This article considers the use of confidence judgments method by decision-makers to analyze the information contained in large databases. The comparative analysis of passenger aircrafts shows that it allows flexibly and objectively allocating the most relevant information from the data array.
The emergence of large corporate databases opens up new prospects in the field of
aircraft design, as well as in other subject fields of project activity. It becomes
possible to estimate comprehensively, over a large number of characteristics, both
quantitative and qualitative, the efficiency of different variants of design decisions against a
background of a huge amount of analogues. It is also important to keep in mind that
the project activity has largely heuristic nature, based on a combination of objective
quantitative analysis within intuitive the designers’ ideas, arising impulses of which
may the expand and transfer the attention focus, and even change the design paradigm
itself. The mechanism of using large databases for the design of complex,
multifunction objects such as aircraft should be oriented towards these features.
In our opinion, it is advisable to use some advanced methods of complex decision
theory, such as multi-criteria optimization, during the formation of such mechanism.
One of the main advantages of these methods is that they provide an adequate active
role of decision-makers along with the use of axiomatic approach to the information
analysis. For all the variety of decision-making methods [
In aviation, for example, two important characteristics are in such conflict: the aircraft
weight and aerodynamic efficiency. Increasing the aerodynamic quality is achieved
by the wing lengthening, but it increases its weight [
Let us consider a corporate database for the aircrafts as a set Y of objects which are characterized by m-dimensional ∈ , vectors f ( y) { f 1 ( y), f 2 ( y), ..., f m ( y)}, y Y . The components of these vectors are separate efficiency characteristics of the object, which are of interest from the viewpoint of decision-makers. For example, a passenger aircraft has the following characteristics considered from an operational point of view: Cruise speed, km/h Number of passengers, pers Flight range, km Service ceiling, m Runway length, m Minimum price in passenger version, million USD Maximum price in passenger version, million USD Starting year of manufacturing Number of built aircrafts Engine power, kgf Fuel capacity, l any characteristics f Traditionally, the simplest way to analyze this data array is to sort by the values of j
, j 1,...,m . It allows to define the locations according to solution variants for this characteristic among analogues. However, since the solution efficiency, in general, is determined mainly by its characteristics, the analytical value of sorting is not high.
More powerful tool for intellectual analysis is the allocation of the total array of
objects which are Pareto efficient. The object is considered as Pareto efficient if there do
not exist at least one dominant object on the entire considered set. It means that any
object according to the characteristics not worse, and at least one - better. Thus,
among the aircrafts, whose characteristics are given in Table 1 (data are taken from
[
m m F ( f ) j f j , j 0, j 1,..., m, j 1, where j , j 1,..., m - weight coefficients.
The use of this method cannot be recommended during the design of such important objects as an aircraft for two main reasons.
Let us notice, that the decision-maker made two judgments by choosing it:
First of all, exactly this kind of account method for uncertainty in the form of linear
convolution is fully adequate for this decision-making task,
Secondly, exactly the chosen experts, the examination organization and methods of
expert opinion processing load to absolutely reliable values of weight coefficients.
Both judgments can be challenged by reasonable positions. First of all, the linear
convolution may not see some Pareto-optimal objects for any values of weight
coefficients. For instance, on Figure 1 all objects for two minimized objects, images of
which lie above the dotted line in a criterion space, will not be recognized as the most
rational for any weight coefficient values in linear convolution, although they are
Pareto-optimal objects [
Actually, the decision-maker can reasonably make only two types of judgments.
confidence may include various particular criteria to different group of importance. For example, “criteria 1 and 4 are the most important ones, criteria 2 and 6 are merely importance, and criterion 5 has the lowest importance”. Let us note, that we do not assume that decision-maker provide a qualitative estimation of the relative importance degree for particular criteria, it refers only to the qualitative comparison which is optional.
struct the pairs of Pareto-incomparable vectors of particular criteria, for which he is certain that one of the vectors is better that another. It is not required that the vectors represent the efficiency of any real objects. If 1 and 2 – in which 1 is surely better than 2, it implements the following restriction on the set S: S {s)} : Fs ( f1 ) Fs ( f 2 ) s S .
