Using Z-number to measure the reliability of new information fusion method and its application in pattern recognition

Highlights

• Proposed a new information fusion method based on Dempster–Shafer Evidence Theory (DST) and K-means clustering.

• The reliability evaluation criterion for fusion results is established based on Z-number.

• Some critical issues in DST, e.g., conflict management, evidence stuck, are well overcome.

• Comparison and discussion prove that the proposed method has better robustness and sensitivity than existing methods.

• The examples and applications show the potential of the proposed method in a data-driven intelligent system.

Abstract

Information fusion has traditionally been a concern. In the fusion process, how to effectively take care of the ambiguity and uncertainty of data is a fascinating problem. Dempster–Shafer evidence theory shows powerful functions in dealing with uncertainty information, and Z-number can comprehensively model the ambiguity and reliability of information. Inspired by this, this paper proposed a new information fusion method based on Dempster–Shafer theory and K-means clustering and it established the reliability evaluation criterion based on Z-number. Comparison and discussion verify the rationality of the proposed method, which also illustrates the method has better robustness and sensitivity than existing methods, some critical issues in DST, e.g., conflict management, evidence stuck, are well investigated and overcome by the proposed method. Number examples and the application further shows the application potential of the proposed method in a data-driven intelligent system.

Introduction

Information fusion has always been seen as the basis for biological environmental perception and behavioral actions. Due to the practical needs of many fields, how to use an effective representation framework to fuse extracted and abstract data information and finally convert it into results that are more conducive to human decision-making has become a hot research direction [1], [2], [3], e.g., emergency alternative selection [4], medical diagnosis [5], [6], [7], [8], [9], complex event processing [10], [11], [12], data cluster [13], [14], failure mode and effects analysis [15], [16], [17], [18], reliability assessment [19], [20], objective optimization [21], [22], [23] and decision making [24], [25], [26], [27].

However, many traditional information fusion methods have an inevitable problem that the uncertainty in the original data has been ignored [28], [29]. However, it will inevitably encounter inaccurate data and even some wrong data in a complex real environment. Therefore, the ambiguity and randomness in the data information are useful to considering. Considering the ambiguity between the focal elements, Dempster–Shafer Evidence Theory (DST) shows more powerful functions in dealing with uncertainty information and modeling [30], [31]. It can satisfy the axiom system which is weaker than probability theory, and has become an important means of information fusion in many fields [32], [33], [34], e.g., decision making [35], [36], [37], reliability measure [38], [39] and uncertain reasoning [40], [41], [42], [43], [44]. In order to solve the defects of the classic DST fusion method [45], [46], Murphy [47] uses the average value instead of the original information to reduce the interference of conflicting information. Deng et al. [48] constructed a similarity matrix to obtain the credibility of different information, making the fusion result more reasonable and reliable. Jiang [49] proposed the correlation coefficient between evidence information and improved the information fusion method based on the evidence distance. Since then, many works have improved the existing fusion methods to varying degrees, such as Song et al. [50], Pan et al. [51] and our previous work [52] and so on. Recently, Ma et al. [53] proposed a new idea. This method balances the relationship between averaging and focusing well, and the supporting information of non-focused elements is retained more. This view has inspired this article to some extent. We believe that conflict information should not be overly negated, because if conflict information is completely meaningless, deleting it is undoubtedly the best solution. This not only makes the focusing function of the fusion method stronger, but also saves extra computational overhead. But in many cases, the conflict information is also important, especially the cause of its occurrence, such as sensor failure, a certain attribute of the target to be tested has a mutation, etc. The retention of conflicting information will prompt further investigation. Yager [54] believes that the nature of conflicts originates from the unknown, and the conflict value should be transferred to the universal set. However, in a strong conflict information environment, simple transfer of conflicting sensitivity is needed, which may provide us with an interesting work.

This paper proposes a new information fusion method based on Dempster–Shafer theory and K-means clustering. The evidence information collected in the information source is clustered, and the basic probability assignment (BPA) value of the finally converged cluster center evidence is combined to obtain the comprehensive result. The proposed method retains more uncertain and conflicting information in the original information, especially in the environment of strong conflict information, it can more effectively perceive the conflict signal in the original information and manage conflicts. In addition, the proposed method can obtain more valuable information compared with the aforementioned methods. For example, in a voting election system, the proposed method can not only fuse a large number of voting information to obtain decision results, but also can observe the situation of groups holding different opinions, e.g., the number of people included in these groups, the opinions they support, and the degree of disagreement among different groups, etc.

In addition, the reliability analysis of the fusion results is also a problem worthy of concern. Because of the ambiguity and randomness of the data information, whether the final fusion result is reliable or not directly affects further analysis and processing. None of the aforementioned methods discuss the reliability of the obtained fusion results. Based on Z-number, we give a method to evaluate the reliability of the fusion result obtained by the proposed fusion method. Z = ($A$, $B$), was first proposed by Zadeh [55], the first component $A$ is the fuzzy measure of the proposition, and the second component $B$ is a measure of the reliability of the first component $A$, which are connected by an hidden probability distribution. In the previous work, we discussed how to effectively use fuzzy measure and probability information to obtain reliability assessment [56], [57]. In this paper, combine the fusion method proposed, we first obtain the fuzzy measure and probability evaluation of the fusion result, then determine the reliability component based on the connotation of Z-number, and finally convert it into the reliability value. This provides meaningful help for evaluating decisions.

The rest of the paper is structured as follows. The second Section introduces some preliminary knowledge. The third Section proposes a new information fusion method based on Dempster–Shafer theory and K-means clustering and how to use Z-number to measure the reliability of fusion results. A number example in Section 4 shows the detailed calculation process of the new method more clearly, and the obtained results are compared and discussed with other methods in the fifth Section to verify this method rationality and effectiveness. Then, the ability to process conflict information shows the robustness and sensitivity of the proposed method. At the end of this section the superiority of the proposed method is summarized. In Section 6, we show a more complex pattern recognition application based on the Iris data set, which is to further illustrate the application potential of the proposed method in fields such as pattern recognition. Finally, the paper ends in the conclusion.