Context-aware Recommendation using Fuzzy Formal Concept Analysis

Jos

e Luis Leiva

, Manuel Enciso

, Carlos Rossi

Pablo Cordero

Angel Mora

and Antonio Guevara

Department of Languages and Computer Science, University of M

alaga, M

alaga, Spain

Department of Applied Mathematics, University of M

alaga, M

alaga, Spain

Keywords:

Context, Recommender System, Fuzzy Logic, Formal Concept Analysis.

Abstract:

Most of the recommender systems are content-based: they provide the user a subset of items close to his

interest by using the item features. In real recommender systems, the main problem is the big amount of items

to be treated. In this work we propose to incorporate context information in a uniform way. We use fuzzy logic

and formal concept analysis as a framework to combine context information and content-based recommender

systems. Concretely, we specify the content by using fuzzy relations, the context by using fuzzy implications

and Simpliﬁcation Logic to develop an intelligent and linear pre-ﬁltering process. We illustrate this method

with an application to the tourism sector.

1 INTRODUCTION

In recent years, the use of recommender systems has

become popular in many different applications to of-

fer a personalized selection of products. The big

amount of items to be recommended causes that in

many cases users feel overwhelmed because they have

to select from a wide range of alternatives (Lym-

beropoulos et al., 2011). In this work we focus on

tourism recommender systems, that should imple-

ment ﬁltering mechanisms to provide a set of points

of interest (POIs) which are accurately adjusted to the

real needs of the tourist.

(Leiva et al., 2012) presented a classiﬁcation of

the types of most commonly used recommender sys-

tems:

• Collaborative: it provides results obtained from

the qualiﬁcations made by users. The user will

be recommended items that people with similar

tastes and preferences liked in the past.

• Content-based: it categorizes items and suggests

products that have similar characteristics to those

requested by the user or to those that he evaluated

positively in the past.

• Demographics: it classiﬁes users by different per-

sonal parameters, and recommendations are made

taking into account the demographic group to

which the user belongs.

• Knowledge-based: it has information about how

an item satisﬁes a user, and establishes a relation-

ship between need and recommendation.

• Utility-based: it recommends those items that

maximize an utility function.

• Case-based: it uses information about resolving

problems (cases) previous to the resolution of the

present case. They can be viewed as a subtype

of the knowledge-based and utility-based recom-

mender systems.

In order to be used in tourism systems, a sig-

niﬁcant problem detected in previous models is not

using context attributes (Adomavicius et al., 2010).

The context is a multifaceted concept that has been

studied in different disciplines, including Computer

Science (mainly in Artiﬁcial Intelligence), Cognitive

Science, Linguistics, Psychology and Organizational

Science (Bazire and Br

ezillon, 2005). In order to

improve the quality of recommendations, the system

should not only use the qualiﬁcations and character-

istics of different POIs, or tourist preferences. Sys-

tems need to handle information of different nature

such as weather, company, schedules, location, time,

etc. (Adomavicius and Tuzhilin, 2011). Some authors

include the user’s emotional status and expand the

deﬁnition to any information that can be character-

ized and that is relevant to the interaction between a

user and an application (Dey and Abowd, 2001).

The types of recommender systems (described

above) that only consider items and users are called

recommender systems in two dimensions (Adomavi-

cius et al., 2010).

617

Luis Leiva J., Enciso M., Rossi C., Cordero P., Mora Á. and Guevara A..

Context-aware Recommendation using Fuzzy Formal Concept Analysis.

DOI: 10.5220/0004594406170623

In Proceedings of the 8th International Joint Conference on Software Technologies (ICSOFT-PT-2013), pages 617-623

ISBN: 978-989-8565-68-6

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

Therefore, in order to improve the recommen-

dations, we have to take into account the contex-

tual information available as additional categories

of data (Leiva et al., 2012). In (Adomavicius and

Tuzhilin, 2011) the authors afﬁrm that the recom-

mender system should take into consideration three

dimensions (users, items and context). They propose

different paradigms of context-aware recommender

systems:

• Contextual pre-ﬁltering (or contextualization of

recommendation input): contextual information

drives data selection or data construction for that

speciﬁc context. The selected data will be the in-

put of a 2D recommender system.

• Contextual post-ﬁltering (or contextualization of

recommendation output): the ratings are predicted

using any traditional 2D recommender system on

the entire data. Afterwards, the resulting set of

recommendations is adjusted (contextualized) for

each user using the contextual information.

