A total uncertainty measure for D numbers based on belief intervals

A new correlation belief function in Dempster-Shafer evidence theory and its application in classification

Uncertain information processing is a key problem in classification. Dempster-Shafer evidence theory (D-S evidence theory) is widely used in uncertain information modelling and fusion. For uncertain information fusion, the Dempster's combination rule in D-S evidence theory has limitation in some cases that it may cause counterintuitive fusion results. In this paper, a new correlation belief function is proposed to address this problem. The proposed method transfers the belief from a certain proposition to other related propositions to avoid the loss of information while doing information fusion, which can effectively solve the problem of conflict management in D-S evidence theory. The experimental results of classification on the UCI dataset show that the proposed method not only assigns a higher belief to the correct propositions than other methods, but also expresses the conflict among the data apparently. The robustness and superiority of the proposed method in classification are verified through experiments on different datasets with varying proportion of training set.

The D numbers risk ranking based method by considering subjective weights and objective weights with incomplete linguistic information

Risk prediction, assessment, and control are key parts of the successful operation and sustainable development of any enterprise. During the process of product failure risk assessment, evaluated risk factors belong to the group of multiple-criteria decision-making (MCDM) problems, including severity, occurrence, and detection when failure occurs. However, the traditional risk ranking method does not consider the subjective and objective weights of the assessment factors, and during risk prediction, assessment, and control, some unknown information in many practical situations is included. These reasons may cause the risk assessment results to be biased. In order to effectively deal with the problem of risk assessment, this paper proposes a D numbers risk ranking method by considering subjective and objective weights between assessment factors under incomplete linguistic information. An illustrative example of screening unit failure risk assessment is used to explain and prove the rationality and correctness of the proposed method. Some risk ranking methods are compared with the proposed D numbers risk ranking method, and the simulation results present that the proposed ranking method handles the issue of incomplete information and provides more reasonable risk ranking results.

A new D numbers’ integration rule based on pessimistic criterion

For D numbers theory, there are some drawbacks in the D numbers’ integration rule. For example, the missing information is ignored in the final decision judgment for multi-attribute decision (MADM). For this problem, some researchers have improved the D numbers’ integration rules based on optimistic criterion for overcoming the shortcoming of D numbers’ integration rule. However, optimistic and pessimistic criterion are two sides of the coin for fuzzy environment. Therefore, in this article, a new D numbers’ integration rules based on pessimistic criterion is proposed. We improve the D numbers’ integration rules to redefine the missing information distribution rules based on pessimistic criterion. The missing information is distributed in inverse proportion to each D number according to the size of the original evidence credibility. Two examples of MADM is applied by the proposed method, the results show that the proposed method can be applied to MADM.

A MULTIMOORA-Based Risk Evaluation Approach for CCUS Projects by Utilizing D Numbers Theory

As the global climate warms, carbon emissions must be reduced in order to alleviate the human climate crisis. Carbon capture, utilization and storage (CCUS) is an emerging technology that can reduce carbon emissions. However, most of the CCUS projects have ended in failure. The reason can be attributed to insufficient risk assessment. To this end, the purpose of this study is to construct a comprehensive risk assessment model for CCUS projects. The main body of this research is divided into two parts. First, in order to evaluate the CCUS project, a risk indicator system is constructed. In what follows, a decision-making framework for risk assessment under the D numbers environment is proposed, including two stages of decision-making preparation and decision-making process. The main task of the preparation stage is to gather evaluation experts and collect decision-making information. In the decision-making stage, this paper takes the D numbers theory as the core (acting on the effective expression and fusion of subjective evaluation information), respectively, proposes the method of determining the weight of risk evaluators, the fusion method of decision-making information from different experts, and the comprehensive decision model based on the MULTIMOORA method. In order to verify the effectiveness of the constructed model, the case of CCUS project site selection in Shengli power plant is analyzed, and the results showed that the third site is the best option. This study finds the importance of a comprehensive and timely risk assessment for the successful implementation of CCUS projects, and suggests that stakeholders carry out a risk assessment of CCUS projects prior to implementation based on the method presented in this paper, so as to improve the success rate.

