OWL-FC: an upper ontology for semantic modeling of Fuzzy Control

FOCUS

OWL-FC: an upper ontology for semantic modelingof Fuzzy Control

C. De Maio G. Fenza D. Furno

V. Loia S. Senatore

Published online: 9 November 2011

Springer-Verlag 2011

Abstract This work introduces an OWL-based upper

ontology, called OWL-FC (Ontology Web Language for

Fuzzy Control), capable to support a semantic definition of

Fuzzy Control. It focuses on the fuzzy rules representation

by providing domain independent ontology, supporting

interoperability and favoring domain ontologies re-usabil-

ity. The main contribution is that OWL-FC exploits Fuzzy

Logic in OWL to model vagueness and uncertainty of the

real world. Moreover, OWL-FC enables automatic dis-

covery and execution of fuzzy controllers, by means of

context aware parameter setting: appropriate controllers

can be activated, depending on the parameters proactively

identified in the work environment. In fact, the semantic

modeling of concepts allows the characterization of con-

straints and restrictions for the identification of the right

matches between concepts and individuals. OWL-FC

ontology provides a wide, semantic-based interoperability

among different domain ontologies, through the specifica-

tion of fuzzy concepts, independently by the application

domain. Then, OWL-FC is coherent to the Semantic Web

infrastructure and avoids inconsistencies in the ontology.

Keywords Ontology OWL-S Fuzzy Control

1 Introduction

The Semantic Web has contributed to change the models of

communication and interactions in last decades, with a

profound impact on the human society. It defines a new

model to connect different sources of information such as

web pages, posts, databases, etc., which enable computers

and people to work in co-operation. Past research in

Semantic Web attracted attention of two-value-based log-

ical methods, but more recent trends aim at handling

imprecise or uncertain information encountered in real

world knowledge (Sanche 2006), through fuzzy models

which can reinforce semantic-based systems and bridge the

gap between vague human-understanding and hard

machine-processing. The use of fuzzy techniques in the

ontology modeling can provide an adequate add-on to

reflect real world capture uncertainty in the relationship

and conceptual information.

This paper presents an OWL-based upper ontology,

called OWL-FC (Ontology Web Language for Fuzzy

Control) which, by means of a set of markup language

constructs, provides semantic specification of Fuzzy Con-

trol in a high-level, semantic form. OWL-FC has been

designed by completely reflecting the modeling of OWL-S

(Martin et al. 2004). In fact, we have built a parallel model

for the deployment of the fuzzy control (instead of OWL-S

web service) capabilities, through the three homonymic

modules: Profile, Model and Grounding, (details

are given in Sect. 3). Behind the benefits of a high-level

abstraction language of specification, this modeling can

easily translate and deploy a Fuzzy Control in a web

service.

C. De Maio (&) G. Fenza D. Furno V. Loia S. SenatoreCORISA (Consorzio Ricerca Sistemi ad Agenti),

Dipartimento di Informatica, Universita degli Studi di Salerno,

via Ponte don Melillo, 84084 Fisciano (SA), Italy

e-mail: [email protected]

G. Fenza


D. Furno


V. Loia


S. Senatore


123

Soft Comput (2012) 16:11531164

DOI 10.1007/s00500-011-0790-4

OWL-FC ontology provides a stable abstract model to

represent fuzzy knowledge for describing fuzzy controls. In

fact, one of the main advantages is the definition of an

ontology which is independent of the knowledge domain:

the same model is exploited to represent different fuzzy

controls and environments. Thanks to this independence,

OWL-FC ontology guarantees a clear separation between

domain knowledge and fuzzy controllers implementation.

Moreover, other benefits of OWL-FC are the automatic

execution of defined controllers as well as the support to

their discovery (i.e., in the case of matchmaking algorithm

design) by enabling context aware parametrization of the

controllers.

The paper is structured as follows. Section 2 surveys the

related works; Sect. 3 briefly introduces the role of OWL-s

in the characterization of our upper ontology. Then, Sect. 4

describes the Fuzzy Control and the OWL-based modeling.

Additional details about the relative OWL-based coding

are given in Sects. 58, where the mapping of our ontology

into a three-layer structuring is shown. An application

scenario depicted in Sect. 9 emphasizes the high flexibility

of OWL-FC in modeling Fuzzy Control and its indepen-

dence from domain ontologies. Finally, considerations and

conclusions close the paper.

