A generalized soft likelihood function in combining multi-source belief distribution functions

Likelihood function has significant advantages in the fields of statistical inference. Based on this theory, Yager proposed a soft likelihood function to make it more widely used. However, Yager’s method can only deal with probabilities expressed by crisp values, and has strict restrictions on the form of data. Due to human subjectivity and lack of effective information, it is inevitable that data uncertainty will be involved. In order to deal with the uncertain data more flexibly and intuitively and solve the complex problems faced in real-world applications, a generalized soft likelihood function in combining multi-source belief distribution functions is proposed in this paper. Different from other existing methods, this paper uses a distribution function to represent uncertain information, which can retain more original information and improve the credibility of the results. The expectation and variance are used to rank the obtained evidences, and the evidence that contributes more to the results is ranked higher. Finally, the reliable likelihood results are obtained. The proposed method extends the method of Yager and can work well in more uncertain environment. Several numerical examples and comparative experimental simulation are used to illustrate the efficiency of the proposed soft likelihood function.