FSM  is  a database model  that has been  recently proposed by  the  authors. FSM  uses basic  concepts of
classification,  generalization,  aggregation  and  association  that  are  commonly  used  in  semantic  modelling  and 
supports  the  fuzziness  of  real-world  at  attribute,  entity,  class  and  relations  intra  and  inter-classes  levels. Hence,  it
provides  tools  to  formalize  and  conceptualize  real-world  within  a  manner  adapted  to  human  perception  of  and
reasoning about this real-word. In this paper we briefly review basic concepts of FSM and provide some notes on an
extended query language adapted to it.ou

Chakhar, Salem

Telmoudi, Abdelkader

English

Name not available

  
PREMIER CONGRES INTERNATIONAL DE 
SIGNAUX, CIRCUITS & SYSTEMES 
Monastir du 18 au 21 Mars 2004 
  
 
 
Some Notes on an Extended Query Language for FSM 
Abdelkader Telmoudi1, and  Salem Chakhar2  
1Ecole Nationale déIngenieurs de Tunis, B.P. 37 Le Belved`re 1002 - Tunis, Tunisie.  
abdelkader.telmoudi@enit.rnu.tn 
 
2LAMSADE, Universite  Paris Dauphine, 
 Place du Marechal de Lattre de Tassigny, F-75775 Paris Cedex 16, France.  
chakhar@lamsade.dauphine.fr 
 
Abstract’ FSM is a database model that has been recently proposed by the authors. FSM uses basic concepts of 
classification, generalization, aggregation and association that are commonly used in semantic modelling and 
supports the fuzziness of real-world at attribute, entity, class and relations intra and inter-classes levels. Hence, it 
provides tools to formalize and conceptualize real-world within a manner adapted to human perception of and 
reasoning about this real-word. In this paper we briefly review basic concepts of FSM and provide some notes on an 
extended query language adapted to it. 
Keywords: ’  Fuzzy class, Fuzzy database, Fuzzy query language, Fuzzy semantic model.  
1 INTRODUCTION
There have been several tentatives to develop data 
models that support the fuzziness of real-world 
[1][4][9]. Most of these works consider that each entity 
in real-world belongs to one and only one class, which 
is very restrictive in many applications (e.g. cosmology, 
archaeology, spatial modelling). In database literature, 
we may enumerate some recent extensions of object-
oriented data models to support the uncertainty of real-
world at the class definition level [5][10][7] and only 
few extensions of semantic data models have been 
proposed [3][6]. In the same direction of research, the 
authors have proposed a new database model, namely 
Fuzzy Semantic Model (FSM) [2], that supports fuzzy 
class definition and authorises an entity to be a member 
of one or more classes with different degrees of 
membership. In this paper we briefly review basic 
concepts of FSM and then provide some notes on an 
extended query language adapted to it. 
2 FUZZY SEMANTIC MODEL 
2.1 Constructs of FSM 
Constructs of FSM (see [2] for a full description of 
FSM) are extensions of the Unifying Semantic Model 
[8] that are enriched with new concepts enabling the 
database system to support fuzziness of real-world.  
The space of entities E is the set of all entities of the 
domain of interest.  A fuzzy entity e in E is a natural or 
artificial entity that we cannot assign to an exact class. 
In other words, a fuzzy entity verifies only (partially) 
some extent properties of one or some classes. Classic 
entities are particular case of fuzzy entities since they 
are assigned to exactly one class.  
A fuzzy class K in E is a collection of fuzzy entities: 
K={(e,ρK(e)): eÎE; ρK(e) > 0}. ρK is a characteristic or 
membership function and ρK(e) represents the  degree of 
membership (or d.o.m) of fuzzy entity e in fuzzy class 
K.  Membership function ρK maps the elements of E to 
the range [0,1], where 0 implies no-membership and 1 
implies full membership. A value between 0 and 1 
indicates the extent to which entity e can be considered 
as an element of fuzzy class K.  
FSM contains several types of basic fuzzy classes 
that are summed up in Table 1. The elements of a fuzzy 
class are called members. Each fuzzy class K may have 
any number of three types of members: (a) true-
members (i.e. entities e with ρK (e)=1), (b) pseudo-
members (i.e. entities e with 0.17 £ ρK (e) < 1), and (c) 
weak-members (i.e. entities e with 0 < ρK (e)< 0.17). 
FSM supports four different relationships: property, 
 2 
 