2 Related works

The imprecise nature of real world information has pushed

scientific community to model knowledge representation

systems for the representation and management of uncer-

tainty, imprecision and vague knowledge. The conceptual

formalism embedded in a common ontology is often based

on crisp logic and may not suitable to represent uncer-

tainty, due to the lack of a clear separation between domain

concepts (Zhai et al. 2008). Introducing tolerance for

imprecision, through the use of Fuzzy Logic, may be

exploited in a great number of application fields.

In literature, fuzzy ontologies have been exploited to

deal with fuzzy knowledge in many application domains,

such us text, image and multimedia objects representation

and retrieval (Parr 2004; Ren et al. 2008). Lee et al. (2005)

proposed an algorithm to create fuzzy ontology for news

summarization; in Tho et al. (2006), a Fuzzy Ontology

Generation Framework (FOGA) for fuzzy ontology gen-

eration on uncertainty information has been presented. In

Abulaish (2006), a fuzzy ontology framework has been

defined, where a concept description is represented by a

fuzzy relation which encodes the degree of a property value

using a fuzzy membership function. Other trends aimed at

producing vague information representation have triggered

a mass of theoretical and applied researches about fuzzy

ontologies, whose main logical infrastructures are Fuzzy

Description Logics (briefly Fuzzy DLs). Classical DLs

with fuzzy capabilities yielding Fuzzy DLs have been

developed to represent the uncertainty in the Semantic

Web: Straccia proposed a fuzzy extension of DLALC (afragment of Description Logic, whose acronym stands for

Attributive Language with Complements), called F ALCin which fuzzy semantics is introduced to describe con-

cepts and roles as fuzzy sets (Stracci 2001) and then, in

Stracci (2005), a fuzzy extension of SHOIN D, i.e., afuzzy version of the ontology description language OWL-

DL and its syntax and semantics. Stoilos et al. (2006)

discuss Fuzzy OWL and uncertainty representation with

rules. They present a fuzzy reasoning engine that imple-

ments a reasoning algorithm for a fuzzy DL language

fKDSHIN . It handles most of OWL features. Yet, theimplementation is proprietary and not directly compatible

with any established Semantic Web technologies and tools.

Despite this trend, OWL-FC is not a fuzzy ontology but

provides Description Logic constructs useful to represent

fuzzy controllers and enable their discovery and execution.

Furthermore, OWL-FC is an OWL-like language thus it is

compatible with existing Semantic Web standards. Among

the scientific works on the development of reasoning

engines for the interpretation of imprecise knowledge,

closely related to our approach, there are several proposals.

On the one hand, XML technologies have already been

used for modeling fuzzy controllers. Indeed, Acampora and

Loia (2011) designed the Fuzzy Markup Language (FML),

a novel computer language skilled for defining detailed

structure of Fuzzy Control independent of its legacy rep-

resentation. Even though it was designed for defining the

behavior of heterogeneous hardware in the context of

ambient intelligence, it is successfully combined with

fuzzy ontologies in order to be applied to several applica-

tion domains (Lee et al. 2010).

On the other hand, in the literature, there are proposal

for fuzzy extensions of Semantic Web Rule Language

(briefly, SWRL),1 which is a rule extension to OWL DL. In

Pan et al. (2006), a fuzzy SWRL (f-SWRL) has been

defined. It includes fuzzy assertions and fuzzy rules, even

though no implementation details are given as highlighted

in Agarwal (2005); f-SWRL actually offers no fuzziness in

the rules definition. Bobillo et al. (2009) instead present a

semantic fuzzy expert system for a fuzzy balanced score-

card. They use OWL ontology to represent knowledge

about variables and provide an interface to FuzzyJess to

execute fuzzy rules. Similarly, Wlodarczyk et al. (2011)

proposes SWRL-F, whose aim is to provide a fuzzy logic

extension to SWRL, based on the standard OWL DL

ontology language and SWRL rule language. One of the

benefits introduced by SWRL-F ontology is that it enables

1 http://www.w3.org/Submission/SWRL/.

