Robert Fullér
What is fuzzy logic and fuzzy ontology?
KnowMobile National Workshop, October 30, 2008, Helsinki.
Thursday, March 4, 2010
Web Ontology Language
• The Web Ontology Language (OWL) is a
family of knowledge representation
languages for authoring ontologies, and is
endorsed by the World Wide Web
Consortium. This family of languages is
based on two semantics: OWL DL and
OWL Lite semantics that are based on
Description Logics.
Thursday, March 4, 2010
Description logic
• Description logics (DL) are a family of
knowledge representation languages which
can be used to represent the terminological
knowledge of an application domain in a
structured and formally well-understood
way. Today description logic has become a
cornerstone of the Semantic Web for its
use in the design of ontologies.
Thursday, March 4, 2010
Semantic Web
• The Semantic Web is an evolving extension
of the World Wide Web in which the
semantics of information and services on
the web is defined, making it possible for
the web to understand and satisfy the
requests of people and machines to use the
web content. The Web is considered as a
universal medium for data, information, and
knowledge exchange.
Thursday, March 4, 2010
Ontology
• An ontology consists of a hierarchical description of
important classes (or concepts) in a particular domain,
along with the description of the properties (of the
instances) of each concept.
• Web content is then annotated by relying on the concepts
defined in a specific domain ontology.
• An ontology is a specification of conceptualization.
• A conceptualization is an abstract, simplified view of the
world that we wish to represent for some purpose. Every
knowledge base, knowledge-based system, or knowledgelevel agent is committed to some conceptualization,
explicitly or implicitly.
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Concept lattice for concepts of the formal context.
Source: W.C. Cho and D. Richards, Ontology construction and concept reuse with
formal concept analysis for improved web document retrieval, Web Intelligence and
Agent Systems: An international journal 5 (2007) 109–126
Thursday, March 4, 2010
The general Recall and Precision are inversely relate.
Source: W.C. Cho and D. Richards, Ontology construction and concept reuse with
formal concept analysis for improved web document retrieval, Web Intelligence and
Agent Systems: An international journal 5 (2007) 109–126
Thursday, March 4, 2010
Source: W.C. Cho and D. Richards, Ontology construction and concept reuse with
formal concept analysis for improved web document retrieval, Web Intelligence and
Agent Systems: An international journal 5 (2007) 109–126
Thursday, March 4, 2010
Description Logics with fuzzy
Domain
•
Web Ontology Language Description Logics (OWL DL) becomes less
suitable in domains in which the concepts to be represented have not a
precise definition. As we have to deal with Web content, it is easily verified
that this scenario is, unfortunately, likely the rule rather than an exception.
•
For instance, just consider the case we would like to build an ontology about
flowers. Then we may encounter the problem of representing concepts like
“Candia is a creamy white rose with dark pink edges to the petals”,
“Jacaranda is a hot pink rose”, “Calla is a very large, long white flower on
thick stalks”. As it becomes apparent such concepts hardly can be encoded
into OWL.
•
As it becomes apparent such concepts hardly can be encoded into OWL DL,
as they involve fuzzy or vague concepts, like “creamy”, “dark”, “hot”,
“large” and “thick”, for which a clear and precise definition is impossible.
Thursday, March 4, 2010
Fuzzy Ontology
•
•
•
A fuzzy ontology is a quintuple F =< I, C,T,N,X > where
•
•
The set of entities of the fuzzy ontology is defined by E = C ∪ I.
•
N denotes the set of non-taxonomy fuzzy associative relationships that relate entities
across tree structures, for example:
I is the set of individuals (objects), also called instances of the concepts.
C is a set of fuzzy concepts (or classes - cf. in OWL - of individuals, or categories, or
types). Each concept is a fuzzy set on the domain of instances.
T denotes the fuzzy taxonomy relations among the set of concepts C. It organizes
concepts into sub-(super-)concept tree structures. The taxonomic relationship T (i, j )
indicates that the child j is a conceptual specification of the parent i with a certain
degree.
- Naming relationships, describing the names of concepts
- Locating relationships, describing the relative location of concepts
- Functional relationships, describing the functions (or properties) of concepts
•
X is the set of axioms expressed in a proper logical language, i.e., predicates that
constrain the meaning of concepts, individuals, relationships and functions.
Thursday, March 4, 2010
A fuzzy ontology scheme.
Source: David Tudor Parry: Fuzzy Ontology and Intelligent Systems for Discovery of Useful Medical
Information, Ph.D. Thesis, Auckland University of Technology, 2005.
Thursday, March 4, 2010
Fuzzy Ontology Generation for Semantic Web.
C = {”Document,” ”Research Area”}
Fuzzy formal context can also be
represented as a cross-table as shown in
Table 1.
The context has three objects representing
three documents, D1,D2,D3.
It also has three attributes Data Mining,
Clustering and Fuzzy Logic representing
three research topics.
The relationship between an object and an
attribute is represented by a membership
value in [0,1].
An α-cut can be set to eliminate relations
that have low membership values.
Source: Quan Thanh Tho, Siu Cheung Hui, Automatic Fuzzy Ontology Generation for Semantic Web, IEEE TRANSACTIONS ON
KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 6, JUNE 2006
Thursday, March 4, 2010
A fuzzy ontology for wine
Source: Silvia Calegari and Davide Ciucci,
INTEGRATING FUZZY LOGIC IN ONTOLOGIES, 8th
International Conference on Enterprise Information
Systems, 2006.
Illustration of a non-taxonomic relation.
Name of fuzzy relation: Taste
Name of instance: cabernet
Name of property: dry
Some possible values:
Taste(cabernet, dry)=0.7 ⇔ Cabernet has a dry taste with value 0.7
Taste(cabernet, very_dry)=0.7×0.7 ⇔ Cabernet has a very dry taste with value 0.49
Taste(cabernet, not_dry)=1-0.7 ⇔ Cabernet has not a dry taste with value 0.3
Thursday, March 4, 2010