decision-rule, membering and interaction.  Property 
relationships relate fuzzy classes to domain classes. 
Each property relationship creates an attribute and each 
attribute has a unique datatype and may be single-
valued, unknown, undefined, null or multi-valued. 
Decision rule relationships are implementation of the 
extents of fuzzy classes, i.e., the set of properties-based 
rules used to assign fuzzy entities to fuzzy classes (see 
2.2).  Membering relationships relate fuzzy entities to 
fuzzy classes through the definition of d.o.m. 
Interaction relationships relate members of one fuzzy 
class to other members of one or several fuzzy classes.  
 
Name Description 
Complete fuzzy class A fuzzy class that all its members have 
a d.o.m equal to 1  
Non-complete fuzzy 
class 
A fuzzy class that has at least one 
member with a d.o.m strictly less than 1 
Strong fuzzy class A fuzzy class whose members can exist 
on their own 
Weak fuzzy class A fuzzy class that the existence of its 
members depend on the existence of 
other classes 
Compact fuzzy class A complete and strong fuzzy class 
Non-compact fuzzy 
class 
A complete and weak fuzzy class 
Fuzzy entity-class A new entity that cannot be assigned to 
any pre-existing fuzzy class 
Domain class A space to which an attribute·s values 
are mapped 
Table 1: FSM basic fuzzy classes 
 
In FSM there are several complex fuzzy classes (see 
Table 2), that permit to implement the semantics of 
real-world among objects in terms of generalization, 
specialization, aggregation, grouping and composition 
relationships, which are commonly used in purely 
semantic modelling.  
2.2 Entity/Class Membership Function in FSM 
As it is underlined above, a fuzzy class is a 
collection of many fuzzy entities having some similar 
properties. Fuzziness is thus induced whenever an 
entity verifies only (partially) some of these properties. 
We denote by PK={piK: K Ì E; i >=1} the set of these 
properties for a given fuzzy class K.  PK is the extent of 
class K. These properties may be derived from the 
attributes of the class and/or from common semantics. 
The extent to which each of these properties determines 
the class K is not the same. Indeed, there are some 
properties that are more discriminative than others. To 
ensure this, we associate to each property piK a 
normalized weight wiK reflecting its importance in 
deciding whether or not an entity e is a member of a 
given class K. To keep the coherence of our model, we 
impose that SiwiK =1. 
On the other hand, an entity may verify fully or 
partially extent properties of a given fuzzy class. Let 
DiK be the basic domain of extent property piK values 
and PiK is a subset of DiK, which represents the set of 
possible values of property piK. The partial membership 
function of an extent property value is   PiK, which maps 
elements of DiK into [0,1]. For any attribute value v Î 
DiK,   PiK(v) = 0 means that fuzzy entity e violets  
property piK and   PiK(v) = 1 means that this entity 
verifies fully the property value. The number v is the 
value of the attribute of entity e on which the property 
piK is defined. More generally, the value of   PiK(v) 
represents the extent to which entity e verifies property 
piK   of fuzzy class K. Accordingly, for any fuzzy entity 
e, the global d.o.m ρK(e) for a fuzzy class K is equal to 
Si wiK “   PiK(v).  
 
Name Description 
Interaction fuzzy 
class 
A fuzzy class that describe the interaction 
of two or more fuzzy classes 
Fuzzy superclass A generalization of one or many, simple 
or complex, fuzzy classes 
Fuzzy subclass A specialization of one or many, simple or 
complex, fuzzy classes 
Composite fuzzy 
class 
A fuzzy class that has other fuzzy classes 
as members  
Aggregate fuzzy 
class 
A fuzzy class that its members are 
heterogeneous and exhaustive collection 
from several fuzzy classes  
Grouping fuzzy class A fuzzy class that its members are 
homogenous collection of members from 
the same fuzzy class 
Table 2: FSM complex fuzzy classes 
 