1154 C. De Maio et al.

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the description of fuzzy logic knowledge and its applica-

tion in SWRL rules. Similar to f-SWRL and SWRL-F, our

approach presents a definition and implementation of a

control system based on the well-known scheme: collect

crisp inputs, fuzzify inputs, perform fuzzy inference, de-

fuzzify inputs, apply crisp outputs. In particular, our system

exploits an OWL-based upper ontology to allow semantic

definition of a Fuzzy Control. Moreover, it enables a

context aware discovery of Fuzzy Control for autonomous

Fuzzy Control usage.

3 OWL-FC: an upper ontology for the Fuzzy Control

The structure and the characterization of our ontology

OWL-FC strictly reflect the modeling of OWL-S (Martin

et al. 2004). Our idea is, indeed, to provide an upper

ontology which naturally reproduces the model of OWL-S

used to apply semantic descriptions to Web Services. OWL-S

enables the deployment of the web services capabilities,

through the three modules: ServiceProfile, ServiceModel

and ServiceGrounding. Generally speaking, the Service-

Profile provides the information needed to discover a service,

while the ServiceModel and ServiceGrounding, together,

enable the use of a service, once found it. Similarly, our

model of OWL-FC provides a complete description of the

Fuzzy Control capabilities, through the three homonymic

modules: Profile, Model and Grounding.

While, in the OWL modeling, the goal of dynamic pub-

lishing and discovering of web services, driven by agents and

supported by ontologies, may be reached exploiting OWL-S

languages as a qualified OWL-based support for semantic

web services, analogously, we can say that the definition

of OWL-FC aims at supporting mapping and conversion

between fuzzy controls generated by different fuzzy systems

or legacy environments, through a common, high-level

abstraction of the specification and semantics.

As a consequence of the described strict analogy of

OWL-FC with OWL-S, a natural, trivial conversion of the

OWL-FC Profile into OWL-S ServiceProfile enables the

deployment of the Fuzzy Control in the form of a simple

web service. Using ontology to support fuzzy controls

specification enables the semantic definition of services.

4 OWL-FC: Fuzzy Control representation

As said, OWL-FC is an upper ontology to model the Fuzzy

Control process. In this section, we describe the main class

of OWL-FC Ontology, in particular, the classes Fuzzy

Control, Profile and Model are defined, through hierarchy

structures, relevant entities and their relationships, rules,

axioms, etc.

The class FuzzyControl specifies a control system based

on fuzzy logic. Fuzzy controllers consist of an input stage,

a processing stage, and an output stage. The input maps

inputs to the appropriate membership functions and truth

values. The processing stage invokes each appropriate rule

and generates a result for each, then combines the results of

the rules. Finally, the output stage converts the combined

result back into a specific control output value.

As OWL-FC structure completely reflects the OWL-S

structure, our ontology structuring for Fuzzy Control is

based on three essential types of knowledge about a

FuzzyControl (shown in Fig. 1), in accordance with the

following associated questions:

What does the Fuzzy Control? The layer Profile isthe answer to this question, because it shows the main

characteristics of the control.

How does it work? The Model shows how the FuzzyControl is used in process.

How does one interact with it? The Groundingsupplies the details of interaction and communication:

more specifically, maps the semantic form of messages

(according to the format and input/output specification

provided in a process model) to the low-level protocol

language. Moreover, the Grounding specifies, for each

semantic type of parameters specified in the Model, the

way of exchanging data elements (i.e., the serialization

techniques employed). This module is not yet imple-

mented in this OWL-FC modeling.

The class FuzzyControl represents a reference class for a

declared Fuzzy Control (see Fig. 1); an instance of the

class FuzzyControl exists for each distinct Fuzzy Control

which has been defined. As shown in Fig. 1, this class has

associated three properties: presents, describedBy and

supports. Obviously, the classes Profile, Model, and

Grounding are the ranges (i.e., targets) of those properties,

respectively. Each instance of FuzzyControl presents a

Profile description, describedBy a Model description, and

Fig. 1 The Fuzzy Control representation in OWL-FC

OWL-FC: an upper ontology for semantic modeling of Fuzzy Control 1155

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supports the modality of accessing and communication

protocol, defined by the Grounding description.

