Sensitivity of Combination Schemes under Conflicting Conditions and a New Method

In the theory of evidential reasoning, Dempster's rule is used for combining belief functions based on independent evidences. There has been a lot of debate over the counter-intuitive nature of results obtained by this rule [4, 8, 14, 15]. Dubois and Prade [1, 3] have shown that Dempster's rule is not robust and is sensitive to inaccurate estimates of uncertainty values. Many authors have suggested modifications which overcome this drawback. In this paper, we first bring out the limitation of the combination rule introduced by Zhang [16]. Subsequently, we focus our study on two other rules. The first one was proposed by Dubois and Prade [2, 3] and is known as Disjunctive rule of combination. Incidentally, this rule also appeared in the Hau and Kashyap's work [5]. The other combination rule was due to Yager [13]. Even though these rules are robust, we show that in some cases these rules treat evidences asymmetrically and give counter-intuitive results. We then propose a combination rule which doesn't have these drawback. An intuitive justification for this rule is also provided. 1 Introduction The Dempster-Shafer theory has attracted the attention of AI researchers, especially those working in the area of development of knowledge based systems primarily because of its ability to represent ignorance and the Dempster's rule of combination. It is well-known that Dempster's rule gives counter-intuitive results in a highly conflicting situation and is not robust. This problem is attributed to the normalization that is carried out in the combination rule. A detail discussion on this problem can be found in [3]. Dubois and Prade have shown that the result of the combination in such cases depends on how one represents an unlikely proposition. There are quite a few combination rules which overcome this sensitivity problem. Dubois and Prade [2, 3] and Yager [13] suggested alterations to Dempster's rule which avoid normalization. These rules are robust but are non-associative. In this paper, we show that in certain situations these rules give counter-intuitive results. We also take up the recent proposal by Zhang [16] and show that although it is commutative and associative, it is not robust. On the backdrop of this discussion, we propose a combination rule which is robust and quite general in nature. We also provide an intuitive justification for this rule.