Compact Preference Representation for Pilot Decision

Recommendation

Denys Bernard

, Jean-Claude Méré

and William Nicolas

Airbus S.A.S, Toulouse, France

ALTEN SO, Toulouse, France

Keywords: Decision Making, Flight Diversion, Compact Representation of Preferences, Qualitative Reasoning.

Abstract: Our goal is to apply compact representations of preferences (Kaci et Al., 2020) in pilot recommendation

functions for future commercial aircraft. The support of a decision assistant would be helpful in a variety of

flight situations, and we focus here on the case of a diversion decision. CRP are based on simple, modular

and intuitive representation of preferences among a set of candidate solutions. Solutions are represented as

vectors of qualitative variables. CRPs help to define a logical language for specifying «preference statements".

Those preference statements are used to sort a set of candidate solutions (or "outcomes"). Each outcome is

represented as a vector of qualitative or propositional variables. The conceptual simplicity of CRP facilitates

knowledge elicitation and explanation processes. We developed a variant of an existing framework named

CP-theories (Wilson, 2011) which fulfils our expressivity and operational constraints. The language and

algorithms of our framework have been applied to support pilots to make the best decision about flight

diversions.

1 INTRODUCTION

The purpose of this study is to adapt and apply a

family of approaches known as "compact

representations of preferences" (abbrev. CRP) (Kaci

et Al., 2020) to the design of pilot recommendation

functions for future commercial aircraft. The support

of a decision assistant would be helpful in a variety of

flight situations, and we focus here on the case of a

decision for diversion.

CRPs are based on simple, modular and intuitive

representations of preference statements. Reasoning

on those statements is used to sort a set of candidate

solutions (or "outcomes"), each of those solutions

being represented as a vector of qualitative variables.

CRPs theories define logical languages to specify

"preference statements". The conceptual simplicity of

CRP facilitates knowledge elicitation and explanation

processes. We introduce a variant of an existing

framework named CP-theories (Wilson, 2011) which

fulfils our expressivity and operational constraints.

The paper first reminds the state-of-the-art of CRPs,

then shows how we adapted the selected pre-existing

https://orcid.org/0000-0002-0131-4795

framework. Finally we detail some diversion

examples where different sets of preference

statements are invoked to face different types of

operational issues.

2 REPRESENTING AND

REASONING ABOUT

PREFERENCES

Compact representations of preferences (Kaci et Al.,

2020) - abbreviated here as CRP - define logic-based

formalisms to specify a knowledge base of unitary

"preference statements", as well as reasoning

mechanisms for: checking the consistency of the

knowledge base; determining the dominance relation

between two options ("outcomes"); ordering a set of

possible options. Among the different frameworks,

graphical approaches use oriented graphs where

nodes represent the variables of the possible

outcomes, and branches represent priorities or

dependencies among variables. Conceptual

foundations of graphical approaches of preferences

Bernard, D., Méré, J. and Nicolas, W.

Compact Preference Representation for Pilot Decision Recommendation.

DOI: 10.5220/0011925000003622

In Proceedings of the 1st International Conference on Cognitive Aircraft Systems (ICCAS 2022), pages 5-9

ISBN: 978-989-758-657-6

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

are detailed in (Shoham, 1997), who draws a parallel

between probabilities and utilities. In particular he

notes that utility independence among variables plays

the same role as events independence in bayesian

networks: by taking account of dependence

relationships, one can drastically reduce the effort

needed to compute and compare utilities of

alternative choices. Shoham develops this parallel

between probability and utility under the form of

"utility networks". Graphical approaches for compact

representation of preferences are built on the concept

of variable dependencies, but without requiring the

definition of a quantitative utility function. For

example CP-nets (conditional preference networks)

