By Ngoc Thanh Nguyen

ISBN-10: 1846288886

ISBN-13: 9781846288883

This booklet is a primary. It fills an incredible hole available in the market and offers a large photo of clever applied sciences for inconsistency solution. the necessity for this solution of information inconsistency arises in lots of useful functions of computers. this type of inconsistency effects from using a number of assets of information in figuring out sensible projects. those assets are usually self reliant and use diversified mechanisms for processing wisdom in regards to the related genuine global. this may bring about compatibility difficulties.

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

Sample text

In clustering theory, this criterion is used for determining the centre of a group, called a centroid. 1 presented below shows the results of the defined functions. The columns represent postulates and the rows represent the defined functions. Satisfying a postulate by a consistency function means that the function satisfies the postulate for all universes. The symbol + means that the presented function satisfies the postulate, the symbol − means that the presented function does not satisfy the postulate, and the symbol ± means partially satisfying the given postulate.

Let A be a nonempty and finite set of alternatives. A profile P on A is defined as a finite set of linear orders on A. A situation is understood as an ordered pair (A, P). For each situation (A, P) and each pair of alternatives x, y ∈ A, a number p(x,y) is defined that is equal to the number of orders included in P in which the alternative x precedes the alternative y. Hence, if an order p contains n alternatives then p(x, y) + p(y, x) = n for x ≠ y. Moreover a binary relation Wp on A is defined as (x, y) ∈ Wp if and only if p(x, y) > p(y, x).

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}). P8. Postulate for simplification: For Y, Z ∈ Π(U) and X (n ) = (n ∗ Y) ∪ Z then the following equation should be true, lim c( X (n ) ) = c(Y).

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

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