques in the belief functions.

Driver behavior assessment based on the G-G diagram in the DVE system

This paper proposes a driving risk model based on the information given from the Driver-Vehicle-Environment (DVE) entities. It develops a two-level strategy to evaluate the driving risk. The first level aims to assess the risk locally in each entity and the second one concludes the global risk. The advantage of this approach is the simultaneous consideration of the parameters related to the DVE system regardless of information type (dynamic and static). It uses the Dempster-Shafer Theory (DST) for information fusion at each level. The approach uses Fuzzy Theory (FT) to design Basic Probability Assignment (BPA) functions, which is the significant part of the belief theory. The drivers’ information for the driver risk evaluation the age and gender. Two parameters in the Vehicle entity are used in the cases of lane keeping and a left/right turn scenarios with utilizing two different developed Fuzzy Inference Systems (FIS). The first system uses an Euclidean acceleration-norm and the velocity of the vehicle; while, the second one, uses lateral/longitudinal acceleration based on G-G diagram and a proposed risk indicator.The results of different scenarios validate the developed risk models using the sixth version of the Proportional Conflict Redistribution (PCR6) combination algorithm.