Towards Cardinality-Aware Evidential Combination Rules in Dempster–Shafer Theory

The Dempster–Shafer theory has garnered significant attention for effectively managing uncertainty across various disciplines. However, the core combination rule within this theory, known as Dempster’s rule, has faced criticism due to its propensity to yield counterintuitive outcomes in highly conflicting situations. To address this limitation, several alternative combination rules have been proposed. These rules can be categorized into three strategies: (i) rules that modify or correct the original bodies of evidence, (ii) rules that redistribute conflicting masses, and (iii) rules that modify both the original bodies of evidence and Dempster’s rule. Furthermore, more sophisticated combination rules have considered the cardinality of focal elements prior to the combination step to enhance decision-making. This paper falls within this category of frameworks and seeks to examine the influence of incorporating the cardinality of the focal set element on the quality of the combination results, utilizing well-established examples from the literature. In addition to comparing the performance of different combination rules, the obtained results underscore the importance of considering the cardinalities of bodies of evidence during the combination process to mitigate abnormal behaviors.