• Contextual modeling (or contextualization of rec-

ommendation functions). In this recommendation

paradigm, contextual information is used directly

in the modeling technique as part of rating estima-

tion.

In our opinion, a recommender system for a con-

solidated tourist destination (probably with thousands

of POIs) should apply the contextual pre-ﬁltering

paradigm. Thus, the recommender system works with

a reduced number of POIs, decreasing the execution

time. Another important advantage of this approach

is that it can be combined with any existing 2D rec-

ommendation techniques.

The recommender system proposed in this paper

uses a content-based contextual pre-ﬁltering, based

on contextual attributes and desirable characteristics

of the POIs. Therefore, it is not necessary to have

information about previous visits or qualiﬁcations of

other tourists.

Some authors (Zenebe and Norcio, 2009) propose

the use of fuzzy logic as a formal basis for recom-

mender systems. Nevertheless we are looking for a

new approach which allows us to also cover another

question proposed in (Adomavicius and Tuzhilin,

2005): incorporation of diverse contextual informa-

tion into the recommendation process. In this paper

we tackle this issue by means of the Formal Concept

Analysis (FCA).

From the point of view of Philosophy, a concept

is a general idea that corresponds to some kind of en-

tity and that may be characterized by some essential

features of the class. When B. Ganter and R. Wille

(Wille, 1982; Ganter and Wille, 1999) conceive a

framework inside the lattice theory to formalize con-

cepts, they probably do not guess the wide diffusion

of their original work.

Nowadays, FCA has become an useful framework

both in the theoretical and in the applied areas. The

works related to FCA cover from data analysis, infor-

mation retrieval, knowledge representation, etc. It is

considered an outstanding tool in emergent environ-

ments like data mining, semantic web, etc.

The main goal of Formal Concept Analysis (FCA)

is to identify in a binary table the relationships be-

tween set of objects and set of attributes. These rela-

tionships establish a Gallois Connection which allows

us to identify the concepts using a formal framework

inside the lattice theory. Apart from building the con-

cept lattice itself, one of the key problems is to ex-

tract the set of attribute implications which hold in

the concept lattice. Implications constitute important

information that is extracted in a separate stage from

data and constitute a dual representation of the lattice

itself. One of the most important advantages in the

use of implications is that they may be managed using

Functional Dependencies Logics (Armstrong, 1974).

Another novelty in this work is the integration of

the context into the FCA method by means of set of

implications. We propose the generation of a set of

fuzzy implications which corresponds with a given

context. Thus, when the user identiﬁes his/her context

(company, weather, etc), the system enriches the spec-

iﬁcation by adding a set of new implications which

corresponds with this context. The new information

is treated with our fuzzy logic to automatically re-

duce the speciﬁcation by removing redundancy. The

reduction in the set of implications allows a more ef-

ﬁcient validation process which prune the original set

of POIs, and therefore the content-based 2D recom-

mender works with a smaller set of POIs. In ﬁgure 1

the system architecture of our proposal is depicted.

The paper is organized as follows: in the next sec-

tion we analyze some related works. Section 3 in-

troduces the theoretical background of our work and

Section 4 describes an executable logic to manage

fuzzy implications, named FSL. It will be used in

section 5 to introduce a context-aware recommender

system with a solid base. Finally some conclusions

and future works are presented.

2 RELATED WORKS

In (Zenebe and Norcio, 2009) fuzzy logic is presented

as a proper framework for tourist recommenders, ad-

dressing the problems described in (Adomavicius and

Tuzhilin, 2005). Particularly, their approach uses fea-

ICSOFT2013-8thInternationalJointConferenceonSoftwareTechnologies

618

Figure 1: Context-based recommender System.

tures of items as background data and users feedback

such as ratings of items as input. That paper provides

a solid and well-founded method to incorporate the

subjectiveness, imprecision and vagueness that usu-

ally appear in items features and user feedback. One

outstanding result of the paper is that, despite of the

ﬂexible and enriched language to specify user interest

and item features, they develop a method to infer rec-

ommendations which shows an improvement in pre-

cision without loss of recall.

Some authors have used FCA methods as

a interesting approach in recommender systems.

