Support Functions and Combination Rules in Hyper-Power Set and Super-Power Set

Abstract

The probability theory and belief function theory are two important tools for dealing with uncertainty. The concepts of probability theory and belief function theory are exchangeable with proper modifications. Rarely, authors are using approaches from probability theory to belief function theory. The branch of belief function theory viz. evidence theory is useful in many fields such as behavioral sciences, investigation bureaus, data mining, etc. The simple support functions are a particular type of belief function. The combination rules of simple support functions are introduced by Dempster [8] in two dimensions for heterogeneous evidence and conflicting evidence. A super-power set includes a hyper-power set and a hyper-power set includes a power set. In this paper, we generalize these combination rules of simple support functions in three dimensions for heterogeneous evidence and conflicting evidence in a hyper-power set and apply these combination rules of simple support functions for two dimensions for heterogeneous evidence and conflicting evidence in a super-power set. This approach is supported by an illustrative example. Also, we discuss the combination rules of simple support functions for higher dimensions in a hyper-power set and a super-power set.