The details of Profiles, Models, and Groundings may

vary from one type of control to another one, i.e., from one

instance of FuzzyControl to another one. They are needed

to specify a Fuzzy Control. In particular, Profiles and

Models provide details about Fuzzy Control process,

whereas the Groundings bind to the specific implementa-

tion protocol.

An example of a instance of FuzzyControl is given in

Listing 1.

This code defines an instance of FuzzyControl concept

(or class), identified as FuzzyControl_1. It presents what

is accomplished by the Fuzzy Control, by an instance

named Profile_3 of the class Profile, is described by an

instance named Model_2 of the concept Model and

supports the communication protocol by the instance

Grounding_0 of the concept Grounding.

5 Profile

As said above, the class Profile describes what the

FuzzyControl does. According to the characterization of a

fuzzy control, this class specifies the functional description

of the Fuzzy Control in terms of inputs and outputs. Fur-

thermore, the profile allows the description of non-func-

tional properties that are used to describe features of the

Fuzzy Control. Let us analyze the main characteristics of

this class. As shown in Fig. 2, there is a two-way relation

between FuzzyControl and Profile, described by the prop-

erties presents and presentedBy:

1. presents: is a relation between an instance of Fuzzy-

Control and an instance of Profile, it basically says that

a Fuzzy Control is represented by a profile.

2. presentedBy: is the inverse of presents; it specifies that

a given profile represent a Fuzzy Control.

In Fig. 2, the concepts Input and Output are associated

with the FuzzyControl by the class Profile, through the

functionality properties:

1. hasInput: the range of this property is composed of the

instances of the class Input.

2. inputOf: is the inverse of hasInput, it links an input to a

specific class Profile.

3. hasOutput: its range is composed of instances of the

class Output, as defined in the ontology.

4. outputOf: is the inverse of hasOutput and links an

output to a specific Profile.

However, there are many other properties associated

with the class Profile; some of them, intended for human

consumption, others useful to attach context parameters to

a Fuzzy Control definition. Some example are:

textDescription: is the description of the Profile. hasName: is the name connected with the Profile. hasParameter: allow adding some parameters, in order

to enhance context aware discovery capabilities, once

associated with the right Fuzzy Control. In fact, using

the OWL subclassing it is possible to create special-

ized ad hoc parameters useful to specify environmen-

tal features such as coordinates, geographic radius,

etc.

The code in Listing 2 describes a simple OW-FC Profile

instance.

This code defines an instance of a FuzzyControl for

detecting risk of landslide. The functional description of

the Fuzzy Control is represented by the instance of

Profile identified by Profile_3 and referencing to

instances of Input and Output. Specifically, their defi-

nitions are linked to the concepts of ontology domain

Humidity and Rainfall (Input), RiskLanslide (Output).

Furthermore, a geographic feature (i.e., OnTheCoast)

and a seasonal one (i.e., Winter) are specified by means

of the properties hasParameter, associated with the

Profile.

5.1 Input

The class Input describes a concept given as input to the

Fuzzy Control process. Each instance of Input is identi-

fied by a name and an identifier through the properties

hasName and rdf:ID, respectively. The specification of

Input plays the key role to mediate between concepts in

the domain knowledge and its fuzzy modeling. In fact,

each instance of the class Input has two properties:

hasURI and hasFuzzyConceptInput. The first one associ-

ates the Input to the concept or property of the domain


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ontology; the second one connects Input to the class

FuzzyConceptInput that defines the fuzzification of the

domain concept specified by hasURI. An instance of the

class FuzzyConceptInput represents a specific fuzzy

concept. Just to give an example, Listing 3 defines inputs

of the Fuzzy Control associated with the previous defi-

nition of Profile.

The aim is to introduce a fuzzy modeling of the domain

concepts Humidity, Rainfall (identified, respectively, as

http: #Humidity and http: #Rainfall). The givencode evidences the connections between the concepts

Humidity and Rainfall of the domain ontology to our upper

ontology.

5.2 Output

This class represents a concept given as output to the Fuzzy

Control process. Like the class Input, this concept has

associated two properties hasName and hasUri. Listing 4

defines the fuzzy concept output RiskLanslide (identified

http: #RiskLanslide) associated with the previousinstance of Profile.

Each instance of Output is connected, through the

property hasFuzzyConceptOutput, to FuzzyConceptOutput.