In (du Boucher-Ryan and Bridge, 2006) the authors

propose FCA as an approach to group items and users

into concepts. That work may be considered a collab-

orative recommender system and it shows how FCA

may be used to ﬁnd neighbours in a efﬁcient and ac-

curate way. A similar and recent approach to the same

problem with similar results may be found in (Li and

Murata, 2010). These works shows that FCA may be

successfully used in collaborative recommenders.

In this paper we work in this line and enrich the

previous results in some points. First, we aim to add

a more ﬂexible speciﬁcation by considering fuzzy re-

lations in FCA. This extension was ﬁrst introduced

in (Belohlavek, 1999). The problems that arise are re-

lated with the development of new methods to infer

the concepts and manage implications in fuzzy rela-

tions. We apply our previous theoretical results pre-

sented in (Belohlavek et al., 2012) to provide a sound

and complete fuzzy logic for functional dependencies

as a framework for the efﬁcient management of im-

plications.

3 BACKGROUND AND

THEORETICAL FRAMEWORK

We incorporate to the speciﬁcation some degree

of imprecision and uncertainty by means of Fuzzy

Logic. Since Lofti Zadeh introduced Fuzzy Set

Theory, the most usual approach is to replace the

truthfulness value set {0,1} (false and true) for

an arbitrary residuated lattice. Our proposal uses

an extension of the residuated lattice, speciﬁcally

([0,1],∨,∧, 0,1, ⊗,→,

∗

,r) in which the unit inter-

val [0, 1] is endowed with the following operations:

the inﬁmum (denoted by ∧) that plays the role of uni-

versal quantiﬁer, the supremum (∨) as the existential

quantiﬁer, an arbitrary left-continuous t-norm (⊗) as

the conjunction, the residuum deﬁned by a → b =

sup{x ∈ [0,1] | x ⊗ a ≤ b}, a truth-stressing hedge

operation

∗

and the difference r. The most used

t-norms are (standard) product, Łukasiewitz product

and G

odel product. Truth-stressing hedges (H

ajek,

2001) are a class of unary truth functions that cap-

tures the semantic of the “very true” notion. The two

boundary cases of hedges are identity and so-called

globalization (i.e. 1

∗

= 1 and x

∗

= 0 for all 1 6= x ∈ L).

Finally, the difference operation is given by: x r y = x

if y < x and 0 otherwise.

A fuzzy set in an universal set U is a mapping

A: U → [0,1] and the set operations are deﬁned point-

wise as follows: for A,B : U → [0,1], for all u ∈ U,

(A ∪ B)(u) = A(u) ∨ B(u), (A ∩ B)(u) = A(u) ∧ B(u),

(A ⊗ B)(u) = A(u) ⊗ B(u), (A → B)(u) = A(u) →

B(u), (Ar B)(u) = A(u)r B(u), and A

∗

(u) = (A(u))

∗

Moreover, ∅ and U are the fuzzy sets in which, for all

u ∈ U, ∅(u) = 0 and U(u) = 1.

The set inclusion can be extended as follows: for

A,B : U → [0, 1], the grade in which A is a subset of B

S(A,B) =

u∈U

(A(u) → B(u))

Particularly, if S(A,B) = 1 we write A ⊆ B and, in

this case, A(u) ≤ B(u) for all u ∈ U.

We are going to work with ﬁnite fuzzy sets, that

is, fuzzy sets in which at most a ﬁnite number of el-

ements has non-zero values. In the notation that we

are going to use, zero-valued elements does not ap-

pear and grade 1 is omitted. So, for example, A =

{b/

0.4

,d/

0.1

, f } denotes that A(b) = 0.4, A(d) = 0.1,

A( f ) = 1 and A(x) = 0 otherwise.

As we have presented before, we organize the in-

formation of the recommender system using the fuzzy

extension of Formal Concept Analysis (FCA) intro-

duced in (Belohlavek, 1999) that may be consider the

most current trend in this area.

Context-awareRecommendationusingFuzzyFormalConceptAnalysis

619

The starting point in fuzzy FCA is the fuzzy re-

lation

that captures the degree in which a given at-

tribute holds on an object. Speciﬁcally, given a ﬁ-

nite set of objects X and a ﬁnite set of attributes Y ,

fuzzy FCA extracts knowledge from a fuzzy relation

I : X × Y → [0,1] where I(x,y) = ϑ means that ϑ is

the degree in which the object x has the attribute y.

