Framework Of Dempster-Shafer Theory Research Articles

Fractal-based basic probability assignment: A transient mass function

Effectively measuring the information content of Basic Probability Assignments (BPA) is a crucial prerequisite for addressing uncertain information within the framework of Dempster-Shafer theory. In previous research, uncertainty and dissimilarity measures for BPAs were often treated separately to counteract the impact of incomplete mutual exclusion between focal elements. In this paper, we introduce a Transient Mass Function (TMF) based on the process of pignistic probability transformation to forge a link between probabilistic and evidential information. As a transient state of BPA, the TMF not only considers the structural features of the focal element but also maintains its numerical content. Carrying out probabilistic information measures on the TMF is equivalent to performing belief information measures on the original BPA. Finally, validated by numerical simulations, TMF provides a unified and effective metric framework for evidential information.

Belief and plausibility measures on pythagorean fuzzy sets and its applications with BPI-VIKOR

Fuzzy sets (FSs) with belief and plausibility measures in Dempster-Shafer theory (DST) are recognized as different methodology to model imperfect, uncertain, and vague information more accurately than probability. Various generalizations of DST to FSs are suggested in the numerous literatures but the generalization of DST to Pythagorean fuzzy sets (PFSs) has not yet been considered so far. In this paper, we first suggest an intuitive and simple way to develop a generalization of DST to PFSs with the characterization of belief function in terms of membership function and plausibility function in terms of 1-nonmemberhip function respectively. We give the interpretation of belief and plausibility on PFSs and then construct belief-plausibility intervals (BPIs) of PFSs. On the basis of suggested BPIs, we use Hausdorff distance to describe the distance between two BPIs and then construct several similarity measures in the generalized context of DST to PFSs. By utilizing the method of VIekriterijumsko KOmpromisno Rangiranje (VIKOR), the suggested belief and plausibility measures on PFSs in the framework of DST enable us to develop a belief-plausibility VIKOR (BP-VIKOR) to manage multicriteria decision-making (MCDM) problems related to daily life settings. Numerical analysis with examples are given to show the suggested method is reasonable, and suitable in the environment of PFSs in the context of generalization of DST.

Power Muirhead mean operators of interval-valued intuitionistic fuzzy values in the framework of Dempster–Shafer theory for multiple criteria decision-making

Multiple criteria decision-making (MCDM) based on interval intuitionistic fuzzy value (IVIFV) is a process of aggregating decision criteria represented by multiple interval-valued intuitionistic fuzzy numbers to select the optimal alternative. Among them, an aggregation operator is an indispensable tool, and the properties of an aggregation operator directly affect the decision results. Existing aggregation operators based on IVIFV have satisfactory results in eliminating the correlation between criteria and removing the influence of outliers on the results. However, there are some unreasonable results due to some undesired properties of IVIFVs. In this paper, IVIFV operation under the Dempster-Shafer theory (DST) framework is applied to combine the power average and Muirhead mean operators and interval intuitionistic fuzzy power Muirhead mean operators under DST framework are presented. Then a method based on the presented operators for MCDM problems is proposed. Finally, a set of numerical experiments are conducted to demonstrate the proposed method. The experimental results suggest that the proposed method not only retains the robustness of the power average operator and the capability of the Muirhead mean operator, but also eliminates a shortcoming that existing interval intuitionistic fuzzy operators cannot handle the case where the weights are in IVIFVs.

BIM-AFA: Belief information measure-based attribute fusion approach in improving the quality of uncertain data

Information modeling and handling in uncertain environments is an important topic in the field of modern artificial intelligence. In practical applications of classification problems, the data harvested by the agent is usually not precise. Based on multi-valued mapping of probabilities expressed by Basic Probability Assignment (BPA), Dempster-Shafer Theory (DST) has a strong ability to model and handle uncertain information. In this paper, we propose a method of fusing attributes to enhance the quality of uncertain data under the framework of DST. The fusion method is based on proposed uncertainty and dissimilarity measures, which performs consistent transformations on belief information in DST. We simulate uncertain data by adding different noises to precise datasets and classify the improved data using common classifiers. With the increasing uncertainty degree of data, the proposed method has higher accuracy and robustness than other methods.

