By Ngoc Thanh Nguyen

This booklet is a primary. It fills a massive hole available in the market and gives a large image of clever applied sciences for inconsistency answer. the necessity for this solution of information inconsistency arises in lots of useful functions of desktops. this type of inconsistency effects from using numerous assets of information in figuring out useful initiatives. those assets are usually self sustaining and use varied mechanisms for processing wisdom in regards to the similar genuine global. this may bring about compatibility difficulties.

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Symmetrical: ∀x,y ∈ U: d(x,y) = d(y,x), where [0, 1] is the closed interval of real numbers between 0 and 1. Thus function d is a half-metric because the above conditions include only a part of the metric conditions. Here there is the lack of a transitive condition because it is too strong for many practical situations [20]. By a microstructure of U we understand the structure of the elements of U. For example, if U is the set of all partitions of some set X then the microstructure of U is a partition of X, and as the macrostructure of U we can define a distance function between partitions of X.

Vn. These votes create a profile P = (p1, p2, . . , pn) ∈ S n, where pi is the vote of vi, for i = 1, . . , n. The problem is based on defining a consensus choice function which should determine a committee on the basis of a set of votes. In the literature there are three approaches for defining consensus choice functions: axiomatic, constructive, and optimization. In the axiomatic approach for the alternatives ranking problem a set of axioms has been fixed for the class of so-called Condorcet social choice functions (a consensus choice function C is a Condorcet function if and only if it satisfies the following Condorcet principle: for all situations (A, P) there should be C(A, p) = {x}, whenever x ∈ A and (x, y) ∈ Wp for all y ∈ A\{x}).

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). The problem is based on defining a consensus choice function which should determine an alternative on the basis of a situation (A, P).

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