By Ngoc Thanh Nguyen

ISBN-10: 1846288886

ISBN-13: 9781846288883

This publication is a primary. It fills an immense hole out there and offers a large image of clever applied sciences for inconsistency answer. the necessity for this solution of information inconsistency arises in lots of sensible purposes of computers. this type of inconsistency effects from using a number of assets of data in understanding sensible projects. those assets are usually independent and use diverse mechanisms for processing wisdom concerning the related genuine global. this may bring about compatibility difficulties.

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**Extra resources for Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing)**

**Example text**

Let D(X) = {d(x,X): x ∈ U} be the set of all such sums. For any profiles X, Y ∈ Π(U) the following dependency should be true, 28 2. Model of Knowledge Conflict ⎛ min ( D( X )) min ( D(Y )) ⎞ ⎟ ⇒ (c(X) ≥ c(Y)). ⎜⎜ ≤ card (Y ) ⎟⎠ ⎝ card ( X ) P7a. Postulate for consistency improvement: Let a and a′ be such elements of universe U that d(a,X) = min {d(x,X): x ∈ X} and d(a′,X) = min {d(x,X): x ∈ U}; then c(X–{a}) ≤ c(X) ≤ c(X ∪ {a′}). P7b. Second postulate for consistency improvement: Let b and b′ be such elements of universe U that d(b,X) = max {d(x,X): x ∈ X} and d(b′,X) = max {d(x,X): x ∈ U}; then c(X ∪ {b′}) ≤ c(X) ≤ c(X – {b}).

7. The following formulae (P8 ∧ P1a) ⇒ P1b and (P8 ∧ P2a) ⇒ P2b are true. Proof. For the first formula assume that for any universe U and any function c ∈ C(U) let c satisfy postulates P8 and P1a. Let Y, Z ∈ Π(U) where Y = {x} and X (n ) = (n ∗ Y) ∪ Z. According to postulate P8 we have lim c( X (n ) ) = c(Y), n → +∞ and according to postulate P1a we have: c(Y) = c({x}) = 1. Thus function c satisfies postulate P1b. A similar proof may be done for the second formula. ♦ 38 2. 4. Consistency Functions In this section we present the definitions of five consistency functions and analyze their satisfaction referring to the defined postulates.

Postulate P8 in some sense is more general than postulates P1b and P2b. The following theorem proves this fact. 7. The following formulae (P8 ∧ P1a) ⇒ P1b and (P8 ∧ P2a) ⇒ P2b are true. Proof. For the first formula assume that for any universe U and any function c ∈ C(U) let c satisfy postulates P8 and P1a. Let Y, Z ∈ Π(U) where Y = {x} and X (n ) = (n ∗ Y) ∪ Z. According to postulate P8 we have lim c( X (n ) ) = c(Y), n → +∞ and according to postulate P1a we have: c(Y) = c({x}) = 1. Thus function c satisfies postulate P1b.