Differently from FuzzyConceptInput, FuzzyConceptOutput

can be used in the defuzzification of Fuzzy Control model.

Let us note in Fig. 2, the class FuzzyConceptOutput is

connected to the class Defuzzifier by means of the prop-

erties isFCOutput and its inverse hasFCOutput.

6 Model

The class Model gives a description about how the fuzzy

control works. Similar to the class Profile, there is a two-

way relation between the classesFuzzyControl and Model,

as shown in Fig. 3. These relations are expressed by the

properties describes and describedBy, detailed as follows:

1. describes: represents a relation which exists between

an instance of FuzzyControl and an instance of Model.

In other words, it asserts that a Model describes a

FuzzyControl.

2. describedBy: this is the inverse property of describes.

Figure 3 shows a representation of the model process,

introducing all the steps of a Fuzzy Control process. The

three main phases are described by the following three

corresponding classes: Fuzzification, Inference and

Defuzzification.

Let us note the Model class contains a single class

Fuzzification, a single class Defuzzification and multiple

specializations of the Inference class. The main properties

that connect the Model class with these ones are:

Fig. 2 The OWL-FC Profilerepresentation


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1. hasFuzzification: this property binds the Model class

with the Fuzzification class and assumes values in the

range of the class Fuzzification.

2. hasDefuzzification: similarly, it acts between the

classes Model and Defuzzification.

3. hasInferences: this property has as range the abstract

class Inference, which is, in turn, specialized in the

classes MamdaniInference and TSKInference. These

classes are the main inference methods applied on the

Fuzzy Control.

The OWL code in Listing 5 is associated with the Model

class.

The code defines an instance of the class Model named

Model_2. It is defined by the instances of the classes

Fuzzification, Inference and Defuzzification, identified by

Fuzzification_5, MamdaniInference_8 and Defuzz-

ification_4, respectively.

6.1 Fuzzification

The class Fuzzification is crucial to the Fuzzy Control

process. The fuzzification procedure achieves the process

to convert an element in the universe of discourse (typi-

cally, crisp values) into a membership value of the fuzzy

set. Just to give an example, let us suppose a fuzzy set A is

defined through a membership function lA on the interval[a, b]; for any x 2 a; b; lAx is the fuzzification valueassociated with the value x.

In the model process representation of Fig. 3, a relation

between the classes Fuzzification to FuzzyConceptInput has

been defined through the property hasFuzzyConcept.

An example of OWL-code describing an instance of the

class Fuzzification is given in Listing 6 as follows:

Herein, the instance Fuzzification_5 of the class Fuzz-

ification takes two fuzzy concepts as input, named,

respectively, HumidityFC and RainfallFC.

6.2 Inference

Fuzzy inference defines the mapping from a given input to

an output using Fuzzy Logic. It is associated with a fuzzy

ifthen rules base, which represents control strategy or

modeling knowledge/experience. For each rule, the infer-

ence engine looks up the membership values of the input

variables in the antecedent part of the rule. The activa-

tion of the premise of the rule inducts the conclusion of

the rule, i.e., the outcome for output variable(s) in the

consequent part of a rule.

The main fuzzy inference schemas are Mamdani and

Takagi-Sugeno (TSK, for short) fuzzy rules. Each infer-

ence schema exploits a set of operators for combining the

variables in the rules. In Fig. 3, MamdaniInference and

TSKInference are two subclasses of the abstract class

Inference. This latter class is related to the classes Accu-

mulation, Activation, And_ Method, Or_Method through

the properties hasAccumulation, hasActivation, hasAnd,

hasOr, respectively.

Listing 7 provides an idea about the modeling of

Mamdani-based inference instance.

Fig. 3 The Model process representation


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This code defines the instance 00MamdaniInference_8of the class MamdaniInference.

Same parameters such as Activation, Accumulation,

AndMethod and OrMethod are set. Then, three rules of

inference, instances of the class Rule, identified by

Rule_35 and Rule_38 have been associated too.

6.3 Defuzzification

The defuzzification is the process for converting fuzzy

information, i.e., one or more fuzzy sets into a single crisp

value. It is a mandatory step because fuzzy sets generated

by fuzzy inference in fuzzy rules must be somehow

mathematically combined (i.e. defuzzified) to come up

with one single number as the output of a fuzzy controller.

