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374 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
A Type-2 Fuzzy Ontology and Its Application
to Personal Diabetic-Diet Recommendation
Chang-Shing Lee, Senior Member, IEEE, Mei-Hui Wang, and Hani Hagras, Senior Member, IEEE
Abstract—It has been widely pointed out that classical ontol-
ogy is not sufficient to deal with imprecise and vague knowledge
for some real-world applications like personal diabetic-diet rec-
ommendation. On the other hand, fuzzy ontology can effectively
help to handle and process uncertain data and knowledge. This
paper proposes a novel ontology model, which is based on inter-
val type-2 fuzzy sets (T2FSs), called type-2 fuzzy ontology (T2FO),
with applications to knowledge representation in the field of per-
sonal diabetic-diet recommendation. The T2FO is composed of
1) a type-2 fuzzy personal profile ontology (type-2 FPPO); 2) a type-2
fuzzy food ontology (type-2 FFO); and 3) a type-2 fuzzy-personal
food ontology (type-2 FPFO). In addition, the paper also presents a
T2FS-based intelligent diet-recommendation agent (IDRA), includ-
ing 1) T2FS construction; 2) a T2FS-based personal ontology fil-
ter;3)aT2FS-based fuzzy inference mechanism;4)aT2FS-based
diet-planning mechanism;5)aT2FS-based menu-recommendation
mechanism;and6)aT2FS-based semantic-description mechanism.
In the proposed approach, first, the domain experts plan the diet
goal for the involved diabetes and create the nutrition facts of
common Taiwanese food. Second, the involved diabetics are re-
quested to routinely input eaten items. Third, the ontology-creating
mechanism constructs a T2FO, including a type-2 FPPO,atype-2
FFO,andasetoftype-2 FPFOs. Finally, the T2FS-based IDRA
retrieves the built T2FO to recommend a personal diabetic meal
plan. The experimental results show that the proposed approach
can work effectively and that the menu can be provided as a ref-
erence for the involved diabetes after diet validation by domain
experts.
Index Terms—Diabetes, diet recommendation,intelligentagents,
interval type-2 fuzzy sets (IT2FSs), type-2 fuzzy ontology (T2FO).
I. INTRODUCTION
D
IABETES mellitus (DM) is a disorder in which blood
levels of glucose are abnormally high due to either an
absoluted deficiency of insulin secretion, as a result of reduced
effectiveness of insulin, or both [1]. A fuzzy-based controller
for glucose regulation in type-1 diabetic patients was proposed
in [15] to control an intensive insulin treatment. In addition,
Manuscript received March 11, 2009; revised July 1, 2009 and October 29,
2009; accepted January 26, 2010. First published February 8, 2010; current
version published April 2, 2010. This work was supported by the National
Science Council of Taiwan under Grant NSC 98-2221-E-024-009-MY3 and
Grant NSC97-2221-E-024-011-MY2.
C.-S. Lee and M.-H. Wang are with the Department of Computer Science and
Information Engineering, National University of Tainan, Tainan 700, Taiwan
(e-mail: leecs@mail.nutn.edu.tw).
H. Hagras is with Computational Intelligence Centre, School of Computer
Science and Electronic Engineering, University of Essex, Colchester, CO4 3SQ,
U.K. (e-mail: hani@essex.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TFUZZ.2010.2042454
a new model for the diabetic neuropath is proposed in [16] to
diagnose the diabetic neuropathy and an ontology-based intel-
ligent fuzzy agent based on fuzzy markup language (FML) was
proposed to implement the diabetes semantic decision mak-
ing [40]. Mani and Bellazzi [31] proposed a stochastic model to
evaluate the adequacy of the diabetes therapeutic protocol and
to highlight periods characterized by increasing glucose insta-
bility. Klein and Meininger [32] explored using control theory
and incorporating a mental model of diabetes into rule-based
training to improve the effectiveness of self-management.
Lifestyle factors, such as diet, physical activity, and obesity,
have a major influence on the development and progression of
the conditions that precede the onset of type-2 diabetes and sub-
sequent complications [17]. For those with diabetes, a proper
diabetes diet is crucial so that the experts recommend eating
a wide variety of foods, including vegetables, whole grains,
fruits, nonfat or low-fat dairy products, beans, lean meats, poul-
try, and fish. However, each person has a unique dietary pat-
tern; therefore, a dietician creates a meal plan, depending on
each case. Therefore, in order to recommend individual meal,
the ontology is a good idea to build a personal dietary pattern
to do a proper food recommendation. Ontology is an explicit
specification of a conceptualization and a formal specification
of a shared conceptualization [33]. Additionally, ontology is
a good knowledge representation and communication model
for intelligent agents [3]. The use of ontologies to provide in-
teroperability among heterogeneous data sources has been ap-
plied in many domains, including medical information systems
[8].
