A generalized TODIM-ELECTRE II method based on linguistic Z-numbers and Dempster–Shafer evidence theory with unknown weight information

How to effectively reflect the randomness and reliability of decision information under uncertain circumstances, and thereby improve the accuracy of decision-making in complex decision scenarios, has become a crucial topic in the field of uncertain decision-making. In this article, the loss –aversion behavior of decision-makers and the non-compensation between attributes are considered. Furthermore, a novel generalized TODIM-ELECTRE II method under the linguistic Z-numbers environment is proposed based on Dempster–Shafer evidence theory for multi-criteria group decision-making problems with unknown weight information. Firstly, the evaluation information and its reliability are provided simultaneously by employing linguistic Z-numbers, which have the ability to capture the arbitrariness and vagueness of natural verbal information. Then, the evaluation information is used to derive basic probability assignments in Dempster–Shafer evidence theory, and with the consideration of both inner and outer reliability, this article employed Dempster’s rule to fuse evaluations. Subsequently, a generalized TODIM-ELECTRE II method is conceived under the linguistic Z-numbers environment, which considers both compensatory effects between attributes and the bounded rationality of decision-makers. In addition, criteria weights are obtained by applying Deng entropy which has the ability to deal with uncertainty. Finally, an example of terminal wastewater solidification technology selection is offered to prove this framework’s availability and robustness. The predominance is also verified by a comparative analysis with several existing methods.

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.

An Improved Method for Multisensor High Conflict Data Fusion

Dempster-Shafer evidence theory can effectively process imperfect information and is widely used in a data fusion system. However, classical Dempster-Shafer evidence theory involves counter-intuitive behaviors with the data of multisensor high conflict in target identification system. In order to solve this problem, an improved evidence combination method is proposed in this paper. By calculating the support degree and the belief entropy of each sensor, the proposed method combines conflict evidences. A new method is used to calculate support degree in this paper. At the same time, inspired by Deng entropy, the modified belief entropy is proposed by considering the scale of the frame of discernment (FOD) and the relative scale of the intersection between evidences with respect to FOD. Because of these two modifications, the effect has been improved in conflict data fusion. Several methods are compared and analyzed through examples. And the result suggests the proposed method can not only obtain reasonable and correct results but also have the highest fusion reliability in solving the problem of high conflict data fusion.

Entropic Explanation of Power Set

A power set of a set S is defined as the set of all subsets of S, including set S itself and empty set, denoted as P(S) or 2S. Given a finite set S with |S|=n hypothesis, one property of power set is that the amount of subsets of S is |P(S)| = 2n. However, the physica meaning of power set needs exploration. To address this issue, a possible explanation of power set is proposed in this paper. A power set of n events can be seen as all possible k-combination, where k ranges from 0 to n. It means the power set extends the event space in probability theory into all possible combination of the single basic event. From the view of power set, all subsets or all combination of basic events, are created equal. These subsets are assigned with the mass function, whose uncertainty can be measured by Deng entropy. The relationship between combinatorial number, Pascal's triangle and power set is revealed by Deng entropy quantitively from the view of information measure.

An Improved Approach of Incomplete Information Fusion and Its Application in Sensor Data-Based Fault Diagnosis

The Dempster–Shafer evidence theory has been widely used in the field of data fusion. However, with further research, incomplete information under the open world assumption has been discovered as a new type of uncertain information. The classical Dempster’s combination rules are difficult to solve the related problems of incomplete information under the open world assumption. At the same time, partial information entropy, such as the Deng entropy is also not applicable to deal with problems under the open world assumption. Therefore, this paper proposes a new method framework to process uncertain information and fuse incomplete data. This method is based on an extension to the Deng entropy in the open world assumption, negation of basic probability assignment (BPA), and the generalized combination rule. The proposed method can solve the problem of incomplete information under the open world assumption, and obtain more uncertain information through the negative processing of BPA, which improves the accuracy of the results. The results of applying this method to fault diagnosis of electronic rotor examples show that, compared with the other uncertain information processing and fusion methods, the proposed method has wider adaptability and higher accuracy, and is more conducive to practical engineering applications.

Fractional Deng Entropy and Extropy and Some Applications

Deng entropy and extropy are two measures useful in the Dempster–Shafer evidence theory (DST) to study uncertainty, following the idea that extropy is the dual concept of entropy. In this paper, we present their fractional versions named fractional Deng entropy and extropy and compare them to other measures in the framework of DST. Here, we study the maximum for both of them and give several examples. Finally, we analyze a problem of classification in pattern recognition in order to highlight the importance of these new measures.

Measuring the Uncertainty in the Original and Negation of Evidence Using Belief Entropy for Conflict Data Fusion

Dempster-Shafer (DS) evidence theory is widely used in various fields of uncertain information processing, but it may produce counterintuitive results when dealing with conflicting data. Therefore, this paper proposes a new data fusion method which combines the Deng entropy and the negation of basic probability assignment (BPA). In this method, the uncertain degree in the original BPA and the negation of BPA are considered simultaneously. The degree of uncertainty of BPA and negation of BPA is measured by the Deng entropy, and the two uncertain measurement results are integrated as the final uncertainty degree of the evidence. This new method can not only deal with the data fusion of conflicting evidence, but it can also obtain more uncertain information through the negation of BPA, which is of great help to improve the accuracy of information processing and to reduce the loss of information. We apply it to numerical examples and fault diagnosis experiments to verify the effectiveness and superiority of the method. In addition, some open issues existing in current work, such as the limitations of the Dempster–Shafer theory (DST) under the open world assumption and the necessary properties of uncertainty measurement methods, are also discussed in this paper.

Information Volume of Mass Function

Given a probability distribution, its corresponding information volume is Shannon entropy. However, how to determine the information volume of a given mass function is still an open issue. Based on Deng entropy, the information volume of mass function is presented in this paper. Given a mass function, the corresponding information volume is larger than its uncertainty measured by Deng entropy. In addition, when the cardinal of the frame of discernment is identical, both the total uncertainty case and the BPA distribution of the maximum Deng entropy have the same information volume. Some numerical examples are illustrated to show the efficiency of the proposed information volume of mass function.

Incomplete Information Management Using an Improved Belief Entropy in Dempster-Shafer Evidence Theory

Quantifying uncertainty is a hot topic for uncertain information processing in the framework of evidence theory, but there is limited research on belief entropy in the open world assumption. In this paper, an uncertainty measurement method that is based on Deng entropy, named Open Deng entropy (ODE), is proposed. In the open world assumption, the frame of discernment (FOD) may be incomplete, and ODE can reasonably and effectively quantify uncertain incomplete information. On the basis of Deng entropy, the ODE adopts the mass value of the empty set, the cardinality of FOD, and the natural constant e to construct a new uncertainty factor for modeling the uncertainty in the FOD. Numerical example shows that, in the closed world assumption, ODE can be degenerated to Deng entropy. An ODE-based information fusion method for sensor data fusion is proposed in uncertain environments. By applying it to the sensor data fusion experiment, the rationality and effectiveness of ODE and its application in uncertain information fusion are verified.