Based only on these two types of judgments, the method which proportion particular
characteristics into a single numerical object’s characteristic, represented in the
database, was developed in [
Stage 1. The uncertainty profile is constructed for the solving problem. It shows the range of complex efficiency criterion values for this decision within all possible ways to take into account the uncertainty for each design solution. The uncertainty profile is given by a pair of functions, which are defined on the set: minorant ( ) = min ( ( )) and majorant ( ) = sS min ( ( )).
sS It should be noted, that obviously irrational decisions z Y , for which there are better solutions z Y by complex criterion in all possible ways of uncertainty, can be identified. The identify conditions for such solutions have the following form: z Y : M (z ) m(z) .
The main purpose of uncertainty profile is to give decision-makers information about the impact of uncertainty during decision-making in the problem. Adding confident judgments, he will be able to estimate how they reduce the uncertainty. Stage 2. If it is possible, the set of uncertainties narrows by taking into account the decision-maker’s confident judgments. The uncertainty accounting methods, which do not correspond to this judgments, are eliminated when we are using confident judgments of the first type. When we have got the confident judgments of the second type, conditions (6) are added to the set description, which eliminates those uncertainty accounting methods that do not carry out these judgments.
At the end of first two stages the initial set of uncertainties can be narrowed. This affect the uncertainty profile of the problem, but it is unlikely to remain only a single element in it, or all variants except one will be eliminated from the plurality of solutions. Thus, the uncertainty retained in the problem. This will be a fatal uncertainty. All uncertainty account methods, which form this fatal uncertainty, are completely equal to the decision-maker as he has already use his ability to make additional content in the problem description using judgments of the first and second types. It is possible that the other types of confident judgments of decision-makers can be found, but they did not fundamentally change the situation: after their usage, fatal uncertainty will remain in the problem.
Stage 3. Rigid and soft ratings for solution variants are calculated, taking into account unavoidable uncertainty. In order not to introduce the unnecessary for understanding and application complex mathematical apparatus, we shall assume that the set contains a finite number of uncertainty accounting methods S: S= { } k 1,..., K .
Then the rigid rating ( ) for
∈ solution is a fraction of uncertainty accounting method, in which the solution is the best compared to the other solutions: RG ( y)
∈ decisions displays the average comprehensive efficiency if this solution compared with solutions, which are the best in different ways of uncertainty concideration: 1 K max F yY s ( f ( y)) k K
.
RM
solution. database.
Stage 4. Decision-maker recognize that the possibility of further uncertainty reducing is exhausted due to its confident judgments. Finally, he chooses a solution with the best (lowest) rigid rating as the most efficient solution. If there are several solutions, we will choose the one, which has the best (lowest) soft rating, as the most efficient
Let us show the use of confident judgments method for data analysis of passenger aircrafts in terms of their operational characteristics. Table 2 shows a fragment of the s t f a irr c A Boeing 737-200 Boeing 737-200 Advance Boeing 737-300 Boeing 737-400 Boeing 737-500 Boeing 737-600 Boeing 737-700 Boeing г 737-800 Tu-204 Tu-204
100 Tu-204
120 Tu-204
200 Tu-204300 Airbus Industry А319-110
Airbus Industry А321-200 h / m k , d e e p s e s i u r C 905 905 Analyzing this data, first of all, we will use one on the traditional comprehensive performance criteria – fuel efficiency. In this case, the only Pareto-optimal object is Tu-204-200, which rigid rating is equal to 100% (Column 2, Table 3). Its fuel efficiency is equal to 19,66 44 grams/pass*km, while the nearest Tu-204-120 it is 23.44 grams/pass*km. At the same time, we can use the other criteria – weight efficiency, which is calculated as the aircraft’s ration of takeoff weight to the number of passengers. In this instance, the only Pareto-optimal variant with 100% rigid rating is another one object – Boeing Боинг 737-400 (Column 3 of Table 3), the weight efficiency of which is 0,41 t/pass, whereas Tu-204-120 has 0,49. However, applying confident judgments method, there is no need to bring subjectivity in the data analysis, coupled with the use of traditional complex criteria. It is enough to list the primary characteristics which are significant to the maintenance viewpoint. They are:
Cruise speed and number of passengers are the most significant criteria. Taking into account the variety of routes for various distances, on which aircrafts are operated within its capabilities, the range and fuel capacity are the following on the importance. They also influence on the running costs, as they are transferred to the minimum and maximum ticket price of an aircraft. Thus, the criteria are distributed into three groups of significance. The results are shown in column 5 of Table 3. Boeing 737-800 saves leading positions, and Airbus Industry A321-200 follows it with a considerable margin.
Thus, the article shows that the application of confident judgments method for analysis of large databases opens new flexible opportunities for its users.