Usually, the fuzzy relation I is showed in a table in

which rows represents objects, columns corresponds

to attributes and in position (x,y) on the table appears

the degree I(x,y).

An important information that can be extracted

from the fuzzy relation is given in terms of attribute

implications. They are formulas of the form A ⇒ B

where A and B are fuzzy sets of attributes. The grade

in which this attribute implication is satisﬁed by a

fuzzy relation I is given by

||A ⇒ B||

x∈X

(S(A,I

)

∗

→ S(B,I

))

where I

denotes the fuzzy set in which I

(y) = I(x,y)

for all y ∈ Y . So, for example,



0.2



⇒



0.8



means that every object that has attribute b to degree

at least 0.2 and attribute d to degree 1, has attribute c

to degree at least 0.8.

Observe that the left and right hand side of the im-

plications (the A and B sets) may be empty. If B if

the empty set, the implication captures an informa-

tion which always valid and it has not to be consid-

ered in the inference process. Nevertheless, if the A

set is empty the implication provides a relevant infor-

mation, particularly in the application we are working

with. For instance, the implication ∅ ⇒



0.8



interpreted as follows: the c attribute must have a de-

gree at least 0.8.

Given a fuzzy relation I, A

=⇒ B denotes that the

implication A ⇒ B holds to degree at least ϑ and it

is equivalent to ensure that A ⇒ ϑ ⊗ B is satisﬁed to

degree 1 (see (Belohlavek et al., 2012) for further de-

tails). We use ϑ ⊗B to denote so-called ϑ-multiple of

B which is a fuzzy set such that (ϑ ⊗B)(y) = ϑ ⊗B(y)

for all y ∈ Y . The cited result ensures that the user

may specify implications with degrees and they can

be translated to implications without degrees to get a

simpler management in the automated methods.

In FCA literature, this fuzzy relation is usually called

“context” but we omit this denomination to avoid confusion

with the term context used in recommender systems.

4 A LOGIC FOR THE

MANAGEMENT OF FUZZY

ATTRIBUTE IMPLICATIONS

For the management of the information given in terms

of implications, an automated method to infer new in-

formation from a set of implications is required. Al-

though there exist in the literature several axiomatic

systems, they have not been developed for the de-

sign of such automated methods. In (Belohlavek

et al., 2012), the authors presented the Fuzzy Attribute

Simpliﬁcation Logic, FSL, providing a sound and

complete axiomatic system for reasoning with impli-

cations and, for ﬁrst time, an automated deduction

method. The system consists of three deduction rules,

[Ax] ` AB ⇒ A (Axiom)

[Sim] A ⇒ B,C ⇒ D ` A(C r B) ⇒ D (Simpliﬁca-

tion)

[Mul] A ⇒ B ` ϑ

∗

⊗A ⇒ ϑ

∗

⊗B (Multiplication)

where A,B,C,D are fuzzy sets and ϑ ∈ [0,1]. Here,

we use the convention of writing AB instead of A ∪ B.

The most relevant characteristic of this axiomatic

system is that the inference rules can be seen as equiv-

alence rules that allows us to remove (simplify) re-

dundant information. This simpliﬁcation is applied

both to implications and to attributes inside of impli-

cations. It is specially appropriated for heterogeneous

environment where different users provide several im-

plications which may cause speciﬁcations with a hide

degree of redundancy. These equivalencies are the

following

1. {A ⇒ B} ≡ {A ⇒ B r A};

2. {A ⇒ B, A ⇒ C} ≡ {A ⇒ BC};

3. {A ⇒ B,C ⇒ D} ≡ {A ⇒ B, A(C r B) ⇒ D r

B} when A ⊆ C.

where A, B, C and D are fuzzy sets.

5 APPLICATION OF FSL TO A

CONTEXT RECOMENDER

SYSTEM

Up to now, we have presented all the theoretical foun-

dations that we combine to incorporate the context

into a recommender system. Our proposal is based

on fuzzy attribute implications and it has the follow-

ing characteristics:

• Fuzzy Logic and fuzzy multivalued FCA have

been shown to be sound formalisms to specify

and reasoning with uncertainty.

ICSOFT2013-8thInternationalJointConferenceonSoftwareTechnologies

620

• We propose a uniﬁed combination of context-

based reasoning inside a content-based recom-

mendation framework.

• We associate each context with a set of fuzzy

implications deﬁned on the items characteris-

tics.

