Mathematical Theory Of Evidence Research Articles

Conditional dependencies in imprecise data handling

Experimental data are meant as instances of random variables. Stochastic distortions are empirically evaluated. Evaluations take form of histograms. Set of rectangle bins of a histogram can be converted to Gaussian like curve enabling exploration of a discernment point neighborhood. Transformation can be made using fuzzy systems concept. Empirical distributions at hand differ. Discrepancies introduce some kind of doubtfulness or ambiguity. Many modern applications embrace uncertainty as an important factor. New solutions include alternative approach towards modelling and processing uncertainty. Mathematical Theory of Evidence is useful and provides supporting measures on exploration of the conditional relationship that requires penetration of neighborhood of a random variable instance. In the paper transformations of probability density distributions using fuzzy sets are proposed. The aim of suggested conversion is to deliver locally injective function to obtain conditional relationships measures.

An Improved Dempster-Shafer Algorithm Using a Partial Conflict Measurement

Multiple evidences based decision making is an important functionality for computers and robots. To combine multiple evidences, mathematical theory of evidence has been developed, and it involves the most vital part called Dempster’s rule of combination. The rule is used for combining multiple evidences.

Combining the Previous Measure of Evidence to Educational Entrance Examination

Background and Objective: Educational entrance examination refers to the extent in selecting the student to enroll through admission into educational institution. It has an entire procedure administered to achieve from primary to higher education. However, not many researches were conducted using mathematical theory of evidence. This study aims to investigate the examination process about the admission into educational institutions using mathematical theory of evidence. Materials and Methods: The assessment on student's entrance examination through the effectiveness of Dempster-Shafer theory can be viewed with its significant contribution by combining the previous measure of evidence. Eight student's entrance examination results were proposed. Results: The result reveals that there were some significant findings in assessing the student's entrance examination using mathematical theory of evidence. Those were obtained degrees of belief of Computer Science with 76.4% for student 1, Computer Science with 64.2% for student 2, Computer Science with 75.4% for student 3, Computer Science with 80.3% for student 4, Computer Science with 67.4% for student 5, Computer Science with 57.1% for student 6, Islamic Studies with 26.3% for student 7, Computer Science with 62.5% for student 8. Conclusion: In this research, mathematical theory of evidence has been successfully developed to assess student's entrance examination and displaying the result of identification process.

Multi-Criteria Optimisation of Liquid Cargo Transport According to Linguistic Approach to the Route Selection Task

AbstractThe main aim of the paper is to present the possibility of use of the multi-criteria optimization method Analytical Hierarchy Process (AHP) to liquid cargo transportation by sea. Finding the optimal solution is not simple. There are many factors influencing the shipping process. In the case of liquid cargo, the most important thing is the safety of the crew, ship, and environment. Therefore, the Mathematical Theory of Evidence is introduced and used to determine the optimal path in terms of time and safety of transport. Moreover, the details of liquid cargo transport process are described with particular attention to ship to ship operations. Besides, the basic concept of the AHP method, steps of the algorithm are introduced. Finally, the multicriteria optimization of the transport of the liquid cargo from the Persian Gulf to Port of Gdansk is done. It is based on the experts′ opinions.

An Improved Dempster-Shafer Algorithm Using a Partial Conflict Measurement

Multiple evidences based decision making is an important functionality for computers and robots. To combine multiple evidences, mathematical theory of evidence has been developed, and it involves the most vital part called Dempster’s rule of combination. The rule is used for combining multiple evidences. However, the combined result gives a counterintuitive conclusion when highly conflicting evidences exist. In particular, when we obtain two different sources of evidence for a single hypothesis, only one of the sources may contain evidence. In this paper, we introduce a modified combination rule based on the partial conflict measurement by using an absolute difference between two evidences’ basic probability numbers. The basic probability number is described in details in Section 2 “Mathematical Theory of Evidence”. As a result, the proposed combination rule outperforms Dempster’s rule of combination. More precisely, the modified combination rule provides a reasonable conclusion when combining highly conflicting evidences and shows similar results with Dempster’s rule of combination in the case of the both sources of evidence are not conflicting. In addition, when obtained evidences contain multiple hypotheses, our proposed combination rule shows more logically acceptable results in compared with the results of Dempster’s rule.