There are many different available methods of defuzzifi-

cation, such as COA (center of area), COG (center of

gravity), ECOA (extended center of area), etc.

The class Defuzzification is related to the class Defuzzifier

(i.e., the class associated with the defuzzification method, see

Fig. 3), which can have more than one instance.

The single defuzzification is related to the number of

Defuzzifier instances, that is equal to the number ofInput

instances of the Fuzzy Control process.

Listing 8 describes an example for the instance of

Defuzzification and Defuzzifier.

The code defines an instance of Defuzzification, identi-

fied by Defuzzification_4. The properties hasMin and

hasMax represent a range used for the specification of

minimum and maximum values of an output variable of the

class Defuzzifer. This definition of range of each output

variable allows limiting each membership function and

avoids unpredictable output values. It is not applicable if

singletons are used for output membership functions.

In this example, the method of defuzzification is COG

(Center of Gravity), defined as an instance of the class

Defuzzifier.

7 Fuzzy concept

The core class in the Fuzzy Control process is the Fuzzy-

Concept which represents a fuzzy concept. Figure 4 shows

the ontological model of the FuzzyConcept class. Each

FuzzyConcept presents more FuzzyTerm connected to it.

Fig. 4 Fuzzy concept class representation


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The hasFuzzyTerm relation establishes the connection of

each fuzzy concept with a specific fuzzy term, described by

a membership function. More specifically, the class

FuzzyTerm has a data property hasLabel, i.e. the linguistic

variable and has a property membershipFunctionOf which

assumes values in the class Shape. In this version, OWL-

FC focuses on the linear shapes. The definition of the class

Point allows us to define points for specific shapes. The-

Shape class is a superclass of classes of N_Point, Singleton,

Trapezoidal and Triangular, that represent the well-known

membership functions associated with a fuzzy term.

Moreover, the definition of each linear shape has a

restriction on the cardinality of an instantiation of Point.

An example built on instances of classes Inference,

FuzzyTerm, Shape and Point is given by OWL code in

Listing 9.

This code defines two instances of the class FuzzyCon-

ceptInput, named HumidityFC, RainfallFC and an

instance of FuzzyConceptOutput, viz.RiskLand-slideFC.

For each fuzzy concept, one or more fuzzy terms are

defined. Then, each term is composed of a label and a

membership function.

8 Fuzzy rules

Generally, a fuzzy controller uses fuzzy rules, which are

linguistic IFTHEN statements involving fuzzy sets,

fuzzy logic and fuzzy inference. Fuzzy rules play a key

role in describing expert control/modeling knowledge

and in linking the input variables of fuzzy controllers to

one or more output variables. The (Mamdani or TSK)

fuzzy rules are used in the inference process to compute

an action to be taken. Each rule has a weight connected

to it.

Thus, the ontological model for fuzzy rules is described

by the Rule class connected to an Antecedent class and one

Consequent class.

8.1 Antecedent and consequent

The property hasAntecedent enables us to associate ante-

cedent clauses to each rule of Fuzzy Control inference in

OWL-FC. Instances of Antecedent, AntecedentClause or

Variable work in the range of hasAntecedent. The class

Antecedent represents the whole IF part of a Rule. The

Antecedent class has associated two operands (by means of

two properties called FirstOperand and SecondOperand)

connected by operators AND or OR and just negated by a

NOT operator. Each one is connected with a Fuzzy Con-

cept Input that has a Fuzzy Term (that can be negated). The

definition of Antecedent class is recursive. In particular,

hasFirstOperand and hasSecondOperand are properties

that admit two kinds of range class: the first one is Ante-

cedent, that implies other two antecedent clauses; the

second one is AntecedentClause that is the atomic part of

antecedent of the fuzzy rule. The definition of Antecedent

enables us to specify more than two clauses in the

antecedent.

Analogously, the property hasConsequent enables us to

associate consequent clauses to each rule of Fuzzy Control

inference in OWL-FC. The class Consequent represents the

whole output of a Rule. Each Consequent class has mul-

tiple ConsequentClause, with a minimum cardinality value

equal to one. The class ConsequentClause specifies a single

clause of the THEN part of a rule. Each class Conse-

quentClause is connected to a class FuzzyConceptOutput

with a specific Fuzzy Term.