• The user introduces in the system all the char-

acteristics of his/her context and then the rea-

soning methods depurate the set of all associ-

ated implications to get an equivalent and sim-

pler set of fuzzy implications.

• The ﬁnal set of implications is used to validate

the items to be recommended. Thus, the origi-

nal set of items is pre-ﬁltered and only a subset

of them will be the input of the recommender

system.

Now, we detail how context information is rep-

resented by means of fuzzy implications. POIs are

represented by a set of attributes which describes its

features (it is cheap or expensive, its atmosphere is

romantic or cheerful, etc.). Real world data are of-

ten complex and difﬁcult to be labelled with a bi-

nary domain without loss of information. For instance

a restaurant may have a very beautiful garden with

some tables where children may enjoy and also an

intimate hall with quiet music for a romantic dinner.

We propose to store these items features by using a

fuzzy relation, as example 1 shows. Thus, each row

corresponds with an object and each column with an

attribute.

Example 1. We consider a group of POIs of a tourism

destination with some attributes to describe them (De-

sign, Atmosphere, Price and Facilities). Each at-

tribute has a set of ﬁnite possible values and let us

suppose that a destination expert manages the system

by giving a degree to each value in the domain. Thus,

we get a table of objects with grades by ﬂattening the

information to obtain a fuzzy relation (see table 1).

The context of the system is represented by a set

of discrete domains C = {C

,. .. ,C

}. Each domain

is associated with a dimension of the context (for in-

stance weather, company, time of the day, etc.) and

it has a ﬁnite set of values: C

= {v

,. .. ,v

}. We de-

ﬁne the user context, named state, as a n-tuple of pairs

(value of the domain, degree).

Example 2. Let Weather, Company and Time of the

day be three context dimensions with the following

domains: Weather={hot, warn, cloudy, rainy}, Com-

pany={alone, friends, couple, family, large group}

and Time={morning, afternoon, evening, night}. A

user may specify his context by means of the state:

[(Hot, 0.8), (afternoon,0.8), (family,0.7)].

We deﬁne a context segment to be an speciﬁc

value of a domain and its associated degree. We pro-

vide a framework where each context segment is as-

sociated with a set of fuzzy implications. As we pre-

sented in section 3, implications may be labelled with

a degree to express the truthfulness of the implication

itself. Thus, the degree of the context segment is in-

herited by all its implications.

Example 3. The implications associated with each

context segment are introduced as follows (observe

that the degree of the context is transferred to the im-

plication):

• Context segment: Hot/

0.8

. Implications:

Expensive/

0.8

,ClosedSpace/

0.8

⇒ Air

Cond./

0.8

, Views/

0.9

, Picturesque/

0.2

OpenSpace/

0.8

⇒ Inexpensive/

0.7

• Context segment: Afternoon/

0.8

. Implications:

OpenSpace/

0.8

⇒ Terrace/

0.6

, Inexpensive/

0.9

• Context segment: Family/

0.7

. Implications:

0.7

⇒ Inexpensive/

0.6

ClosedSpace/

0.8

0.7

⇒ Air Cond./

0.9

As we mention in Section 4, the implication

0.7

⇒

Inexpensive/

0.6

in the last context segment indicates

that if the user is accompanied by his family with de-

gree 0.7 then the restaurant need to be inexpensive

with a degree greater than 0.6.

When a system manages a certain amount of infor-

mation, we have to provide an automatic way to an-

alyze and extract the important information to reduce

the computation cost. In our approach we propose

to use the automatic methods developed over FSL to

depurate the speciﬁcation of the context and obtain a

canonical set of implications. There is a lot of works

related with the search of basis in FCA. An up to date

and complete work is (Bertet and Monjardet, 2010)

where the authors identify a set of properties that may

be cover by different basis deﬁnitions (minimal, di-

rect, canonical, etc). These characteristics may be

combined providing a diferent notion of basis. The

work of Bertet and Monjardet is focussed on crisp

FCA and it is still an open problem the deﬁnition of

suitable deﬁnitions for fuzzy implications basis for

fuzzy FCA.

Nevertheless, as example 4 shows, it is possible to

illustrate the beneﬁts of using FSL to get an equiva-

lent and simpler set of implications.