(Boutilier et Al., 2004), define a preference theory as

a pair (G, CT) where G is a dependency graph over

the variables, and CT is a function which assigns a

conditional preference table to each variable; The

conditional preference table for variable X defines the

preferences over possible values of X, for each

possible value assignment of the parents of X in G, all

other things being equal. In CP-nets, the rule that all

the variables other than the parent variables in the net

must be equal for the preference statement to trigger

("ceteris paribus" assumption), is too constraining in

cases where some variables are always less important

than others, or when some variables are not relevant

for a particular use case. For this purpose, (Brafman

et Al., 2006) enriched the graphical language of CP-

nets as TCP-nets (trade-offs-enhanced CP nets) by

representing variable priorities. TCP-nets not only

display dependencies (like CP-nets), but also show

priority relations. It is then possible in a TCP-net to

state that under certain circumstances, a variable X is

much more important than variable Y. In such a case,

one can ignore Y to evaluate solution dominance.

Example in diversion scenario: if the safety margin is

degraded, flight time is a more important criterion

than cost of maintenance at diversion airport, which

can then be ignored when comparing two options

which are different regarding safety margins.

CP-theories (Wilson, 2011) further generalise

preferences networks. For a set of variables V, a cp-

theory is a set of statements of form:

u: x>x' [W] (1)

Where: u is a value assignment to a subset U ⊂ V,

x and x' are possible values of a variable X, s.t. X∉U,

and W ⊆ V-U-{X}. Such a statements says that an

outcome t u x w is preferred to any outcome t u x' w'

where: t is a value assignment on V-(U∪{X}∪W)

("ceteris paribus" variables); u is a specified value

assignment on U (set of preconditions); w and w' are

any value assignments on W (indifferent variables).

Wilson proposes efficient tree-based algorithms

for evaluating consistency and dominance in cp-

theories.

The compact representations of preferences have

also been considered from the viewpoint of logic.

There, a possible outcome is a possible world, where

a set of formulas in a primary logical language holds.

A preference statement in such a logic says that if

certain formulas hold in world W1, and other

formulas hold in world W2, then W1 is preferred to

W2. For example (Bienvenu et Al., 2010) provides a

general logical theory of preferences ("prototypical

preference logic") by extending a propositional

language L with preference statements formed as:

α ⊳ β ‖ F

(2)

Where α and β are formulas of L, F is a set of

formulas of L. It expresses that we prefer an outcome

O1 over outcome O2 if O1⊨α, O2 ⊨ β, and O1 and

O2 agree on the formulas in F. The prototypical

preference logic generalises most of the graphical

representations and CP-theories.

In the literature, computing preference relations

often uses graph algorithms: To decide whether an

outcome dominates another one, the algorithm tries to

find a path of elementary preference relations through

the possible outcomes. For example in CP-nets, a

preference relation between two outcomes is obtained

by generating a "flipping sequence" i.e. a sequence

outcomes, where two consecutive outcomes differ

only by one variable. Determining that an outcome is

preferred over another one consists in finding a

flipping sequence from the first one to the other one.

This principle is extended in (Wilson, 2011) whose

algorithm generates a "cs-tree" (complete search tree)

where the terminal leaves are the possible outcomes,

and the intermediate nodes are partially instantiated

variable assignments.

3 A VARIANT OF CP-THEORIES

FOR PILOT DECISION

ASSISTANCE

Our approach is inspired from cp-theories (Wilson,

2011). We had to make a few adaptations to the initial

theory in order to better fit some requirements of our

application:

- Like in classical expert systems, preference

statements will be elaborated with human

ICCAS 2022 - International Conference on Cognitive Aircraft Systems

pilots. We need to improve the expressivity of

preference statements in cp-theories to

facilitate knowledge elicitation.

- The computation time at system utilisation is

critical, but we can mitigate this risk through

off-line pre-processing.

- The set of preference statements to be used

depends on the particular operational situation

treated (use case).

