On combination rule in Dempster–Shafer theory using OWA‐based soft likelihood functions and its applications in environmental impact assessment

Abstract

Dempster–Shafer theory (DST) was presented as an effective mathematical tool to represent uncertainty. Its significant innovation is to allow the allocation of the belief of mass to sets or intervals, and it becomes a valuable method in the field of decision making and evaluation when accurate information is not available or when knowledge is expressed subjectively by humans. A crucial research issue in DST is the combination of multi‐sources of evidence. In this paper, a novel combination rule for Dempster–Shafer structures is developed based on ordered weighted average (OWA)‐based soft likelihood functions proposed by Yager. First, the belief intervals, including the belief measures and plausibility measures, of all the hypotheses in the frame of discernment (FOD) are calculated. Second, the representative value of belief interval is defined based on golden rule introduced by Yager. Third, the soft likelihood value of each hypothesis is calculated based on the proposed OWA‐based soft likelihood function for belief interval, which can be considered as the combined evidence. The final evaluation results can be employed for practical applications, such as decision making and evaluation. In addition, the improved evidence combination rule is presented which takes into account the weight of evidence. Several illustrative examples are conducted to manifest the use of the developed methods. Finally, an application for environmental impact assessment is given to demonstrate the usefulness of the developed combination rule in DST.

Combining conflicting evidence based on Pearson correlation coefficient and weighted graph

“…Some other works have also been presented. 22,23 Most of these evidence combinations use the technique of averaging BPA to reduce the influence of conflicting evidence, namely, averaging BPA based on the reliability of every evidence, which can be calculated by similarity, 24,25 distance, 20 information volume, 26,27 and eXtropy. 28 In statistics, Pearson correlation coefficient 29 is a linear correlation coefficient for measuring the relationship, or association, of two variables, which is developed by Karl Pearson with wide applications.…”

“…Some other works have also been presented 22,23 . Most of these evidence combinations use the technique of averaging BPA to reduce the influence of conflicting evidence, namely, averaging BPA based on the reliability of every evidence, which can be calculated by similarity, 24,25 distance, 20 information volume, 26,27 and eXtropy 28 …”

A modified soft‐likelihood function based on POWA operator

“…Due to the flexibility of soft‐likelihood functions to process uncertain information, there are many studies on soft‐likelihood functions. Specially, Fei et al 20 proposed a new pythagorean fuzzy decision model based on the soft‐likelihood function, Li et al 21 proposed a new combination rule based on OWA soft‐likelihood function and Dempster‐Shafer theory, and Wang et al 22 based on belied entropy and soft‐Likelihood function studyed the improvement of divergence measure to fuse multisource data and so on.…”

On Pythagorean fuzzy decision making using soft likelihood functions

“…It has been extended to Dempster‐Shafer evidence theory for combining the basic probability assignments by Jiang and Hu . In our previous research, the concept of soft likelihood for IFSs was proposed based on the ordered weighted averaging (OWA) operators for MCDM. In addition, a novel aggregation method was presented based on OWA operators under interval‐valued fuzzy environments motivated by soft likelihood functions.…”