An example of a rule, involving instances of classes

Inference, FuzzyTerm, Shape is given in Listing 10.


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The rule of the inference process is identified by

Rule_35. This instance is composed of an antecedent,

Antecedent_36, and a consequent Consequent_37. In

particular, the given OWL code represents the following

rule: IF Humidity is high AND Rainfall is high THEN

RiskLandslide is high.

9 A case study

A use case is described in order to give a concrete appli-

cation example of our OWL-FC. Benefits deriving by

OWL-FC as well as drawbacks using traditional approa-

ches which are based on application ontology are evi-

denced too.

The application domain is landslides risk prevention

and detection. The goal is to model a knowledge-based

system that exploits ontologies to provide answers and

alerts about the presence of landslides risks.

The system modeling foresees a data sensing base that

collects data coming from environmental sensors. Specifi-

cally, data are gathered on the basis of a domain ontology

that models humidity and rainfall detection as described in

Listing 11.

The code defines the concept Sensor, which represents

the generic sensor; then two specializations of it yield

concepts Humidity and Rainfall of the domain ontology:

these specific sensors allow detecting humidity and rainfall,

respectively. The next step is the detection of landslides

risk. For this purpose, human domain expertise is required

to model risk landslide condition. Traditional approaches

exploit semantic technologies (i.e., OWL, SWRL, etc.) and

DL reasoning capabilities to design systems that recognize

landslides risk and provide the right answers by looking

up among the available ones in database.

In this OWL-FC approach, landslides risks conditions

are defined by integrating fuzzy logic in the process of

reasoning, as better detailed in the next section.

9.1 Approach based on an application ontology

Application ontology is an ontology designed for a specific

application scope. It usually uses canonical ontologies to

define ontological classes and relationships between clas-

ses. Specifically, application ontologies are employed for

modeling cross-domain experiments, data annotation and

for generating data driven views across reference ontolo-

gies for specific use. In our example, risk landslide con-

ditions are modeled by means of OWL constructs. Indeed,


123

one of the statement is that there is risk landslide when

Humidity and Rainfall data sensing fall into a specific,

well-defined ranges. Listing 12 describes this situation.

In this code, the concept of RiskLandslide has been

represented as an intersection class computed by between

the class representing the concept of HighHumidity and the

class representing the concept of HighRainfall. For each

concept, the range (defined through the minInclusive and

maxInclusive) has been specified too.

Then, through SPARQL queries and description logic

reasoner, it is possible to reply to request about the pres-

ence of landslides risk. Let us point out that the belonging

to RiskLandslide class is defined in a sharp way: the

bounding is well-defined and no belonging gradations can

be modeled. Detection of landslide risk is affected by

environmental conditions and features such as geographic

locations, seasons of the year and so on. The system should

support the discovery of the right set of valuable conditions

that are necessary to detect possible risks of landslide.

In order to obtain qualitative and accurate answers, it is

crucial to model the uncertainty according to the meaning

of concepts involved in the specific application domain and

exploit context parameters to support discovery of those

conditions which trigger the detection of landslide risk.

9.2 Approach based on OWL-FC

OWL-FC provides a general-purpose OWL-based model-

ing of fuzziness, which is independent of a specific domain:

no direct human intervention is required to adapt the con-

cepts of the domain ontology (representing the real

implementation system) to the OWL-FC language. The

association of the domain and application ontologies with

OWL-FC is achieved defining in the Fuzzy Control Profile

a direct mapping between concepts of the respective

ontologies and input/output concepts of Fuzzy Control. In

other words, thanks to OWL-FC Input and Output classes,

it is possible to relate specific domain concepts to fuzzy

controls. In particular, concepts defined in specific appli-

cation domain ontologies can be mapped in OWL-FC

upper ontology by means of property hasUri, whose

domain is represented by Parameter, a super class of Input

and Output.

An example of landslide risk modeling is shown in

Fig. 5. Herein, the level of mapping necessary to use

OWL-FC with domain ontology is evidenced: the fuzzy

concepts defined in OWL-FC are instanced in correspon-

dence of the concepts defined in the reference domain. Just

as an example, in the fuzzy rule of Fig. 5, Humidity rep-

resents (the name of) an instance of Input class and it is

related to the class of domain ontology Humidity through

the URI identified by the property hasUri (for details,

consult Listing 3 relative to Input_Humidity, in Sect. 5.1).