A Novel Conflict Management Method Based on Uncertainty of Evidence and Reinforcement Learning for Multi-Sensor Information Fusion

Dempster-Shafer theory (DST), which is widely used in information fusion, can process uncertain information without prior information; however, when the evidence to combine is highly conflicting, it may lead to counter-intuitive results. Moreover, the existing methods are not strong enough to process real-time and online conflicting evidence. In order to solve the above problems, a novel information fusion method is proposed in this paper. The proposed method combines the uncertainty of evidence and reinforcement learning (RL). Specifically, we consider two uncertainty degrees: the uncertainty of the original basic probability assignment (BPA) and the uncertainty of its negation. Then, Deng entropy is used to measure the uncertainty of BPAs. Two uncertainty degrees are considered as the condition of measuring information quality. Then, the adaptive conflict processing is performed by RL and the combination two uncertainty degrees. The next step is to compute Dempster's combination rule (DCR) to achieve multi-sensor information fusion. Finally, a decision scheme based on correlation coefficient is used to make the decision. The proposed method not only realizes adaptive conflict evidence management, but also improves the accuracy of multi-sensor information fusion and reduces information loss. Numerical examples verify the effectiveness of the proposed method.

MADA problem: A new scheme based on D numbers and aggregation functions

Describing and processing complex as well as ambiguous and uncertain information has always been an inescapable and challenging topic in multi-attribute decision analysis (MADA) problems. As an extension of Dempster-Shafer (D-S) evidence theory, D numbers breaks through the constraints of the constraint framework and is a new way of expressing uncertainty. The soft likelihood function based on POWA operator is one of the most useful tools recently developed for dealing with uncertain information, since it provides a more excellent performance for the aggregation of multiple compatible evidence. Recently, a new MADA model based on D numbers has been proposed, called DMADA. In this paper, inspired by the above mentioned theories, based on soft likelihood functions, POWA aggregation and D numbers we design a novel model to improve the performance of representing and processing uncertain information in MADA problems as an improvement of the DMADA approach. In contrast, our advantages include mainly the following. Firstly, the proposed method considers the reliability characteristics of each initial D number information. Secondly, the proposed method empowers decision makers with the possibility to express their perceptions through attitudinal features. In addition, an interesting finding is that the preference parameter in the proposed method can clearly distinguish the variability between candidates by adjusting the space values between adjacent alternatives, making the decision results clearer. Finally, the effectiveness and superiority of this model are proved through analysis and testing.

Interval-valued belief entropies for Dempster-Shafer structures

In practical application problems, the uncertainty of an unknown object is often very difficult to accurately determine, so Yager proposed the interval-valued entropies for Dempster-Shafer structures, which is based on Dempster-Shafer structures and classic Shannon entropy and is an interval entropy model. Based on Dempster-Shafer structures and classic Shannon entropy, the interval uncertainty of an unknown object is determined, which provides reference for theoretical research and provides help for industrial applications. Although the interval-valued entropies for Dempster-Shafer structures can solve the uncertainty interval of an object very efficiently, its application scope is only a traditional probability space. How to extend it to the evidential environment is still an open issue. This paper proposes interval-valued belief entropies for Dempster-Shafer structures, which is an extension of the interval-valued entropies for Dempster-Shafer structures. When the belief entropy degenerates to the classic Shannon entropy, the interval-valued belief entropies for Dempster-Shafer structures will degenerate into the interval-valued entropies for Dempster-Shafer structures. Numerical examples are applied to verify the validity of the interval-valued belief entropies for Dempster-Shafer structures. The experimental results demonstrate that the proposed entropy can obtain the interval uncertainty value of a given uncertain object successfully and make decision effectively.

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.

