New PDF release: Advanced Methods for Inconsistent Knowledge Management

By Ngoc Thanh Nguyen

ISBN-10: 1846288886

ISBN-13: 9781846288883

This publication is a primary. It fills a huge hole available in the market and gives a large photograph of clever applied sciences for inconsistency solution. the necessity for this answer of information inconsistency arises in lots of sensible functions of desktops. this sort of inconsistency effects from using a variety of assets of data in understanding useful projects. those assets are usually self reliant and use varied mechanisms for processing wisdom in regards to the comparable genuine global. this may bring about compatibility difficulties.

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Additional info for Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing)

Example text

3. 1. Basic Notions In this section we present some notions needed for use in the next sections. 2 (conflict body, subject, and content), we assume in this model that the conflict subject is given and for this subject the set of all potential opinions which may be included in the conflict content may be determined. We investigate the properties of behaviour of different cases of conflict content. By U we denote a finite set of objects representing the potential opinions for the conflict subject.

Proof. We show that there exists a universe U for which any function c from C(U) if satisfying postulates P1a and P2a cannot satisfy postulate P7a. Let then U = {a,b} and a ≠ b, then d(a,b) = max d ( x, y ) > 0. x , y∈U Let X = U; according to postulate P2a we have c(X) = 0. Because function c satisfies postulate P1a we have c(X − {a}) = c({b}) = 1. In addition, we have d(a,X) = min{d(t,X): t ∈ X} and c(X − {a}) = 1 > c(X) = 0, so function c cannot satisfy postulate P7a. ♦ 36 2. 5. Postulates P1a and P4 in general are inconsistent with postulate P7a; that is, formula (P1a ∧ P4) ⇒ ¬P7a is u-true.

Then profile X\X’ should not have a smaller consistency than X; that is, c(X\X ′ ) ≥ c(X) , where c ∈ {c2, c3, c4}. Proof. (a) For function c2 the proof follows immediately from the notice that Diam( W X ) ≤ Diam( W X \ X ' ). (b) For function c3 we have d(X ) = 1 M M ∑ wiX . i =1 Because for each xi ∈ X ′ there is wiX = Diam( W X ), therefore there should be d(X ) ≥ d(X \ X ') ; that is, c3(X\X ′) ≥ c3(X). (c) For function c4 the proof is similar as for function c3 ♦ This property shows another way for improving consistency referring to functions c2, c3, and c4, which is based on removing from a profile those elements generating the maximal average distance.

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Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing) by Ngoc Thanh Nguyen

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