3 AN EXTENDED QUERY LANGUAGE  
 In this section we present some notes on an ongoing 
conceptual query language for accessing FSM-based 
databases and illustrate some examples of data retrieve 
operations. All examples of this section rely on the 
database schema illustrated in Figure 1.  For the sake of 
clarity, only necessary classes and relationships are 
depicted in this figure.  
In the example database, GALAXY is an aggregate 
fuzzy class whose members are unique collections of 
members from COMETS, STARS, and PLANETS 
grouping fuzzy classes.  These last ones are 
homogenous collections of members from strong fuzzy 
classes COMET, STAR, and PLANET, respectively. 
NOVAE and SUPERNOVAE are two attribute-defined 
fuzzy subclasses of STAR basing on Type_of_Star 
attribute. SCIENTIST is a collection of   astronomists 
and DISCOVEY is an interaction fuzzy class between 
SUPERNOVAE and SCIENTIST.  
The general definitions of a fuzzy class and a fuzzy 
subclass in FSM are as follows (note that attributes· 
definitions are partially inspired from [7]).   
 3 
 
CLASS <class_name> WITH DOM OF <gdom> 
{ 
SUPERCLASS: 
OF  <sclass_name_1> WITH DOM <scdom_1> 
... 
OF  <sclass_name_k> WITH DOM <scdom_k> 
 
EXTENT: 
{<Ext_attr_1> | <Ext_sphrase_1>} WITH WEIGHT  <w1>  
... 
{<Ext_attr_n> | <Ext_sphrase_n>} WITH WEIGHT <wn> 
 
ATTRIBUTES: 
Attr_1_name: [FUZZY] DOMAIN <domaine_1>: TYPE OF 
<type_1> WITH DOM OF <dom_1>:  [REQUIRED][UNIQUE] 
... 
Attr_r_name: [FUZZY] DOMAIN <domaine_r>: TYPE OF <type_r> 
WITH  DOM OF <dom_r>: [REQUIRED][UNIQUE] 
 
CONTENTS: 
[ENUMERATED COMPOSITION FROM <class_list_1>] 
[SELECTED COMPOSITION ON ATTRIBUTES <attr_list_1> 
FROM <class_list_2>] 
[AGGREGATION OF <class_list_3>] 
[GROUPING FROM <class_name_2>] 
 
INTERACTION: 
<inter_name_1> WITH <c_name_1> INVERSE IS <i_inter_name_1> 
... 
<inter_name_z> WITH <c_name_z> INVERSE IS <i_inter_name_z> 
} 
 
SUBCLASS <sclass_name> WITH DOM OF <scdom>  
{ 
SPECIALIZATION: 
OF  <class_name_1> WITH DOM <scdom_1>: 
[BY ENUMERATION]  
[ON ATTRIBUTES  <attr_list_1>]  
[ON SEMANTICS <sphrase_list_1>]  
[BY INTERSECTION WITH <class_list_1>] 
[BY DIFFERENCE WITH <d_class_name_1>]  
OF  <class_name_q> WITH DOM <scdom_q>: 
 ... 
EXTENT: 
{<Ext_attr>|<Ext_sphrase>} WITH WEIGHT <w1>  
... 
{<Ext_attr>|<Ext_sphrase>} WITH WEIGHT <ws> 
 
ATTRIBUTES: 
Attr_1_name: [FUZZY] DOMAIN <domaine_1>: TYPE OF 
<type_1> WITH DOM OF <dom_1>: [REQUIRED][UNIQUE] 
... 
Attr_t_name: [FUZZY] DOMAIN <domaine_t>: TYPE OF <type_t> 
WITH DOM OF <dom_t>: [REQUIRED][UNIQUE] 
 
INTERACTION: 
<inter_name_1> WITH <c_name_1> INVERSE IS <i_inter_name_1> 
... 
<inter_name_y> WITH <c_name_y> INVERSE IS <i_inter_name_y> 
} 
Subclasses may have their own subclasses and if this 
is the case, they must have SUPERCLASS components.  
As examples, fuzzy classes GALAXY, STAR and 
SUPERNOVAE in the example database may be 
implemented as follows:  
 
CLASS galaxy WITH DOM OF gdom 
{ 
EXTENT: 
Location WITH WEIGHT 1.0  
ATTRIBUTES: 
Name: TYPE OF string WITH DOM 1.0: REQUIRED UNIQUE 
Age:  FUZZY DOMAIN {very young, young, old, very old}: TYPE 
OF integer WITH DOM OF 1.0: REQUIRED 
Location:  FUZZY DOMAIN {in, near, very near, distant, very 
distant}: TYPE OF real WITH DOM OF 1.0  
 