A service-oriented approach to e-healthcare must consider
semantics because in healthcare, every description must have a
unique and clear meaning. Therefore, defining and maintaining
expressive ontologies for e-healthcare is crucial [9]. There are
some researches that applied ontology to healthcare, such as the
respiratory waveform recognition [10] and electrocardiogram
application [11]. In addition, Orgun and Vu [8] proposed a mul-
tiagent system with an ontology to facilitate the flow of patient
information across a whole healthcare organization. However, it
is widely pointed out that classical ontologies are not sufficient
to represent the imprecise and vague knowledge [2], which has
lead to the birth of fuzzy ontology to handle this type of knowl-
edge in several real-world applications.
Fuzzy logic systems (FLSs) have been credited with pro-
viding an adequate methodology to design robust systems that
are able to deliver satisfactory performance when contending
with the uncertainty, noise, and imprecision attributed to real-
world environments and applications. Moreover, FLSs provide
a framework to represent the information in a human-readable
1063-6706/$26.00 © 2010 IEEE
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 375
form [18]. As a result, FLSs have been used in wide range
of applications, including fuzzy ontologies. Several researchers
have explored the use of fuzzy ontologies where Lee et al.[3]
proposed a fuzzy ontology and applied it to news summariza-
tion. Quan et al. [4] presented the automatic fuzzy ontology
generation for semantic help-desk support. Knappe et al.[5]
proposed a fuzzy ontology-based query enrichment. Calegari
and Farina [2] introduced the fuzzy ontologies and scale-free
networks analysis. Hudelot et al. [6] proposed the fuzzy-spatial-
relation ontology for image interpretation. Quan et al. [7] pro-
posed the automatic fuzzy ontology generation for the semantic
web.
The majority of the FLSs, which are used so far, employ
the traditional type-1 FLSs that utilize crisp and precise type-1
fuzzy sets (T1FSs). Hence, the type-1 FLSs can operate un-
der specific operation conditions. The linguistic and numerical
uncertainties can cause problems in determining the exact and
precise antecedents and cosequent membership functions (MFs)
during the FLS design. In addition, user behavior and prefer-
ences change from one person to another over time; also, the
domain experts vary in their opinions. Hence, the effectiveness
of the type-1-based agents will degrade when dealing with high
uncertainty levels that are associated with the diabetes domain,
which include the following:
1) uncertainties associated with sensed measurements and
analysis associated with diabetes patient that are affected
by the conditions of the measurements and the context of
the diabetes patient;
2) uncertainties associated with the changing behavior, exer-
cise patterns, and context of the patient;
3) linguistic uncertainties, where words mean different things
to different people;
4) inter- and intrauser uncertainties, which are associated
with the diabetes experts and dietitians, the experts’ opin-
ions can vary over time (intrauser uncertainties), and there
is always a variation of opinion between the various ex-
perts (interuser uncertainties).
The approaches outlined above for diabetes and ontology are
based on type-1 fuzzy logic approaches to achieve a group con-
sensus on a set of known solutions. However, these approaches
do not aim to model and handle the uncertainties involved within
the group-decision process.
Type-2 FLSs could be used to handle the uncertainties in
the group-decision-making process as they can model the un-
certainties between expert preferences using type-2 fuzzy sets
(T2FSs). A T2FS is characterized by a fuzzy MF, i.e., the mem-
bership value (or membership grade) for each element of this
set is a fuzzy set in [0,1], unlike a T1FS, where the membership
grade is a crisp number in [0,1] [19]. The MFs of T2FSs are
three-dimensional and include a footprint of uncertainty (FOU).
Hence, T2FSs provide additional degrees of freedom that can
make it possible to model the interuser (group) uncertainties,
which involve the varying opinions and preferences of experts.
The T2FSs can model the requirements of a person specifica-
tion that is reflective of all the experts’ opinions, which can
then be used to provide a good recommendation for the diabetes
patient.
This paper combines the type-2 fuzzy systems and the ontol-
ogy model to propose a novel type-2 fuzzy ontology (T2FO).
Moreover, we apply the T2FO to diabetes and nutrition do-
main to propose a T2FS-based intelligent ontological agent for
diabetic-diet recommendation. In the proposed approach, first,
the T2FS-based intelligent diet-recommendation agent (IDRA)
retrieves the meal records and the predefined type-2 fuzzy food
ontology (type-2 FFO), and then, the type-2 fuzzy-personal
food ontology (type-2 FPFO) is acquired by carrying out the
ontology-creating mechanism. The T2FSs construction is then
responsible for constructing T2FSs for all kinds of food and
each person’s diet goal. Next, the T2FS-based fuzzy inference
mechanism combines fuzzy operators with the type-2 FPFO
to get the remaining calories for dinner intake. Finally, the
T2FS-based diet-planning mechanism,theT2FS-based menu-
recommendation mechanism, and the T2FS-based semantic-
description mechanism follow the personal food-guide pyramid,
which is predefined by domain experts to do a personal-meal
plan for dinner. The experimental results show that the proposed
method can work effectively and the menu can be provided as
a reference for the involved diabetes after diet validation by the
domain experts. The remainder of the paper is organized as fol-
lows. Section II describes the T2FSs. Section III introduces the
T2FO. Section IV introduces the T2FS-based IDRA. The exper-
imental results are shown in Section V. Finally, conclusions and
discussions are drawn in Section VI
II. T
YPE-2 FUZZY SET
In this section, the T2FS is introduced. The following two
subsections describe the definition and associated terminologies
of the T2FS.