An evidential MULTIMOORA approach to assessing disaster risk reduction education strategies under a heterogeneous linguistic environment

Reducing the losses caused by disasters and strengthening the construction of public security are the key measures for achieving sustainable development. The lack of public awareness of emergency preparedness poses a serious obstacle to the realization of this goal, and as a result of it, emergency management urgently needs to pay attention to disaster risk reduction (DRR) education. The selection of disaster risk reduction education strategies (DRRESs) is crucial for promoting DRR knowledge and cultivating the DRR ability of citizens. Therefore, this study proposes a comprehensive strategy evaluation method based on Dempster-Shafer theory (DST) and the MULTIMOORA method in a heterogeneous linguistic environment. To comprehensively evaluate the performance of DRRESs, an evaluation index system containing three levels of criteria is constructed, providing a powerful basis for strategy assessment. To flexibly express evaluators’ cognition and judgement of strategies, this study allows evaluators to use various linguistic expressions. Furthermore, to calculation in the evaluation process convenient, different linguistic representations are unified as the basic probability assignment (BPA) in DST, and the effective aggregation of multi-expert information is realized based on the idea of evidence fusion. The MULTIMOORA method is introduced into the DST framework, and an evidential MULTIMOORA approach is proposed to realize the multi-dimensional evaluation of DRRESs from different perspectives. Finally, an empirical analysis of the proposed evaluation method is conducted with a practical DRRES selection problem as the case. The consistency of the evaluation results with the real selection illustrates the validity of this study. Furthermore, several management suggestions are proposed to improve the formulation and implementation of DRRESs through in-depth analysis of the evaluation results.

An Approach to Generalization of the Intuitionistic Fuzzy Topsis Method in the Framework of Evidence Theory

Abstract A generalization of technique for establishing order preference by similarity to the ideal solution (TOPSIS) in the intuitionistic fuzzy setting based on the redefinition of intuitionistic fuzzy sets theory (A IFS) in the framework of Dempster-Shafer theory (DST) of evidence is proposed. The use of DST mathematical tools makes it possible to avoid a set of limitations and drawbacks revealed recently in the conventional Atanassov’s operational laws defined on intuitionistic fuzzy values, which may produce unacceptable results in the solution of multiple criteria decision-making problems. This boosts considerably the quality of aggregating operators used in the intuitionistic fuzzy TOPSIS method. It is pointed out that the conventional TOPSIS method may be naturally treated as a weighted sum of some modified local criteria. Because this aggregating approach does not always reflects well intentions of decision makers, two additional aggregating methods that cannot be defined in the framework of conventional A IFS based on local criteria weights being intuitionistic fuzzy values, are introduced. Having in mind that different aggregating methods generally produce different alternative rankings to obtain the compromise ranking, the method for aggregating of aggregation modes has been applied. Some examples are used to illustrate the validity and features of the proposed approach.

Developed cosine similarity measure on belief function theory: An application in medical diagnosis

In this study, we consider a new aspect of belief function or Dempster-Shafer theory to define a belief set and cosine similarity measure between two belief sets under uncertainty. For this purpose, firstly, the concept of belief sets will be represented as a triple vector space that is characterized by truth-belief degree, uncertainty-belief degree; and falsity-belief degree. Then, the cosine similarity measure between two belief sets is proposed to determine the degree of similarity between them. This measure is directly defined upon the framework of Dempster-Shafer theory without switching by other theories. Finally, an application of a new method in the decision-making process is provided in the medical diagnosis, when values were presented on the structure of belief set. Furthermore, a numerical example of the medical diagnosis is presented to show the effectiveness and flexibility of the proposed method.

