Dempster–Shafer (DS) evidence theory is the most significant and effective method for uncertainty modeling and reasoning. How to measure the uncertainty in DS evidence theory precisely remains an outstanding problem. Various types of uncertainty measures for evidence have been presented. However, they all suffer some limitations. To address this issue, we propose a novel total uncertainty measure for the DS evidence theory framework that can quantify the uncertainty in the evidence. The new total uncertainty measure uses the Hellinger distance between the belief interval of every singleton and the most uncertain interval. Compared with the existing uncertainty measurement methods, the proposed approach is more sensitive to changes in evidence. The effectiveness and rationality of the brand new total uncertainty measure are illustrated by numerical examples and practical applications.

As an important method for uncertainty modeling, Dempster-Shafer (DS) evidence theory has been widely applied in practical applications. However, the counter-intuitive results are often generated when fusing different sources of highly conflicting evidence with Dempster’s combination rule. Several different methods for measuring the evidence conflict have been proposed. Nevertheless, these methods showed focus only on a single criterion to measure the conflicting evidence. Mono-criteria factor for the measurement of the conflict between evidence is, however, often unreliable and inaccuracy. Because vari-ous factors affect the degree of conflict between the evidence, such as imperfection, dissimilarity, disparity, and uncertainty. To address this issue, multiple criteria factors are utilized to measure the degree of conflict between the evidence in this paper. An improved analytic hierarchy process is proposed to determine the weights of each body of evidence by considering multiple criteria. Firstly, calculating the quantitative value of the evaluation index of each evidence under every criterion. The covariance matrix of the criterion layer is determined based on the covariance between the quantitative values of each criterion. Then, the pairwise comparison matrix of the criterion layer can be obtained by transforming the covariance matrix. Next, the variance among the quantitative values of each criterion is applied to construct the fuzzy preference relation matrix. The fuzzy preference relation matrix is used to replace the pairwise comparison matrix of the scheme layer. After that, the weight of the criterion layer and the scheme layer are combined to acquire the final weights of each evidence. Finally, the original evidence is modified with the final weights of the evi-dence before using Dempster’s combination rule. Two numerical experiments are given to verify the effi-ciency of the proposed approach. The result shows that the proposed method is more efficient and feasible in managing the conflicting evidence than other approaches available in the literature described.

As an important method for uncertainty modeling, Dempster–Shafer (DS) evidence theory has been widely used in practical applications. However, the results turned out to be almost counter-intuitive when fusing the different sources of highly conflicting evidence with Dempster’s combination rule. In previous researches, most of them were mainly dependent on the conflict measurement method between the evidence represented by the evidence distance. However, it is inaccurate to characterize the evidence conflict only through the evidence distance. To address this issue, we comprehensively consider the impacts of the evidence distance and evidence angle on conflicts in this paper, and propose a new method based on the mutual support degree between the evidence to characterize the evidence conflict. First, the Hellinger distance measurement method is proposed to measure the distance between the evidence, and the sine value of the Pignistic vector angle is used to characterize the angle between the evidence. The evidence distance indicates the dissimilarity between the evidence, and the evidence angle represents the inconsistency between the evidence. Next, two methods are combined to get a new method for measuring the mutual support degree between the evidence. Afterward, the weight of each evidence is determined by using the mutual support degree between the evidence. Then, the weights of each evidence are utilized to modify the original evidence to achieve the weighted average evidence. Finally, Dempster’s combination rule is used for fusion. Some numerical examples are given to illustrate the effectiveness and reasonability for the proposed method.

Hesitant fuzzy set (HFS) is a mighty mathematical tool to represent the hesitant fuzzy information, which can reveal the situation of hesitancy in practical problems. More recently, HFS has been generally utilized in multi-criteria decision-making (MCDM) problem. How to cope with the hesitant fuzzy information effectively is crucial to address the problem of MCDM under hesitant fuzzy environment. In this study, a novel hesitant fuzzy utility function is proposed to depict the hesitant fuzzy information contained in the hesitant fuzzy element (HFE) and realizes the transformation from the hesitant fuzzy information to the crisp value. Firstly, a novel hesitant degree measure is presented to eliminate the drawbacks of traditional methods. The new hesitant degree measure can effectively describe the reliability of the HFE. Afterward, a novel approach of the hesitant fuzzy utility function is constructed by combining the hesitant fuzzy score value and the hesitant degree of the HFE. To generate accurate decision results, we introduce the gained and lost dominance score (GLDS) approach in our work. Then, a new hesitant fuzzy GLDS method is presented based on the GLDS method and the hesitant fuzzy utility function. Furthermore, we utilize the hesitant fuzzy utility value of the alternative to construct the comparison matrix between the criteria, which is used to identify the weight value of the criteria. Ultimately, a practical application is provided to demonstrate the validity and rationality of the proposed method, and comparative analysis with the existing decision making approaches.