Abstract
The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.
Highlights
Information representation has been a crucial issue since the emergence of artificial and intelligent systems [1,2]
The proposed negation of basic probability assignment (BPA) reassigns the BPA of a certain element according to the cardinality of intersection of the element and each remaining element in the power set
Particular assumptions have been made for two special elements, the empty set ∅ and the whole set θ in the power set to guarantee that the proposed negation method fits in with our intuition
Summary
Information representation has been a crucial issue since the emergence of artificial and intelligent systems [1,2]. We try to extend the negation method of a probability distribution in classical probability theory to a basic probability assignment in D-S theory, which provides a novel view of the expression of uncertainty and unknown in D-S theory. A novel negation method of basic probability assignment (BPA) in Dempster-Shafer theory is proposed in a matrix form as well as the BPA which is analogous to the fact that a probability distribution can be represented as a vector. To study the evolution of a BPA vector in the repeated negation process, a total uncertainty measure Hb (m) proposed by Pal et al [31,32] is adopted in this paper to measure the uncertainty of basic probability assignment (BPA).
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