Belief and Plausibility Measures on Intuitionistic Fuzzy Sets with Construction of Belief-Plausibility TOPSIS

Belief and plausibility measures in Dempster–Shafer theory (DST) and fuzzy sets are known as different approaches for representing partial, uncertainty, and imprecise information. There are several generalizations of DST to fuzzy sets proposed in the literature. But, less generalization of DST to intuitionistic fuzzy sets (IFSs), that can somehow present imprecise information better than fuzzy sets, was proposed. In this paper, we first propose a simple and intuitive way to construct a generalization of DST to IFSs with degrees of belief and plausibility in terms of degrees of membership and nonmembership, respectively. We then give belief and plausibility measures on IFSs and construct belief-plausibility intervals (BPIs) of IFSs. Based on the constructed BPIs, we first use Hausdorff metric to define the distance between two BPIs and then establish similarity measures in the generalized context of DST to IFSs. By employing the techniques of ordered preference similarity to ideal solution (TOPSIS), the proposed belief and plausibility measures on IFSs in the framework of DST enable us to construct a belief-plausibility TOPSIS for solving multicriteria decision-making problems. Some examples are presented to manifest that the proposed method is reasonable, applicable, and well suited in the environment of IFSs in the framework of generalization of DST.

An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval

It is still an open issue to measure uncertainty of the basic probability assignment function under Dempster-Shafer theory framework, which is the foundation and preliminary work for conflict degree measurement and combination of evidences. This paper proposes an improved belief entropy to measure uncertainty of the basic probability assignment based on Deng entropy and the belief interval, which takes the belief function and the plausibility function as the lower bound and the upper bound, respectively. Specifically, the center and the span of the belief interval are employed to define the total uncertainty degree. It can be proved that the improved belief entropy will be degenerated to Shannon entropy when the the basic probability assignment is Bayesian. The results of numerical examples and a case study show that its efficiency and flexibility are better compared with previous uncertainty measures.

Evidence updating with static and dynamical performance analyses for industrial alarm system design

In the Dempster–Shafer theory (DST) of evidence, the alarm evidence updating-based method can effectively deal with the uncertainty of the monitored process variable so as to significantly reduce the false alarm rates (FAR) and missed alarm rates (MAR) of the industrial alarm system. But the price of the decrease of FAR and MAR is the increase of the averaged alarm delay (AAD). In order to obtain better comprehensive performance, besides the accuracy indices (FAR and MAR), the sensitivity index (AAD) should be considered simultaneously in the alarm system parameter optimization design. In the framework of DST, firstly, this paper defines the static and dynamical performance indices in the alarm evidence space which are compatible with FAR/MAR/AAD in the process variable space. But the former can measure the performance of the DST-based alarm systems more naturally and elaborately than the latter; secondly, a systematic parameter optimization design procedure for the alarm system is investigated by using these new indices and the tradeoff among them. Finally, two typical numerical experiments and an industrial case are provided to illustrate the effectiveness of the static and dynamical indices for improving the comprehensive performance of the DST-based alarm systems.

Multi-Attribute Decision Making Based on Intuitionistic Fuzzy Power Maclaurin Symmetric Mean Operators in the Framework of Dempster-Shafer Theory

It is well known that there are some unfavorable shortcomings in the ordinary operational rules (OORs) of intuitionistic fuzzy number (IFN), and there exists a close and forceful connection between the intuitionistic fuzzy set (IFS) and Dempster-Shafer Theory (DST). We can utilize this relationship to present a transparent and fruitful semantic framework for IFS in terms of DST. In the framework of DST, an IFN can be converted into a basic probability assignment (BPA) and operations on IFNs can be represented as operations on a belief interval (BI), which can break away from the revealed shortcomings of the OORs of the IFN. Although there are many operators to aggregate the IFN, the operator to aggregate the BPA is rare. The Maclaurin symmetric mean (MSM) operator has the advantage of considering interrelationships among any number of attributes. The power average (PA) operator can reduce the influences of extreme evaluation values. In addition, for measuring the difference between IFNs, we replace the Hamming distance and Euclidean distance with the Jousselme distance (JD). In this paper, we develop an intuitionistic fuzzy power MSM (IFPMSMDST) operator and an intuitionistic fuzzy weighted power MSM (IFPWMSMDST) operator in the framework of the DST and provide their favorable properties. Then, we propose a novel method based on the proposed operators to solve multi-attribute decision-making (MADM) problems without intermediate defuzzification when their attributes and weights are both IFNs. Finally, some examples are utilized to demonstrate that the proposed methods outperform the previous ones.