The following notations are borrowed from

(Wilson, 2011):

- Domain(X) is the domain of feature X

- If U ⊆ F, IU denotes the set of possible value

assignments to features in U. So an outcome is

an element of IF

- If u∈ IU and X∈U, u(X) denotes the value that

u assigns to X

- If V ⊆ U, u(V) denotes the projection of u on

The driving idea of our approach is to represent a

preference statement as a vector of relations: A

criterion on feature X is defined by a binary relation

R on Domain(X) (e.g. X="flight time", R=shorter).

A criterion defines a binary relation on outcomes: it

includes all the pairs of outcomes whose X features

are related by R. The following notation is introduced

for criteria:

CRIT(X,R) =

{(o

, o

) s.t. o

, o

∈ I

(X), o

(X)) ∈ R}

(3)

The preference relation for a particular use case is

defined by a set of preference statements. A

preference statement is a binary relation on F, defined

as the intersection of criterions, one criterion for each

feature:

P = CRIT(X

, R

) ∩…∩ CRIT(X

) (4)

With F={X

… X

} and each R

denotes a relation

on Domain (X

) ✕ Domain(X

To ensure that preference statements are acyclic,

it must be imposed that one at least of the criteria is

irreflexive. To follow the spirit of CP-theories at

statement elicitation, the default relation for a given

variable is equality ("ceteris paribus assumption").

From the pilot perspective, decision assistant

functions have to support the pilot in diverse

diversion situations ("use cases"). Our preference

knowledge base is naturally structured accordingly,

i.e. it can be represented as a mapping which

associates a pair {Fu, Qu} to each use case u, where

Fu is the list of features relevant for u, and Qu is the

set of statements to be applied in case u.

To reduce computation times in operation, the

decision assistant uses a pre-processed knowledge

base of preference statements. This knowledge base

is computed offline, from the initial set of explicit

statements augmented by its transitive closure.

More formally, the pre-processing step works as

follows:

Let R

and R

be binary relations on the same

domain D, R

•R

is the product relation defined as

(Bouyssou, 2005):

{(x

) s.t. x

∈ D,

∃x

∈ D s.t.(x

)∈R

∧ (x

) ∈R

}

(5)

Because preference relations are transitive, a new

preference statement can be obtained by the product

of two preference statements. The new relation P

•P

is also a preference statement in our framework

because it can be rewritten into the standard form,

thanks to the following property. With

=∩

i=1..n

CRIT(X

, R

) and P

=∩

i=1..n

CRIT(X

, R

•P

= ∩

i=1..n

CRIT(X

, R

•R

) (6)

The product preference statement is obtained by

the conjunction of product relations at the level of

each feature. Then it becomes possible to derive all

the relevant preference statements by transitivity,

based on the products of binary preferences.

The computing process requires that product

operations have been defined to combine the binary

relations for each feature. This supposes that binary

relations on each feature can be combined to derive

new valid relations. This property obtains easily for

qualitative features as soon as any binary relation can

be represented by a boolean matrix, and the product

of relations corresponds to the product of their

matrices (Bouyssou, 2005). For quantitative features,

we have to restrict the relations used in preference

statements to the disjunctions of basic =, <, >

relations.

4 EXAMPLE APPLICATION ON

DIVERSION ASSISTANCE

Reasoning about pilot preferences is only one module

in an information processing chain whose objective is

to push informed decision proposals towards the

Compact Preference Representation for Pilot Decision Recommendation

pilot. CRP are used here to formalise and to reason

about pilot explainable rules to select a diversion

airport among several candidate solutions. For

example, if a passenger is sick, the following

statements will apply: "a safe diversion flight is

always preferred to a flight whose safety level is

degraded". "Among two equally safe diversion

flights, I will prefer an airport with medical services,

provided the flight time is not much longer than to the

other one", "among two reachable airports, if none of

them have medical services, I will prefer the shortest

time to get to the nearest hospital".

The functional architecture works as follows:

When a diversion is required, a short list of

candidate airports for diversion is selected (typically,

the few closest airports, including the ones which

have been identified as possible diversion airports at

flight preparation).

Flight plans are calculated for the airports of the

short list to evaluate quantitative variables (time,

distance,...), and diverse descent strategies.

