A new method of conflicting evidence management based on non-extensive entropy and Lance distance in uncertain scenarios

Handing uncertain information is one of the research focuses currently. For the sake of great ability of handing uncertain information, Dempster-Shafer evidence theory (D-S theory) has been widely used in various fields of uncertain information processing. However, when highly contradictory evidence appears, the results of the classical Dempster combination rules (DCR) can be counterintuitive. Aiming at this defect, by considering the relationship between the evidence and its own characteristics, the proposed method is a new method of conflicting evidence management based on non-extensive entropy and Lance distance in uncertain scenarios. Firstly, the Lance distance function is used to measure the degree of discrepancy and conflict between evidences, and the credibility of evidence is expressed by matrix. Introducing non-extensive entropy to measure the amount of information about evidence and express the uncertainty of evidence. Secondly, the discount coefficient of the final fusion evidence is measured by considering the credibility and uncertainty of the evidence, and the original evidence is modified by the discount coefficient. Then, the final result is obtained by evidence fusion with DCR. Finally, two numerical examples are provided to illustrate the efficiency of the proposed method, and the utility of our work is demonstrated through an application of the active lane change to avoid obstacles to the autonomous driving of new energy vehicles. The proposed method has a better identification accuracy, reaching 0.9811.

Conflicting evidence combination based on Belief Mover’s Distance

The Dempster-Shafer evidence theory has been extensively used in various applications of information fusion owing to its capability in dealing with uncertain modeling and reasoning. However, when meeting highly conflicting evidence, the classical Dempster’s combination rule may give counter-intuitive results. To address this issue, we propose a new method in this work to fuse conflicting evidence. Firstly, a new evidence distance metric, named Belief Mover’s Distance, which is inspired by the Earth Mover’s Distance, is defined to measure the difference between two pieces of evidence. Subsequently, the credibility weight and distance weight of each piece of evidence are computed according to the Belief Mover’s Distance. Then, the final weight of each piece of evidence is generated by unifying these two weights. Finally, the classical Dempster’s rule is employed to fuse the weighted average evidence. Several examples and applications are presented to analyze the performance of the proposed method. Experimental results manifest that the proposed method is remarkably effective in comparison with other methods.

Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.

Possibility belief interval-valued soft set and its application in decision making

The aim of this article is to present the concept of restricted union and extended intersection of belief interval-valued soft sets, along with its properties. In addition, we propose the concept of possibility belief interval-valued soft set theory and investigate their properties. For suitability of possible applications, there are seven kinds of operations (e.g., union, intersection, restricted union, extended intersection, complement, soft max-AND, and soft min-OR) on the possibility belief interval-valued soft sets are defined and their basic theoretical are given. Then, we construct two algorithms by using soft max-AND and soft min-OR operations of possibility interval-valued soft sets for fuzzy decision-making problem. Lastly, we introduce an algorithm using a possibility interval-valued soft set to solve the decision-making problems and clarify its applicability by a numerical example.

Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system

Multi-sensor data fusion plays an irreplaceable role in actual production and application. Dempster-Shafer theory (DST) is widely used in numerous fields of information modeling and information fusion due to the flexibility and effectiveness of processing uncertain information and dealing with uncertain information without prior probabilities. However, when highly contradictory evidence is combined, it may produce results that are inconsistent with human intuition. In order to solve this problem, a hybrid method for combining belief functions based on soft likelihood functions (SLFs) and ordered weighted averaging (OWA) operators is proposed. More specifically, a soft likelihood function based on OWA operators is used to provide the possibility to fuse uncertain information compatible with each other. It can characterize the degree to which the probability information of compatible propositions in the collected evidence is affected by unknown uncertain factors. This makes the results of using the Dempster's combination rule to fuse uncertain information from multiple sources more comprehensive and credible. Experimental results manifest that this method is reliable. Example and application show that this method has obvious advantages in solving the problem of conflict evidence fusion in multi-sensor. In particular, in target recognition, when three pieces of evidence are fused, the target recognition rate is 96.92%, etc.