Example 4. From the speciﬁcation of the above ex-

ample, if we have that the context provided by the user

is {Hot/

0.8

, Afternoon/

0.8

, Family/

0.7

} then the set of

implication is built by adding all the above implica-

tion in a uniﬁed set:

Context-awareRecommendationusingFuzzyFormalConceptAnalysis

621

Table 1: FCA representation of POIs.

Design Atmosphere Price Facilities

OpenSpace ClosedSpace Quiet Lively Picturesque Inexpensive Moderate Expensive Air Cond. Views Terrace

Standard Restaurant 0.3 0.8 0.8 0.5 0.2 0.7 0.3 0.3 0.3 0.3 0.3

Michelin Star 0.1 0.8 0.9 0.2 0.1 0 0.1 0.9 0.9 0.5 0.1

Burger 0.3 0.8 0.3 0.8 0.1 0.9 0.3 0.1 0.8 0.1 0.4

Tapas Bar 0.3 0.8 0.2 0.8 0.9 0.9 0.5 0.1 0.5 0.1 0.1

Pizzeria 0.1 0.9 0.3 0.8 0.7 0.9 0.5 0.3 0.8 0.3 0.5

Beach Fresh Fish 0.9 0.2 0.3 0.8 0.8 0.5 0.7 0.8 0.3 0.9 0.9

{Expensive/

0.8

,ClosedSpace/

0.8

⇒ Air Cond./

0.8

Views/

0.9

, Picturesque/

0.2

;

OpenSpace/

0.8

⇒ Inexpensive/

0.7

;

OpenSpace/

0.8

⇒ Terrace/

0.6

, Inexpensive/

0.9

;

0.7

⇒ Inexpensive/

0.6

;

ClosedSpace/

0.8

0.7

⇒ Air Cond./

0.9

}

Using the inference rules of FSL we may remove

redundant information and we obtain an equivalent

and simpler set of implications:

{expensive/

0.8

,ClosedSpace/

0.8

⇒ Views/

0.9

Picturesque/

0.2

;

OpenSpace/

0.8

⇒ Terrace/

0.6

;

0.7

⇒

Inexpensive/

0.6

;

ClosedSpace/

0.8

0.7

⇒ Air Cond./

0.9

}

It should be noted that the redundancy removal al-

gorithm has a quadratic complexity with respect to

the number of implications. This number is much

lower than the number of POIs (usually several thou-

sands) in any touristic destination. Finally, our system

make use of the information associated with the user

context, provided by the uniﬁed and depurated set of

implications, to stretch the set of POIs to be recom-

mended to the user. For each POI in the FCA table,

we validate the set of implications, removing all the

POIS that does not satisﬁed them. The complexity of

this last step is O(n) where n is the number of POIs.

This way, we have designed a linear contextual pre-

ﬁltering process.

Example 5. As in example 4, if the user context is

the afternoon of a hot day, traveling with his family,

our contextual pre-ﬁltering process reduces the list of

restaurants of table 1 to Burger and Pizzeria, since:

• Michelin star does not satisfy

Expensive/

0.8

,ClosedSpace/

0.8

⇒ Views/

0.9

Picturesque/

0.2

• Beach Fresh Fish does not satisfy

0.7

⇒

Inexpensive/

0.6

• Standard restaurant and Tapas bar do not sat-

isfy ClosedSpace/

0.8

0.7

⇒ Air Cond.

0.9

This way, the set of POIs to be managed by

the content-based recommender is signiﬁcatively re-

duced.

6 CONCLUSIONS AND FUTURE

WORKS

Content-based recommender systems may be signi-

ﬁcatively improved by including contextual informa-

tion. To achieve this goal, we use fuzzy logic and

formal concept analysis as a solid framework to com-

bine context information and content-based recom-

menders. More speciﬁcally, we use Simpliﬁcation

Logic to develop an intelligent and linear pre-ﬁltering

process. This process generates a set of implications

which captures the context information and that it is

used to validate the items to be recommended. The

method is applied in two steps: in the ﬁrst one we

translate the context information provided by a user

as an state, i.e. a simpliﬁed set of fuzzy implications,

and in the second step, the implications are used to

ﬁlter the items which fulﬁlls them.

This work may be extended by considering two

future works related with the two steps of the pre-

ﬁltering process. First, the implications induced by

the context may be enriched with implications auto-

matically extracted from the user interests stored in

the content. We propose to use formal concept analy-

sis to extract this information. As a second trend, we

propose to substitute the recommender algorithms by

formal concept analysis techniques.

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