EFMCDM: Evidential fuzzy multicriteria decision making based on belief entropy

Multicriteria decision making (MCDM) has become one of the most frequently applied decision making methodologies in various fields. However, uncertainty is inevitably involved in the process of MCDM due to the subjectivity of humans. To address this issue, a novel evidential fuzzy MCDM method, called EFMCDM, is proposed by integrating Dempster-Shafer theory with belief entropy. In particular, each criterion can be modeled as evidence, and all the alternatives compose the frame of discernment in the framework of Dempster-Shafer theory. To generate more appropriate basic probability assignments (BPAs) of the criteria, the EFMCDM method considers both the subjective and objective weighting of the criteria that are leveraged in MCDM problems. Thereafter, the classic Dempster's rule of combination is leveraged to fuse the multiple pieces of evidence into composite evidence. On this basis, the alternatives are ranked to determine the optimal alternative. In addition, the EFMCDM method can quantitatively model uncertainty and help to decrease the uncertainty caused by subjective human cognition to improve decision making. Finally, the rationality, effectiveness, and robustness of the EFMCDM method are demonstrated through experimental evaluations.

The operations on interval-valued intuitionistic fuzzy values in the framework of Dempster–Shafer theory

This work was motivated by the revealed limitations and drawbacks of the classical definition of interval-valued intuitionistic fuzzy set (IVIFS) proposed by Atanassov and Gargov and operations on interval-valued intuitionistic fuzzy values (IVIFV). It is shown that the classical definition of Atanassov’s IVIFS may lead to controversial results. Therefore, a new more constructive definition of IVIFS is proposed. It is shown that this new definition makes it possible to present IVIFVs in the framework of Dempster–Shafer theory (DST) as belief intervals with bounds presented by belief intervals. A new set of operations on IVIFVs in the framework of DST is proposed. It is proved that these operations provide IVIFVs in the sense of new definition of interval-valued intuitionistic fuzzy set. A critical analysis of commonly used operations for comparison of intuitionistic fuzzy values and IVIFVs is made. As a result, a new more justified operation for comparison of IVIFVs in the framework of interval extended Dempster–Shafer theory is proposed. It is proved that introduced set of operations on IVIFVs is free of revealed limitations and drawbacks of commonly used operations based on the classical definition of Atanassov’s IVIFS. The corresponding methods for aggregation of local criteria presented by interval-valued intuitionistic fuzzy values in the framework of interval-extended Dempster–Shafer theory are proposed and analysed. The proposed approach makes it possible to introduce the new interval-valued intuitionistic weighted geometric operators for the cases when the weighs are presented by intuitionistic and IVIFVs. These operators are not defined in the framework of classical approach.

Distance Function of D Numbers Based on Exclusive Degree

The mathematical framework of Dempster-Shafer theory is based on some strong hypotheses regarding the frame of discernment and basic probability assignment, which limit the ability of it to represent some types of information. To overcome the shortcomings, a novel theory called D numbers theory is proposed. In this paper, a new distance function of D numbers based on exclusive degree is proposed to measure the distance between two D numbers. The proposed function is an generalization of distance between two BPAs, which inherits the advantage of Dempster-Shafer theory and strengthens the capability of uncertainty modeling. When the exclusive degree between each pair of D numbers equals to 1, the proposed function can be degenerated as the distance function defined by Anne-Laure Jousselme.

A new approach to the rule-base evidential reasoning in the intuitionistic fuzzy setting

A new approach to the rule-base evidential reasoning based on the synthesis of fuzzy logic, Atannasov’s intuitionistic fuzzy sets theory and the Dempster-Shafer theory of evidence is proposed. It is shown that the use of intuitionistic fuzzy values and the classical operations on them directly may provide counter-intuitive results. Therefore, an interpretation of intuitionistic fuzzy values in the framework of Dempster-Shafer theory is proposed and used in the evidential reasoning. The merits of the proposed approach are illustrated with the use of developed expert systems for diagnostics of type 2 diabetes. Using the real-world examples, it is shown that such an approach provides reasonable and intuitively obvious results when the classical method of rule-base evidential reasoning cannot produce any reasonable results.