CONTENTS: 
AGGREGATION OF comets, stars, planets 
} 
 
CLASS star WITH DOM sdom 
{ 
SUPERCLASS: 
OF supernovae WITH DOM scdom_sn 
OF novae WITH DOM scdom_n 
 
EXTENT: 
Luminosity WITH WEIGHT 0.7  
Weight WITH WEIGHT 0.3  
 
ATTRIBUTES: 
S_Name: TYPE OF string WITH DOM 1.0: REQUIRED UNIQUE 
Type_of_Star: TYPE OF symbolic (novae, supernovae) WITH DOM 
1.0: REQUIRED  
Age:  FUZZY DOMAIN {very young, young, old, very old}: TYPE 
OF integer WITH DOM OF 1.0: REQUIRED 
Location:  FUZZY DOMAIN {in, near, very near, distant, very 
distant}: TYPE OF real WITH DOM 1.0: REQUIRED 
Luminosity:  FUZZY DOMAIN [0.0001Ls-100000Ls]: TYPE OF real 
WITH DOM OF 1.0 
Weight: FUZZY DOMAIN [0.1Ws-100Ws]: TYPE OF real WITH 
DOM OF 1.0: REQUIRED 
} 
 
SUBCLASS supernovae WITH DOM sndom 
{ 
EXTENT: 
Luminosity WITH WEIGHT 0.3  
Weight WITH WEIGHT 0.7  
 
ATTRIBUTES: 
SN_Name: TYPE OF string WITH DOM 1.0: REQUIRED UNIQUE 
Type_of_SN: TYPE OF string WITH DOM 1.0: REQUIRED 
 
SPECIALIZATION: 
OF star WITH DOM scdom ON ATTRIBUTES Type_of_Star  
 
INTERACTION: 
discoverer WITH  scientist INVERSE IS discovers  
} 
The symbols Ls and Ws above are luminosity and 
weight of the sun, respectively; they are often used as 
measurement units. In the following, we provide some 
notes on an ongoing conceptual query language through 
some examples of data retrieve operations.  
The syntax of a retrieve query in FSM is as follows: 
[FROM ({<class_name> WITH DOM <op1> <class_level> |  
                <member_type> MEMBER  OF <class_name>})] 
RETRIEVE  {<attribute_list>|(<attr_ name> OF <inter_name>)} 
[ORDER BY  <order_list>] 
[WHERE (<selection_express> [WITH DOM <op2> <attr_level>])] 
The argument of the FROM statement is a list of 
classes· names with their respective levels of selection 
(class_level) or a specific type of members 
 4 
 
(member_type), which can take the value of True, 
Pseudo or Weak. Only members that have a global 
d.o.m verifying the arithmetic comparison ensured by 
the operator op1 or have a type of member_type are 
considered in the selection process. The attribute_list in 
the RETRIEVE statement is the list of attributes to be 
delivered to the user.  This statement permits also to 
select attributes of any class that is in interaction with 
one or more classes in the FROM statement. The 
ORDER BY statement is used to choose the way the list 
of entities is ordered. The selection_express in the 
WHERE statement is a set of symbolic, numerical or 
logical conditions that should be verified by the 
attributes of all selected entities.  When it is necessary, 
attributes-based conditions may be combined with 
appropriate selection levels (attr_level) and only 
entities that their attributes· values have a partial d.o.m 
verifying the arithmetic comparison ensured by the 
operator op2 are selected. Some examples of data 
retrieve operations are enumerated below. 
 
Query1. Retrieve the name and type of supernovae 
that have d.o.m equal or greater to 0.7 and have 
luminosity greater to 5Ls with partial d.o.m equal or 
greater to 0.9. 
 
FROM supernovae WITH DOM ³ 0.7 
RETRIEVE SN_Name, Type_of_SN 
WHERE Luminosity > 5Ls WITH DOM ³ 0.9 
 
Query2. Retrieve the name of all true supernovae, 
and the name and laboratory of their discoverers.  
 