CED: A Distance for Complex Mass Functions

Evidence theory is an effective methodology for modeling and processing uncertainty that has been widely applied in various fields. In evidence theory, a number of distance measures have been presented, which play an important role in representing the degree of difference between pieces of evidence. However, the existing evidential distances focus on traditional basic belief assignments (BBAs) modeled in terms of real numbers and are not compatible with complex BBAs (CBBAs) extended to the complex plane. Therefore, in this article, a generalized evidential distance measure called the complex evidential distance (CED) is proposed, which can measure the difference or dissimilarity between CBBAs in complex evidence theory. This is the first work to consider distance measures for CBBAs, and it provides a promising way to measure the differences between pieces of evidence in a more general framework of complex plane space. Furthermore, the CED is a strict distance metric with the properties of nonnegativity, nondegeneracy, symmetry, and triangle inequality that satisfies the axioms of a distance. In particular, when the CBBAs degenerate into classical BBAs, the CED will degenerate into Jousselme et al.'s distance. Therefore, the proposed CED is a generalization of the traditional evidential distance, but it has a greater ability to measure the difference or dissimilarity between pieces of evidence. Finally, a decision-making algorithm for pattern recognition is devised based on the CED and is applied to a medical diagnosis problem to illustrate its practicability.

Complex Pignistic Transformation-Based Evidential Distance for Multisource Information Fusion of Medical Diagnosis in the IoT

Multisource information fusion has received much attention in the past few decades, especially for the smart Internet of Things (IoT). Because of the impacts of devices, the external environment, and communication problems, the collected information may be uncertain, imprecise, or even conflicting. How to handle such kinds of uncertainty is still an open issue. Complex evidence theory (CET) is effective at disposing of uncertainty problems in the multisource information fusion of the IoT. In CET, however, how to measure the distance among complex basis belief assignments (CBBAs) to manage conflict is still an open issue, which is a benefit for improving the performance in the fusion process of the IoT. In this paper, therefore, a complex Pignistic transformation function is first proposed to transform the complex mass function; then, a generalized betting commitment-based distance (BCD) is proposed to measure the difference among CBBAs in CET. The proposed BCD is a generalized model to offer more capacity for measuring the difference among CBBAs. Additionally, other properties of the BCD are analyzed, including the non-negativeness, nondegeneracy, symmetry, and triangle inequality. Besides, a basis algorithm and its weighted extension for multi-attribute decision-making are designed based on the newly defined BCD. Finally, these decision-making algorithms are applied to cope with the medical diagnosis problem under the smart IoT environment to reveal their effectiveness.

Evidence combination based on prospect theory for multi-sensor data fusion

Multi-sensor data fusion (MSDF) is an efficient technology to enhance the performance of the system with the involvement of different kinds of sensors, which are broadly utilized in many fields at present. However, the data obtained from multi-sensors may have different degrees of uncertainty in the practical applications. Evidence theory is very useful to convey and manage uncertainty without a priori probability, so that it has been proverbially adopted in the information fusion fields. However, in the face of conflicting evidences, it has the possibility of producing counterintuitive results via conducting the Dempster's combination rule (DCR). To solve the above-mentioned issue, a hybrid MSDF method is exploited through integrating a newly defined evidential credibility measure of evidences based on prospect theory and the evidence theory. More specifically, a series of concepts for the evidential credibility measure are first presented, including the local credibility degree, global credibility degree, evidential credibility estimation and credibility prospect value function to comprehensively describe the award and punish grades in terms of credible evidence and incredible evidence, respectively. Based on the above researches, an appropriate weight for each evidence can be obtained. Ultimately, the weight of each evidence is leveraged to amend the primitive evidences before conducting DCR. The results attained in the experiments demonstrate that the hybrid MSDF approach is efficient and superior to handle conflict evidences as well as the application in data fusion problems.

