NDLI: Measuring ambiguity in the evidence theory

Content Provider	IEEE Xplore Digital Library
Author	Jousselme, A.-L. Chunsheng Liu Grenier, D. Bosse, E.
Copyright Year	1996
Abstract	In the framework of evidence theory, ambiguity is a general term proposed by Klir and Yuan in 1995 to gather the two types of uncertainty coexisting in this theory: discord and nonspecificity. Respecting the five requirements of total measures of uncertainty in the evidence theory, different ways have been proposed to quantify the total uncertainty, i.e., the ambiguity of a belief function. Among them is a measure of aggregate uncertainty, called AU, that captures in an aggregate fashion both types of uncertainty. But some shortcomings of AU have been identified, which are that: 1) it is complicated to compute; 2) it is highly insensitive to changes in evidence; and 3) it hides the distinction between the two types of uncertainty that coexist in every theory of imprecise probabilities. To overcome the shortcomings, Klir and Smith defined the TU₁ measure that is a linear combination of the AU measure and the nonspecificity measure N. But the TU₁ measure cannot solve the problem of computing complexity, and brings a new problem with the choice of the linear parameter delta. In this paper, an alternative measure to AU for quantifying ambiguity of belief functions is proposed. This measure, called Ambiguity Measure (AM), besides satisfying all the requirements for general measures also overcomes some of the shortcomings of the AU measure. Indeed, AM overcomes the limitations of AU by: 1) minimizing complexity for minimum number of focal points; 2) allowing for sensitivity changes in evidence; and 3) better distinguishing discord and nonspecificity. Moreover, AM is a special case of TU₁ that does not need the parameter delta
Sponsorship	IEEE Systems, Man, and Cybernetics Society
Starting Page	890
Ending Page	903
Page Count	14
File Size	279037
File Format	PDF
ISSN	10834427
Volume Number	36
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-09-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Gold Measurement uncertainty Aggregates Information theory Information entropy Councils Collaborative work Decision support systems Research and development uncertainty measure Aggregate uncertainty ambiguity Dempster–Shafer theory
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Information Systems Electrical and Electronic Engineering Human-Computer Interaction Computer Science Applications Software

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