FROM True MEMBER OF supernovae   
RETRIEVE SN_Name, Name OF discoverer, 
Laboratory OF discoverer 
 
Query3. Retrieve location, luminosity and weight of 
all stars having d.o.m. greater to 0.75 and of type 
supernovae of type SN II and  of weight greater to 10 
Ws  with partial d.o.m greater to 0.5 .  
 
FROM star WITH DOM > 0.75 
RETRIEVE Location, Luminosity, Weight 
WHERE Type_of_Star=supernovae and type_of_SN= 
SN II and weigtht > 10Ws WITH DOM > 0.5 
 
Query4. Retrieve dates of discover and names of all 
supernovae of type SN I that are located in milky way 
galaxy with a d.o.m. greater to 0.5 and having 
luminosity greater to 17Ls with d.o.m less to 0.7. 
 
FROM discovery, supernovae, galaxy 
RETRIEVE SN_Name, Discovry_Date,  
WHERE Type_of_SN = SN I and  (galaxy.Name=milky-
way and galaxy.Location= supernovae.Location WITH 
DOM >0.5) and Luminosity >  17Ls  WITH DOM < 0.7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4 CONCLUSION 
In this paper, we have briefly reviewed basic 
concepts of FSM’ a database model that has been 
recently proposed by the authors’ and provide some 
notes on an extended query language adapted to it.  In 
current time, we investigate the problem of the 
definition of partial membership functions through 
possibility and evidence theories. We are also 
concerned with several topics related to the 
implementation of a prototype of FSM.   
REFERENCES 
[1] W.P. Buckles, F.E. Petry, ”A fuzzy model for relational 
databases,„ Fuzzy Sets Systems, vol. 33, pp. 213-226, 1992.  
[2] S. Chakhar, A. Telmoudi, ”Extending database capabilities: 
Fuzzy semantic model,„ Proc. Int. Conf. Sci. of Electronic, 
Technologies of Inf. and Telecommunications 2004, to appear. 
[3] G.Q. Chen, E.E. Kerre, ”Extending ER/EER concepts towards 
fuzzy conceptual data modeling,„ Proc. of the 1998 IEEE Int. 
Conf. on Fuzzy Systems, pp. 1320-1325, 1998. 
[4] D. Dubois, H. Prade, ”Using fuzzy sets in database systems: 
Why and how?,„ Proc. Flexible Query Answering Systems,  pp. 
89-103, 1996. 
[5] R. George, R. Srikanth, F.E. Petry, B.P. Buckles, ”Uncertainty 
management issues in object-oriented data model,„ IEEE Trans. 
Fuzzy Systems, vol. 4, pp. 179-192, 1996. 
[6] W.Y. Liu, N. Song, ”The fuzzy association degree in semantic 
data models,„ Fuzzy Sets Systems, vol. 117, pp. 203-208, 2001. 
[7] Z.M. Ma, W.J. Zhang, W.Y. Ma, ”Extending object-oriented 
databases for fuzzy information modeling,„ Inf. Sys., in press.  
[8] S. Ram, ”Intelligent database design using unifying semantic 
model,„ Inf. and Management, vol. 29, pp. 191-206, 1995.  
[9] A. Yazici, R. George, ”Fuzzy database modeling,„ Heidelberg: 
Springer-Verlag, 1999.  
[10] A. Yazici, R. George, D. Aksoy, ”Design and implementation 
issues in fuzzy object-oriented data model,„ Inf. Sci., vol. 108, 
pp. 241-260, 1998.  
Figure 1: Graphical representation of the example database 
  GALAXY  
Agg 
Grp Grp Grp 
  PLANETS    STARS    COMETS  
 PLANET          STAR           COMET         
A 
 SCIENTIST   SUPERNOVAE         
 DISCOVERY 
 NOVAE         


Some notes on an extended query language for FSM

Portsmouth University Research Portal (Pure)

A fuzzy model for relational databases,„

Design and implementation issues in fuzzy object-oriented data model,„

Extending database capabilities: Fuzzy semantic model,„

Extending ER/EER concepts towards fuzzy conceptual data modeling,„

Extending object-oriented databases for fuzzy information modeling,„ Inf. Sys.,

Some notes on an extended query language for FSM

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