A SWOT method to evaluate safety risks in life cycle of wind turbine extended by D number theory

Wind power is a typical clean and renewable energy, which has been widely regarded as one of the replaceable energies in many countries. Wind turbine is the key equipment to generate wind power. It is necessary to evaluate the risks of each stage of the wind turbine with regard to occupational health and safety. In this study, the stage of production of life cycle of wind turbine is considered. The aim of this study is to propose a new method to identify and evaluate the risk factors based on strengths-weaknesses-opportunities-threats (SWOT) analysis and D number theory, named D-SWOT method. A wind turbine firm is used to demonstrate the detailed steps of the proposed method. SWOT is conducted to identify the risk factors of production stage of the wind turbine company. Experts are invited to perform the risk assessment, and D number theory is carried out to do the processes of information representation and integration. After that, some suggestions are provided to the company to lower the risks. The D-SWOT method obtains the same results as the previous method of hesitant fuzzy linguistic term set (HFLTS). Compared with HFLTS method, D-SWOT method simplifies the process of information processing, and D-SWOT method is more intuitional and concise. Besides, a property of pignistic probability transformation of D number theory (DPPT) is proposed in the manuscript, which extends D number theory and has been used in the process of decision making of D-SWOT.

Complex Entropy and Its Application in Decision-Making for Medical Diagnosis

In decision-making systems, how to measure uncertain information remains an open issue, especially for information processing modeled on complex planes. In this paper, a new complex entropy is proposed to measure the uncertainty of a complex-valued distribution (CvD). The proposed complex entropy is a generalization of Gini entropy that has a powerful capability to measure uncertainty. In particular, when a CvD reduces to a probability distribution, the complex entropy will degrade into Gini entropy. In addition, the properties of complex entropy, including the nonnegativity, maximum and minimum entropies, and boundedness, are analyzed and discussed. Several numerical examples illuminate the superiority of the newly defined complex entropy. Based on the newly defined complex entropy, a multisource information fusion algorithm for decision-making is developed. Finally, we apply the decision-making algorithm in a medical diagnosis problem to validate its practicability.

Conflict Management for Target Recognition Based on PPT Entropy and Entropy Distance

Conflicting evidence affects the final target recognition results. Thus, managing conflicting evidence efficiently can help to improve the belief degree of the true target. In current research, the existing approaches based on belief entropy use belief entropy itself to measure evidence conflict. However, it is not convincing to characterize the evidence conflict only through belief entropy itself. To solve this problem, we comprehensively consider the influences of the belief entropy itself and mutual belief entropy on conflict measurement, and propose a novel approach based on an improved belief entropy and entropy distance. The improved belief entropy based on pignistic probability transformation function is named pignistic probability transformation (PPT) entropy that measures the conflict between evidences from the perspective of self-belief entropy. Compared with the state-of-the-art belief entropy, it can measure the uncertainty of evidence more accurately, and make full use of the intersection information of evidence to estimate the degree of evidence conflict more reasonably. Entropy distance is a new distance measurement method and is used to measure the conflict between evidences from the perspective of mutual belief entropy. Two measures are mutually complementary in a sense. The results of numerical examples and target recognition applications demonstrate that our proposed approach has a faster convergence speed, and a higher belief degree of the true target compared with the existing methods.

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.

Relieving Cost of Epidemic by Parrondo's Paradox: A COVID-19 Case Study

COVID-19, also known as SARS-CoV-2, is a coronavirus that is highly pathogenic and virulent. It spreads very quickly through close contact, and so in response to growing numbers of cases, many countries have imposed lockdown measures to slow its spread around the globe. The purpose of a lockdown is to reduce reproduction, that is, the number of people each confirmed case infects. Lockdown measures have worked to varying extents but they come with a massive price. Nearly every individual, community, business, and economy has been affected. In this paper, switching strategies that take into account the total "cost" borne by a community in response to COVID-19 are proposed. The proposed cost function takes into account the health and well-being of the population, as well as the economic impact due to the lockdown. The model allows for a comparative study to investigate the effectiveness of various COVID-19 suppression strategies. It reveals that both the strategy to implement a lockdown and the strategy to maintain an open community are individually losing in terms of the total "cost" per day. However, switching between these two strategies in a certain manner can paradoxically lead to a winning outcome-a phenomenon attributed to Parrondo's paradox.