Performance improvement of intrusion detection with fusion of multiple sensors

Intrusion detection has become a challenging task with the rapid growth in numbers of computer users. The present-day technology requires an efficient method to detect intrusion in the computer network system. Intrusion detection system is a classifier which collects evidences for the presence of intrusion and raises an alarm for any abnormalities present. However, the use of intrusion detection system encounters two major drawbacks: higher false alarm rate and lower detection rate; these limit the detection performance of intrusion detection system. A prospective approach for improving performance is through the use of multiple sensors/intrusion detection system. Evidence theory is a mathematical theory of evidence which is used to fuse evidences from multiple sources of evidence and outputs a global decision. The work in this paper discusses the limitations and issues with evidence theory and proposes a modified framework for fusion of alarms of multiple intrusion detection systems.

The Impact of the Reliability of Teleinformation Systems on the Quality of Transmitted Information

Abstract The work describes the impact the reliability of the information quality IQ for information and communication systems. One of the components of IQ is the reliability properties such as relativity, accuracy, timeliness, completeness, consistency, adequacy, accessibility, credibility, congruence. Each of these components of IQ is independent and to properly estimate the value of IQ, use one of the methods of modeling uncertainty. In this article, we used a hybrid method that has been developed jointly by one of the authors. This method is based on the mathematical theory of evidence know as Dempstera-Shafera (DS) theory and serial links of dependent hybrid named IQ (hyb).

Dempster's rule of combination

The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule corresponds intuitively to the pooling of evidence. As a special case, the rule yields a rule of conditioning which generalizes the usual rule for conditioning probability measures. The rule of combination was studied extensively, but only in the case of finite sets of possibilities, in the author's monograph A Mathematical Theory of Evidence. The present paper describes the rule for general, possibly infinite, sets of possibilities. We show that the rule preserves the regularity conditions of continuity and condensability, and we investigate the two distinct generalizations of probabilistic independence which the rule suggests.

On Nautical Observation Errors Evaluation

Mathematical Theory of Evidence (MTE) enables upgrading models and solving crucial problems in many disciplines. MTE delivers new unique opportunity once one engages possibilistic concept. Since fuzziness is widely perceived as something that enables encoding knowledge thus models build upon fuzzy platforms accepts ones skill within given field. At the same time evidence combining scheme is a mechanism enabling enrichment initial data informative context. Therefore it can be exploited in many cases where uncertainty and lack of precision prevail. In nautical applications, for example, it can be used in order to handle data feature systematic and random deflections. Theoretical background was discussed and computer application was successfully implemented in order to cope with erroneous and uncertain data. Output of the application resulted in making a fix and a posteriori evaluating its quality. It was also proven that it can be useful for calibrating measurement appliances. Unique feature of the combination scheme proven by the author in his previous paper, enables identifying measurement systematic deflection. Based on the theorem the paper aims at further exploration of practical aspects of the problem. It concentrates on reduction of hypothesis frame reduction and random along with systematic errors identifications.

The Mathematical Theory of Evidence and Measurement Uncertainty - Comparison of Measurement Results Expressed in Terms of Random-Fuzzy Variables

In the previous papers, it was shown how possibility distributions can be effectively employed to represent and propagate uncertainty in measurements. In particular, it was shown how the Random-Fuzzy variables (RFVs) can be effectively employed to represent a measurement result. The effects of the systematic and random contributions to uncertainty can be well identified in the RFV, and all confidence intervals at all confidence levels are provided, so that complete information about the measurement result is given. Moreover, this distinction also allows one to model the propagation of the systematic and the random contributions in two different ways, according to their different nature and different behavior when they combine.

The mathematical theory of evidence and measurement uncertainty - Expression and combination of measurement results via the random-fuzzy variables

The mathematical theory of evidence and measurement uncertainty - Expression and combination of measurement results via the random-fuzzy variables

The mathematical theory of evidence and measurement uncertainty

The concept of measurement uncertainty and the way it should be treated are considered by the "Guide to the Expression of Uncertainty in Measurement," known as GUM that follows an intrinsically probabilistic approach. Presently, the GUM has been universally accepted and its recommendations followed to associate an uncertainty value to the measured value. For this reason, in this paper, we start from the GUM and its fundamental concepts and definitions to introduce an interesting and promising generalization of these same concepts in terms of Theory of Evidence.

