Modelling uncertain positive and negative reasons in decision aiding

Abstract

The use of positive and negative reasons in inference and decision aiding is a recurrent issue of investigation. A language enabling us to explicitly take into account such reasons is Belnap's logic and the four valued logics derived from it. In this paper, we explore the interpretation of a continuous extension of a four-valued logic as a necessity degree (in possibility theory). It turns out that, in order to take full advantage of the four values, we have to consider "sub-normalized" necessity measures. Under such a hypothesis four-valued logics become the natural logical frame for such an approach.

Preferences in artificial intelligence

“…Further more, using such a formalism, it becomes possible to generalise the concordance/discordance principle (used in several decision aiding methods) as shown in [254] and several characterisation problems can be solved (see for instance [257]). More recently (see [208], [111], [19], [81], [197], [198], [258]) it has been suggested to use the extension of such logics for continuous valuations.…”

On the Semantics of Bipolarity and Fuzziness

“…( , ) , ( , ) (1)- (2) was first proposed for the case L= [0,1] in [29] (and have been further analyzed in [36]), in which it is proven that it is the unique continuous t-norm-based extension simultaneously verifying that the states i and k are mutually exclusive (since if i>0 then k=0…”

“…In relation with preference modelling and decision analysis, the notion of independent positive and negative information has also appeared in, among others, cumulative prospect theory (see [21,37]), outranking concordance-discordance ELECTRE methods (see [32]), Atanassov intuitionistic fuzzy sets (AFS, see [1]) and, more recently, in DDT logic [35]. Current applications of type-2 bipolarity along with fuzzy logic are promising and increasing (see [15,29,30,38])…”

“…Though their influence (more than considerable in fields as decision theory [14,17,26,29] or machine learning [19]) has spread separately, in the last few decades both notions have started to appear together in many developments on these and other fields (see for instance [4,6,13,15,30,31,38]), which comes to show its high relevance as a topic of research inside soft computing [20] and logics [36].…”

“…a decision to be taken [23,29]) by checking separately both the positive and negative sides of the available information (e.g. an alternative could be good for certain criteria and bad for other set of criteria) in order to acquire a more expressive and relevant knowledge.…”