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.

A New Multi-Sensor Fusion Target Recognition Method Based on Complementarity Analysis and Neutrosophic Set

To improve the efficiency, accuracy, and intelligence of target detection and recognition, multi-sensor information fusion technology has broad application prospects in many aspects. Compared with single sensor, multi-sensor data contains more target information and effective fusion of multi-source information can improve the accuracy of target recognition. However, the recognition capabilities of different sensors are different during target recognition, and the complementarity between sensors needs to be analyzed during information fusion. This paper proposes a multi-sensor fusion recognition method based on complementarity analysis and neutrosophic set. The proposed method mainly has two parts: complementarity analysis and data fusion. Complementarity analysis applies the trained multi-sensor to extract the features of the verification set into the sensor, and obtain the recognition result of the verification set. Based on recognition result, the multi-sensor complementarity vector is obtained. Then the sensor output the recognition probability and the complementarity vector are used to generate multiple neutrosophic sets. Next, the generated neutrosophic sets are merged within the group through the simplified neutrosophic weighted average (SNWA) operator. Finally, the neutrosophic set is converted into crisp number, and the maximum value is the recognition result. The practicality and effectiveness of the proposed method in this paper are demonstrated through examples.

Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis

With the increasing automation of mechanical equipment, fault diagnosis becomes more and more important. However, the factors that cause mechanical failures are becoming more and more complex, and the uncertainty and coupling between the factors are getting higher and higher. In order to solve the given problem, this paper proposes a single-valued neutrosophic set ISVNS algorithm for processing of uncertain and inaccurate information in fault diagnosis, which generates neutrosophic set by triangular fuzzy number and introduces the formula of the improved weighted correlation coefficient. Since both the single-valued neutrosophic set data and the ideal neutrosophic set data are considered, the proposed method solves the fault diagnosis problem more effectively. Finally, experiments show that the algorithm can significantly improve the accuracy degree of fault diagnosis, and can better satisfy the diagnostic requirements in practice.

An Improved Total Uncertainty Measure in the Evidence Theory and Its Application in Decision Making

Dempster–Shafer evidence theory (DS theory) has some superiorities in uncertain information processing for a large variety of applications. However, the problem of how to quantify the uncertainty of basic probability assignment (BPA) in DS theory framework remain unresolved. The goal of this paper is to define a new belief entropy for measuring uncertainty of BPA with desirable properties. The new entropy can be helpful for uncertainty management in practical applications such as decision making. The proposed uncertainty measure has two components. The first component is an improved version of Dubois–Prade entropy, which aims to capture the non-specificity portion of uncertainty with a consideration of the element number in frame of discernment (FOD). The second component is adopted from Nguyen entropy, which captures conflict in BPA. We prove that the proposed entropy satisfies some desired properties proposed in the literature. In addition, the proposed entropy can be reduced to Shannon entropy if the BPA is a probability distribution. Numerical examples are presented to show the efficiency and superiority of the proposed measure as well as an application in decision making.

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.

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.

Combined Conflict Evidence Based on Two-Tuple IOWA Operators

Due to poor natural factors and human interference, the information that was obtained by sensors tends to have high uncertainty and high conflict with others. A combination of highly conflicting evidence with Dempster’s rule often produces results that run counter to intuition. To solve the above problem, a conflict evidence combination methodology is proposed in this article, which contains the distance of evidence, classical conflict coefficient, and two-tuple IOWA operator. Both the classical conflict coefficient and Jousselme distance indicate the degree of evidence conflict, and it is clear that the two parameters are symmetrical. First, the two-tuple IOWA operator is proposed. Second, the orness is determined by aggregated data; then, the weighting vector is calculated by a maximal entropy method. Finally, the weighted average is the evidence in the system by a two-tuple IOWA operator; then, the Dempster combination rule is utilized to fuse information. Compared with other existing methods, the presented methodology has high performance when dealing with conflict evidence and has strong anti-interference ability.