A Macroscopic Forecasting Framework for Estimating Socioeconomic and Environmental Performance of Intelligent Transport Highways

The anticipated introduction of new forms of intelligent transport systems (ITS) represents a significant opportunity for increased cooperative mobility and sociotechnical changes within the transport system. Although such technologies are currently technically feasible, various socioeconomic and environmental barriers impede their arrival. This paper uses a recently developed ITS performance assessment framework, i.e., Environmental Fusion (EnvFUSION), to perform dynamic forecasting of the performance for three key ITS technologies: active traffic management (ATM), intelligent speed adaptation (ISA), and an automated highway system (AHS) using a mathematical theory of evidence. A consequential lifecycle assessment (c-LCA) is undertaken, which forms part of a data fusion process using data from various sources. The models forecast improvements for the three ITS technologies in line with social acceptability, economic profitability, and major carbon reduction scenarios up to 2050 on one of the U.K.'s most congested highways. An analytical hierarchy process (AHP) and the Dempster-Shafer theory (DST) are used to weight criteria that form part of an intelligent transport sustainability index (ITSI). Overall performance is then synthesized. Results indicate that there will be a substantial increase in socioeconomic and emissions benefits, provided that the policies are in place and targets are reached, which would otherwise delay their realization.

Systematic Errors Handling with MTE

Mathematical Theory of Evidence (MTE)1,2 extended for possibilistic platform3,4 enables modelling and processing uncertainty. It enables upgrading new models and solving crucial problems in many disciplines. Evidence combining scheme as mechanism enriching initial data informative context is useful in many cases. In nautical applications, for example, it can be exploited in order to make a fix and evaluate its accuracy. MTE delivers new unique opportunity once one engages possibilistic concept. Approaches towards theoretical evaluation of tasks including imprecise nautical data were already proposed. Nevertheless one of important issue that is indication and evaluation of a measurement systematic error remain unexplored. In nautical practice in order to calculate fixed correction one has to know directions or distances to a landmarks. Engaging MTE apparatus in order to cope with random and systematic errors is the main topic of the paper.

On the Validity of Dempster's Fusion Rule and its Interpretation as a Generalization of Bayesian Fusion Rule

The purpose of this paper is to focus on and discuss both: (i) the validity of the Dempster's rule of combination and foundations of Dempster–Shafer theory and (ii) the real compatibility (or not) of the Dempster's rule with the Bayes fusion rule. We analyze and explain, on the basis of a generic example, the inconsistent behavior of the Dempster's rule of combination, introduced by Shafer in his mathematical theory of evidence, as a valid method to combine sources of information. We identify the cause and the effect of the dictatorial power behavior of this rule and of its impossibility to manage the conflicts between the sources no matter of their level. For comparison purpose, we present the respective solutions obtained by the more efficient proportional conflict redistribution rule number 5 proposed originally in Dezert–Smarandache theory framework. The inherent contradiction of Dempster–Shafer theory foundations is identified and proved. Then, a deep analysis of the compatibility of the Dempster's fusion rule with the Bayes fusion rule (from a fusion standpoint) is made on the basis of proposed new interesting formulation of the Bayes rule. We prove that the Dempster's rule does not behave as the Bayes fusion rule in general, because both methods deal very differently with the prior information when it is really informative (not uniform). Only in the very particular case where the basic belief assignments to combine are Bayesian and when the prior information is uniform (or vacuous), the Dempster's rule remains consistent with the Bayes fusion rule. It is proved, that in more general cases, the Dempster's rule is incompatible with the Bayes rule and it is not a generalization of the Bayes fusion rule.

