Vector Quality Assessment of Glide Landing Process of an Aircraft

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Introduction

In Chapter 8, we consider the problem of multicriteria synthesis. Depending on the type of multicriteria problem a scalar convolution has a different physical meaning. In the analysis problem, this convolution is an evaluation function, its value expresses quantitatively a measure of the quality of multicriteria object for given values of the argument x. In the optimization problem, the scalar convolution acts as objective function. As a result of its extremalization, it turns out a compromise-optimal vector of arguments x*. Usually there is considered such an optimization problem, in which it is assumed for definiteness, that all the criteria у₀(х) require minimization. Then the mathematical problem of vector optimization is represented as

.

The concept of a non-linear compromise scheme involves a scalar convolution in the form

(1) where α_k=const – the formal parameters defined on the simplex and having dual physical meaning. On the one hand – they are weights expressing the preferences of decision-makers on specific criteria. On the other – they are the coefficients of the substantional regression model of the utility function of the decision maker, built on the basis of the concept of a nonlinear compromise scheme.

Decision of multiobjective optimization problems on the basis of the concept of non-linear compromises scheme is described in (Voronin, A.N. at al 1999).

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Multicriteria Evaluation Problems

In contrast to optimization problems the multicriteria evaluation belongs to the class of analysis tasks. Here, the convolution (1) is not the objective, but the evaluation function, and its value expresses quantitatively a measure of the quality of multicriteria object for the given and known values of the argument x.

When multicriteria evaluating of alternatives it is often necessary to obtain not only analytical but also qualitative assessment. To do this, the expression of the scalar convolution must be normalized and correlated with the gradations of a normalized fundamental scale. The general concept of the fundamental ordinal scale is described in (Saaty, T.L. 1990).

The interval normalized scale is presented by Table 1. It shows the relationship between qualitative gradations of properties of objects and the corresponding quantitative estimates y₀ and Y₀.

Table 1.