TREATING UNCERTAINTIES IN A NUCLEAR SEISMIC PROBABILISTIC RISK ASSESSMENT BY MEANS OF THE DEMPSTER-SHAFER THEORY OF EVIDENCE

The analyses carried out within the Seismic Probabilistic Risk Assessments (SPRAs) of Nuclear Power Plants (NPPs) are affected by significant aleatory and epistemic uncertainties. These uncertainties have to be represented and quantified coherently with the data, information and knowledge available, to provide reasonable assurance that related decisions can be taken robustly and with confidence. The amount of data, information and knowledge available for seismic risk assessment is typically limited, so that the analysis must strongly rely on expert judgments. In this paper, a Dempster-Shafer Theory (DST) framework for handling uncertainties in NPP SPRAs is proposed and applied to an example case study. The main contributions of this paper are two: (i) applying the complete DST framework to SPRA models, showing how to build the Dempster-Shafer structures of the uncertainty parameters based on industry generic data, and (ii) embedding Bayesian updating based on plant specific data into the framework. The results of the application to a case study show that the approach is feasible and effective in (i) describing and jointly propagating aleatory and epistemic uncertainties in SPRA models and (ii) providing ‘conservative’ bounds on the safety quantities of interest (i.e. Core Damage Frequency, CDF) that reflect the (limited) state of knowledge of the experts about the system of interest.

Combining sources of evidence with reliability and importance for decision making

The combination of sources of evidence with reliability has been widely studied within the framework of Dempster-Shafer theory (DST), which has been employed as a major method for integrating multiple sources of evidence with uncertainty. By the fact that sources of evidence may also be different in importance, for example in multi-attribute decision making (MADM), we propose the importance discounting and combination method within the framework of DST to combine sources of evidence with importance, which is composed of an importance discounting operation and an extended Dempster’s rule of combination. Three evidence combination axioms are proposed and explored to uncover the differences between reliability and importance in evidence reasoning. Furthermore, a general scheme is proposed for combination of sources of evidence with both reliability and importance. An example of car performance evaluation is studied to show the efficiency of the new general scheme.

Multimodal Remote Sensing Data Fusion via Coherent Point Set Analysis

We present a novel fusion algorithm for electronic-reconnaissance (ER) satellite and optical imaging satellite data using coherent point set (CPS) analysis. This work is motivated by a large-scale maritime surveillance problem, where ship groups in the observations are of particular interest for tactical and strategic operations. Fusion of observations from ER satellite and optical imaging satellite is a challenging task. On the one hand, dense and continuous measurement is not available for optical imagery. On the other hand, it is difficult to extract robust features from ER measurements. Considering that the size of a ship is often less than the distance among different ships, we treat each ship as a mass point. The contributions of our work are threefold. First, multisensor data fusion is accomplished by CPS association. To the best of our knowledge, this letter is the first to investigate CPS for multimodal remote sensing data fusion. Second, a novel geometry descriptor, which encodes the topological characteristics of a point set, is presented. Third, we combine both topological features and attributive features within the framework of Dempster-Shafer theory for CPS analysis. The proposed method has been tested using different sets of simulated data and recorded data. Experimental results demonstrate the effectiveness of the proposed method.

Modeling partially reliable information sources: A general approach based on Dempster–Shafer theory

Combining testimonial reports from independent and partially reliable information sources is an important epistemological problem of uncertain reasoning. Within the framework of Dempster-Shafer theory, we propose a general model of partially reliable sources, which includes several previously known results as special cases. The paper reproduces these results on the basis of a comprehensive model taxonomy. This gives a number of new insights and thereby contributes to a better understanding of this important application of reasoning with uncertain and incomplete information.