MINIMIZATION OF MOBILE AD HOC NETWORKS ROUTING ATTACKS USING DS MATHEMATICAL THEORY

Mobile Ad hoc Networks (MANET) have been highly vulnerable to attacks due to the dynamic nature of its network infrastructure. Among these attacks, routing attacks have received considerable attention since it could cause the most devastating damage to MANET. Even though there exist several intrusion response techniques to mitigate such critical attacks, existing solutions typically attempt to isolate malicious nodes based on binary or naı¨ve fuzzy response decisions. However, binary responses may result in the unexpected network partition, causing additional damages to the network infrastructure, and naı¨ve fuzzy responses could lead to uncertainty in countering routing attacks in MANET. In this paper, we propose a risk-aware response mechanism to systematically cope with the identified routing attacks. Our risk-aware approach is based on an extended Dempster-Shafer mathematical theory of evidence introducing a notion of importance factors. In addition, our experiments demonstrate the effectiveness of our approach with the consideration of several performance metrics

Information technology of ranking of expert estimates on the basis of the theory of evidence

The article concerns the use of modern theories for the analysis of expert information. The results of our research in this area are presented. The main purpose of research is the development of techniques of analysis and aggregation of group expert estimates to solve the problems of ranking. The use of modern approaches of analysis of expert information allows us to take into consideration the forms of interaction of expert judgments, and some specific types of uncertainty, in the frameworks of which the experts’ estimates were formed. This article considers the technology of expert information processing on the basis of methods of mathematical theory of evidence, taking into account alternative techniques of evidence combining. The suggested technique allows to identify and analyze and only relevant alternatives or groups of alternatives. It can significantly reduce the time of the examination, and increase the efficiency of obtained expert information. We suggest the use of the technology for the formation of the collective opinion of an expert group in the case of inaccurate and incomplete expert information. The considered approach suggests new possibilities for the creation of information technologies of expert estimates structuring under conditions of uncertainty, which can be the basis of an automated decision-making support system

Wavelet‐based neural networks applied to automatic detection of road surface conditions using tire noise from vehicles.

The detection of road surface conditions is an important process in efficient road management. In particular, in snowy seasons, prior information about the road conditions such as an icy state, helps road users or automobile drivers to obviate serious traffic accidents. This paper proposes a novel approach for automatically detecting the states of the road surface from tire noises of vehicles. The method is based on a wavelet transform analysis, artificial neural networks, and the mathematical theory of evidence. The proposed method employs the wavelet transform using multiresolution signal decomposition techniques. The proposed classification is carried out in sets of multiple neural networks using learning vector quantization networks. The outcomes of the networks are then integrated using the voting decision‐making scheme. It seems then feasible to detect passively and readily the states of the surface, i.e., as a rule of thumb, the dry, wet, snowy, and slushy state, automatically.

Deriving Evidence Theoretical Functions in Multivariate Data Spaces: A Systematic Approach

The mathematical theory of evidence is a generalization of the Bayesian theory of probability. It is one of the primary tools for knowledge representation and uncertainty and probabilistic reasoning and has found many applications. Using this theory to solve a specific problem is critically dependent on the availability of a mass function (or basic belief assignment). In this paper, we consider the important problem of how to systematically derive mass functions from the common multivariate data spaces and also the ensuing problem of how to compute the various forms of belief function efficiently. We also consider how such a systematic approach can be used in practical pattern recognition problems. More specifically, we propose a novel method in which a mass function can be systematically derived from multivariate data and present new methods that exploit the algebraic structure of a multivariate data space to compute various belief functions including the belief, plausibility, and commonality functions in polynomial-time. We further consider the use of commonality as an equality check. We also develop a plausibility-based classifier. Experiments show that the equality checker and the classifier are comparable to state-of-the-art algorithms.

Combining classifiers for word sense disambiguation based on Dempster–Shafer theory and OWA operators

In this paper, we discuss a framework for weighted combination of classifiers for word sense disambiguation (WSD). This framework is essentially based on Dempster–Shafer theory of evidence [G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, 1976] and ordered weighted averaging (OWA) operators [R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man, and Cybernetics 18 (1988) 183–190] We first determine various kinds of features which could provide complementarily linguistic information for the context, and then combine these sources of information based on Dempster’s rule of combination and OWA operators for identifying the meaning of a polysemous word. We experimentally design a set of individual classifiers, each of which corresponds to a distinct representation type of context considered in the WSD literature, and then the discussed combination strategies are tested and compared on English lexical samples of Senseval-2 and Senseval-3.