A New Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Belief Function and Plausibility Function

In group decision making (GDM), the quality of the solution relies primarily on the quality and the expertize of decision makers. At that point, deriving the weights, which reflects their importance or perceived reliability of decision makers, presents as a new challenge. In addition to that, the uncertainty is also a common problem for GDM. These problems are also faced in the sensor fusion problem where information from multiple sources must be aggregated.Therefore, in this study, a large scale GDM approach for sensor fusion is proposed. Since the proposed method is a clustering-based method, it provides acceptable results in the sensor networks consisting of multiple sensors. It can work under uncertainty as a result of converting the raw data obtained from sensors to the basic probability assignments. It also considers the reliability of the sensors clusters by assigning three objective weights. In addition to these objective weights, the proposed method enables to assign subjective weights to integrate supervisors/intelligence analyst experiences and knowledge in the problem field. The applicability and the validity of the proposed method are checked through two real classification data sets: ionosphere and forest type mapping data set. Experiments show that the classification rate is increased significantly when the proposed method is applied to two data sets. Finally, effect of extension parameter, objective weights, reliability threshold, number of clusters and clustering method on the classification rate and the detection probability are examined, and future studies are provided in conclusion.classification, Dempster-Shafer theory of evidence, large scale group decision making, sensor fusion, sensor weighting | INTRODUCTIONAs the complexity of the problem grows with the complexity of the socioeconomic environment, it gets more difficult for a single decision maker to cover all the relevant characteristic of a decision problem. Hence, in the real world, it is required to fuse the group of decision makers' opinion to obtain a feasible and satisfactory decision making result by using group decision making (GDM) approaches. 1,2 Here, the quality of the solution relies primarily on the quality and the expertize of decision makers in the problem area and how to aggregate decision makers' evaluations. 3 Therefore, it is critical to find a good way of aggregating decision makers' opinions whose expertize, background, and knowledge differ. In the literature, it is mostly assumed that the decision makers have the same importance level. 4 However, disregarding the weights of decision makers can cause improper and inaccurate outcomes that cannot be compensated for in the final solution. Therefore, when decision makers do not share similar levels of expertize, background, or knowledge, it is better to assign weights to the decision makers reflecting their importance or perceived reliability. At that point, deriving the weights of decision makers presents as a new challenge. Koksalmis and Kabak 5 presents the objectiv...

Section: Literature Reviewmentioning

confidence: 99%

Sensor fusion based on Dempster‐Shafer theory of evidence using a large scale group decision making approach

Köksalmiş

Kabak

2020

“…Many math tools are presented to model uncertainty, such as Z numbers, D numbers, and entropy model . Among then, evidence theory is widely used due to its efficiency to deal with uncertainty.…”

Section: Preliminariesmentioning

confidence: 99%

“…Many math tools are presented to model uncertainty, such as Z numbers, [53][54][55] D numbers, [56][57][58][59][60][61] and entropy model. [62][63][64][65][66][67] Among then, evidence theory is widely used due to its efficiency to deal with uncertainty. In this section, the traditional D-S evidence, 1 the Pearson correlation coefficient, 52 the Spearman correlation coefficient, 68 and the DEMATEL method are introduced.…”

Section: Preliminariesmentioning

confidence: 99%

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

Deng

2019

Self Cite

Dempster‐Shafer is widely used to address the problems of uncertainty. One assumption mentioned in this theory is that the distribution of information should be independent. In practice, the requirement cannot be fulfilled. One of the efficient methods to deal with dependent evidence is to calculate the correlation discounting. However, existing coefficient can only be applied to show the direct relation between evidence A and B but do not take the indirect relationship into consideration. To address this issue, in this paper, a new method to combine dependent evidence based on decision‐making trial and evaluation laboratory is presented, not only considering the relation between evidence A and B and the relation between evidence B and C, but also considering the transitive influence between evidence A and C. Finally, the experiments on some benchmark data sets are illustrated to show the efficiency of the proposed method.

“…One assumption of evidence theory is the close world, which means the mass function of empty set is zero . In addition, due to the fact that the BPA is the most important concept of evidence theory, many operations such as belief structure, correlation, negation, entropy, and divergence are developed.…”

Section: Preliminariesmentioning

confidence: 99%

TDBF: Two‐dimensional belief function

Deng

2019

Self Cite

How to efficiently handle uncertain information is still an open issue. In this paper, a new method to deal with uncertain information, named as two-dimensional belief function (TDBF), is presented. A TDBF has two components, T = (m m , A B ), both m A and m B are classical belief functions, while m B is a measure of reliable of m A . The definition of TDBF and the discounting algorithm are proposed. Compared with the classical discounting model, the proposed TDBF is more flexible and reasonable. Numerical examples are used to show the efficiency and application of the proposed method. K E Y W O R D S belief function, conflict management, Dempster-Shafer evidence theory, information fusion, two-dimensional belief function, Z-numbers 1 | INTRODUCTIONIt is inevitable to deal with uncertain information in real word. 1-3 There are many articles that take advantage of uncertain information processing problems. 4 To address this issue, many methods have been proposed, such as probability theory, 5 Dempster-Shafer evidence theory, 6,7 fuzzy sets, 8-10 rough sets, 11 Z-numbers, 12 R-numbers, 13,14 and D numbers. [15][16][17][18][19][20] Among these methods, Dempster-Shafer evidence theory 6,7 is one of the most widely used math tools in many engineering applications such as pattern recognition 21,22 and decision-making. 23 Evidence theory has many advantages to handle uncertain information. [24][25][26] For example, the belief function is more flexible to model uncertainty compared with probability distribution. In addition, Dempster's combination rule can combine evidence from different sources without prior information. 27,28 However, it should be pointed out that illogical results may be obtained by classical Dempster combination rule when collected evidence highly conflicts each other. [29][30][31][32][33] Z-numbers is proposed by Zadeh. 12 A Z-number has two components, Z = (A, B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliability (certainty) of the first component. 12 Similarly, in evidence theory, discounting coefficient is a measure of sensor report's reliability, for example, discounting factors based on dissimilarity measure, 34 dynamic discounting rates. 35 Nevertheless, the simple value is not enough and reasonable to express the experts evaluation under uncertain situation. To solve this problem, a new math model named as two-dimensional belief function (TDBF) is proposed in this paper.A TDBF is an ordered pair of basic probability assignments (BPAs) denoted as T = (m m , A B ). The first component m A is a classical BPA, which usually is collected from the sensors. The second component m B is a measure of reliability for the first component, which can be collected by the experts. The frame of discernment of m B set Y N Θ = { , }, where "Y" denotes "positive" and "N" denotes "negative." The power set of Y N Θ = { , } consists of two singletons {Y} and {N}, an universal Θ and t...