Evidential Estimation of an Uncertain Mixed Exponential Distribution under Progressive Censoring

In this paper, the evidential estimation method for the parameters of the mixed exponential distribution is considered when a sample is obtained from Type-II progressively censored data. Different from the traditional statistical inference methods for censored data from mixture models, here we consider a very general form where there is some uncertain information about the sub-class labels of units. The partially specified label information, as well as the censored data are represented in a united frame by mass functions within the theory of belief functions. Following that, the evidential likelihood function is derived based on the completely observed failures and the uncertain information included in the data. Then, the optimization method using the evidential expectation maximization algorithm (E2M) is introduced. A general form of the maximal likelihood estimates (MLEs) in the sense of the evidential likelihood, named maximal evidential likelihood estimates (MELEs), can be obtained. Finally, some Monte Carlo simulations are conducted. The results show that the proposed estimation method can incorporate more information than traditional EM algorithms, and this confirms the interest in using uncertain labels for the censored data from finite mixture models.

A New Evaluation Methodology for Quality Goals Extended by D Number Theory and FAHP

Evaluation of quality goals is an important issue in process management, which essentially is a multi-attribute decision-making (MADM) problem. The process of assessment inevitably involves uncertain information. The two crucial points in an MADM problem are to obtain weight of attributes and to handle uncertain information. D number theory is a new mathematical tool to deal with uncertain information, which is an extension of evidence theory. The fuzzy analytic hierarchy process (FAHP) provides a hierarchical way to model MADM problems, and the comparison analysis among attributes is applied to obtain the weight of attributes. FAHP uses a triangle fuzzy number rather than a crisp number to represent the evaluation information, which fully considers the hesitation to give a evaluation. Inspired by the features of D number theory and FAHP, a D-FAHP method is proposed to evaluate quality goals in this paper. Within the proposed method, FAHP is used to obtain the weight of each attribute, and the integration property of D number theory is carried out to fuse information. A numerical example is presented to demonstrate the effectiveness of the proposed method. Some necessary discussions are provided to illustrate the advantages of the proposed method.

Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully.

An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory

Emergency decision-making has become as one of the hot issues in recent years. The aim of emergency decision-making is to reduce the casualties and property losses. All the processes of emergency decision-making are full of incompleteness and hesitation. The problem of emergency decision-making can be regarded as one of the multi-attribute decision-making (MADM) problems. In this manuscript, a new method to solve the problem of emergency decision-making named D-PLTS is proposed, based on D number theory and the probability linguistic term set (PLTS). The evaluation information given by experts is tidied to be the form of PLTS, which can be directly transferred to the form of the D number, no matter whether the information is complete or not. Furthermore, the integration property of D number theory is carried out to fuse the information. Besides, two examples are given to demonstrate the effectiveness of the proposed method. Compared with some existing methods, the D-PLTS is more straightforward and has less computational complexity. Allocation weights that are more reasonable is the future work for the D-PLTS method.

Determining Weights in Multi-Criteria Decision Making Based on Negation of Probability Distribution under Uncertain Environment

Multi-criteria decision making (MCDM) refers to the decision making in the limited or infinite set of conflicting schemes. At present, the general method is to obtain the weight coefficients of each scheme based on different criteria through the expert questionnaire survey, and then use the Dempster–Shafer Evidence Theory (D-S theory) to model all schemes into a complete identification framework to generate the corresponding basic probability assignment (BPA). The scheme with the highest belief value is then chosen. In the above process, using different methods to determine the weight coefficient will have different effects on the final selection of alternatives. To reduce the uncertainty caused by subjectively determining the weight coefficients of different criteria and further improve the level of multi-criteria decision-making, this paper combines negation of probability distribution with evidence theory and proposes a weights-determining method in MCDM based on negation of probability distribution. Through the quantitative evaluation of the fuzzy degree of the criterion, the uncertainty caused by human subjective factors is reduced, and the subjective error is corrected to a certain extent.

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.