The features needed to reason about the different

solutions for the particular use case are calculated

(e.g. quantitative to qualitative conversion, when

relevant).

The solutions are ranked by using the logical

framework described above.

Justified recommendations are sent back to the

pilot, who can accept the first proposal or another one

in the list, or ask for explanations, or ask to consider

additional solutions.

In many real situations, a few more interaction

loops will be needed (question answering, what if

questions, requirements for more airports…), which

do not change the principle of this functional

architecture.

The Decision-Making analysis should be as close

as possible to natural reasoning of pilots in operation.

For example if a passenger is sick, the aim of the

diversion decision is to land as fast as possible to an

airfield where the passenger will be quickly attended

by medical services. The pilot must first ensure flight

safety, a safe diversion solution will always be

preferred to an option where safety margins are

significantly degraded, whatever the other features.

Among the solutions where safety is ensured, the pilot

will prefer airports with adequate facilities to take

care of the sick passenger. Among the safe diversions

to airports where the passenger can be attended, the

diversion flights with minimum travel time will be

preferred. The example also shows how the facilities

about passenger handling can be taken into account.

In the case of engine fire, flight time has to

become the dominant criterion as soon as the safety

margins are degraded. Different descent strategies

might also impact the final choice, which results in

proposing the less bad solution from a compromise

between degraded solutions.

In case of closure of the destination airport, beyond

safety, the decision assistant has to take into account

a different set of features, including more commercial

and economic aspects. The preference statements to

be invoked here consider the availability of ground

support teams, the availability of services and

commodities for passengers, and the impact on airline

flight schedules.

5 DISCUSSION

We proposed a framework to model and reason about

preferences which is derived from cp-theories

(Wilson, 2011). In our approach, preference

statements are handled as conjuncts of feature level

criteria. This approach is suitable for the development

of a pre-processing step of the knowledge base to

improve on-line processing times. The new

framework had to fulfil specific requirements for our

application. In particular the language for statements

is more expressive: it does not require to focus on a

single feature for each statement; disjunctions are

allowed in feature level criteria; preference

statements are not limited to qualitative (or

propositional) criteria; they admit limited usage of

quantitative comparison. It can be demonstrated that

our language for preference statements is more

expressive than preference statements in cp-theories

(cp-theories can be reformulated in our language).

How do CRP compare with classical numerical

approaches to multi-criteria decision making? Those

methods usually fall into two categories: the compare

and aggregate approaches, and the aggregate and

compare approaches (Gonzales, Perny 2020). Our

approach could be classified as a compare and

aggregate one: each preference statement operates a

comparison at feature level; then the result is

aggregated to decide if the statement triggers or not.

Nevertheless, our approach differs from

multi6criteria decision techniques on several aspects:

each preference statement is an independent module:

it uses its own rules to compare the features, and it

considers only the few features which are relevant

(the remaining features are assumed to be equal or

indifferent). This modularity cumulated with the

property that the language used is mostly qualitative,

facilitates the elicitation of preferences by human

experts. Quantitative multi-criteria approaches

nevertheless have a strong competitive advantage:

ICCAS 2022 - International Conference on Cognitive Aircraft Systems

they are suitable for automated learning of numerical

functions for comparison and aggregation. But our

problem is not well fitted for automated learning

because of the diversity of use cases (each with its

own list of relevant criteria), the scarcity of accurate

and documented diversion data, and the dependency

of decisions to airline policy and aircraft types.

Moreover, the decisions proposed must be justified to

the pilot. In summary, the framework presented in

this abstract is operationally well adapted because it

privileges knowledge elicitation with expert pilots,

performance at run time, and explanation of the

ranking of the solution proposed.

In the following steps, we will finalise the use

cases and their preference statements with test pilots;

we are also working on improving the explanation

processes and developing the capability to customise

the knowledge base, including by taking into account

pilot's feedback during the interactions with the

assistant.

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Compact Preference Representation for Pilot Decision Recommendation