That means a direct mapping exists between the concept

Humidity of the domain ontology and the instance

HumidityFC of the FuzzyConceptInput class.

Let us note that more than one fuzzy model of the same

domain concept is admitted.

Another important aspect to outline about OWL-FC

modeling is the possibility to add not functional parameters

to the profile definition of a Fuzzy Control. In fact, we can

consider some not functional parameters such as geo-

graphical references for location (i.e. coast), season (i.e.

winter), etc. (see Sect. 5). These features facilitate the

discovery process in the selection of the right Fuzzy


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Control for detecting the critical situation. Moreover, in our

example, the OWL-FC control will be selected only for

requests coming from coastal area, since we have corre-

lated the Fuzzy Control profile with Input_Winter and

Input_OnTheCoast context parameters by means of profile

property hasProperty (see Listing 2). This emphasizes that

OWL-FC upper ontology is able to achieve context aware

discovery of fuzzy controls depending on context param-

eters specified in the profile definition. Therefore, it is

possible to enable different fuzzy controls according to the

given different context conditions. For instance, the Fuzzy

Control defined in this case study is suitable for all regions

whose context is defined by high values of humidity and

rainfall and the season is the winter; otherwise, in different

context conditions (e.g., with values of humidity and

rainfall similarly high yet it is summer and we are at sea)

probably another ad hoc OWL-FC control could be

necessary.

Another interesting application domain example for

context aware control could be the forecasting of the traffic

jam: the modeling is strictly dependent on many context

factors such as date-time, day of week, geographical area,

weather, etc. According to the most meaning factors in a

certain context, it is possible to enable the most appropriate

fuzzy controls.

In nutshell, OWL-FC allows us to reuse domain ontol-

ogies; it provides context aware control and monitoring by

easy definition of a semantic context/Fuzzy Control

matchmaking algorithm. Moreover, the fuzzy controls

guarantee a relaxed membership to an ontology concept

compared with crisp boundaries of traditional approaches

(see Sect. 9.1): the system can identify situation near to be

interesting or warning (for example, in the case of

emergency risks retrieval).

10 Conclusion

OWL-FC defines an upper ontology which allows the

modeling of fuzzy control systems in a semantic way and,

thanks to the Fuzzy Control profile, it can achieve an

automatic context aware discovery of them. In particular,

OWL-FC reproduces the model of OWL-S and enables the

automatic usage of fuzzy controllers.

The combination of OWL and Fuzzy Logic favors in the

definition of a highly expressive language, yet, there are

still several situations where this merging cannot accu-

rately represent real world knowledge, especially in rep-

resenting vague and imprecise information. Such kind of

information is evident in many applications such as mul-

timedia processing and retrieval, information fusion, etc.

Our next objective for future works is to analyze the lim-

itations of languages through the combination of Descrip-

tion Logics and Fuzzy Logic, in order to cope the problems

related to semantic modeling and reasoning.

Moreover, we are investigating on the possibility of

enabling the composition of fuzzy controls, by exploiting

the analogy with OWL-S-based representation of web

services. Another challenge is related to use OWL-FC to

represent fuzzy controls automatically extracted through

fuzzy data analysis techniques. In this way we can wrap

interaction with a description logic reasoner by introducing

OWL-FC-based execution engine.

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Fig. 5 An example of OWL-FC-based modeling: landslides

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The independence of OWL-FC

from a domain ontology is

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of concepts in the fuzzy control

(specified by the fuzzy rule) to

concepts of the ontology


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OWL-FC: an upper ontology for semantic modeling of Fuzzy ControlAbstractIntroductionRelated worksOWL-FC: an upper ontology for the Fuzzy ControlOWL-FC: Fuzzy Control representationProfileInputOutput

ModelFuzzificationInferenceDefuzzification

Fuzzy conceptFuzzy rulesAntecedent and consequent

A case studyApproach based on an application ontologyApproach based on OWL-FC

ConclusionReferences

Documents

OWL-FC: an upper ontology for semantic modeling of Fuzzy Control