NDLI: A general framework for measuring inconsistency through minimal inconsistent sets

Content Provider	Springer Nature Link
Author	Mu, Kedian Liu, Weiru Jin, Zhi
Copyright Year	2010
Abstract	Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIV C, defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIV C. Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.
Starting Page	85
Ending Page	114
Page Count	30
File Format	PDF
ISSN	02191377
Journal	Knowledge and Information Systems
Volume Number	27
Issue Number	1
e-ISSN	02193116
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-04-21
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Inconsistency measure Belief bases Minimal inconsistent subsets Shapley value Information Systems and Communication Service Business Information Systems
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Information Systems Human-Computer Interaction Hardware and Architecture Software

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