A. Definition of the Type-2 Fuzzy Set and Its
Associated Terminologies
Type-1 FLSs employ the crisp and precise T1FSs. For exam-
ple, consider a T1FS representing the linguistic label of “Low”
temperature in Fig. 1(a). Hence, if the input temperature x is
15
◦
C, then the membership of this input to the “Low” type-1 set
will be the certain and crisp membership value of 0.4. However,
the center and endpoints of this T1FS will vary due to the various
uncertainties highlighted above. Hence, if this linguistic label
was employed with a fuzzy logic controller (FLC) to control
temperature, then the type-1 FLC would need to be continu-
ously tuned to handle all the faced uncertainties. Alternatively,
we would need to have a group of separate type-1 sets and type-1
FLCs, where each FLC will handle a certain situation.
On the other hand, a T2FS is characterized by a fuzzy MF, i.e.,
the membership value (or membership grade) for each element
of this set is a fuzzy set in [0,1]. For example, if the linguistic
label of “Low” temperature is represented by a T2FS,asshown
in Fig. 1(b), then the input x of 15
◦
C will no longer have a single
value for the MF. Instead, the MF takes on values wherever the
vertical line intersects the blurred area shaded in gray, which
is bounded by a lower membership function (LMF) and an
upper MF (UMF), as shown in Fig. 1(b). Hence, 15
◦
C will have
primary membership values that lie in the interval [0.2, 0.6].
376 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
Fig. 1. (a) T1FS.(b)T2FS-primary MF. (c) T2FS-secondary MF. (d) Three-
dimensional view of a T2FS.
Each point of this interval will have also a weight associated
with it. Hence, this will create an amplitude distribution in the
third dimension to form what is called a secondary MF, which
can be a triangle (which is drawn in solid line), as shown in
Fig. 1(c). In case the secondary MF is 1, for all the points
in the primary membership, and if this is true for ∀ x ∈ X,
then we have the case of an interval T2FS, which is drawn in
dotted lines in Fig. 1(c). Hence, the input x of 15
◦
C will have
primary membership interval and an associated secondary MF.
Continuing this for all x ∈X, we create a three-dimensional MF,
as shown in Fig. 1(d), which is a type-2 MF that characterizes
a T2FS.TheMFsofT2FSs are three dimensional and include
an FOU [which is shaded in gray in Fig. 1(d)]. It is the new
three dimension of T2FSs and the FOU that provide additional
degrees of freedom that make it possible to directly model and
handle uncertainties.
A T2FS
˜
A is characterized by a type-2 MF µ
˜
A
(x, u) [19],
where x ∈ X and u ∈ J
x
⊆ [0, 1], and
˜
A is denoted as follows:
˜
A = {((x, u),µ
˜
A
(x, u))|∀x ∈ X ∀u ∈ J
x
⊆ [0, 1]} (1)
in which 0 ≤ µ
˜
A
(x, u) ≤ 1.
˜
A can also be expressed as follows
[19]:
˜
A =
x∈X
u∈J
x
µ
˜
A
(x, u)
(x, u)
,J
x
⊆ [0, 1] (2)
where
denotes union over all admissible x and u [20]. For
discrete universes of discourse,
is replaced by
[20].
According to Mendel and John [20], the name that we use
to describe the entire type-2 MF is associated with the name of
the secondary MFs. For example, when f
x
(u) = 1 ∀ u ∈ J
x
⊆
[0,1], then the secondary MFs are interval sets, and if this is true
for ∀ x ∈ X, then we have the case of an interval type-2 MF,
which characterizes the interval T2FSs [19]. Interval secondary
MFs reflect a uniform uncertainty at the primary memberships
of x [19]. Since all the memberships in an interval set are unity,
in the sequel, an interval set is represented just by its domain
interval, which can be represented by its left and right endpoints
as [l, r] [21]. The two endpoints are associated with two type-1
MFs that are referred to as upper and lower MFs [21]. The upper
and lower MFs are two type-1 MFs, which are bounds for the
FOU(
˜
A)ofaT2FS
˜
A [21]. The UMF is associated with the
upper bound of FOU(
˜
A) and is denoted by ¯µ
˜
A
(x) ∀x ∈ X [19].
The LMF is associated with the lower bound of FOU(
˜
A) and is
denoted by µ
˜
A
(x) ∀ x ∈ X [21]. The interval T2FS
˜
A can be
represented in terms of upper and lower MFs and is denoted as
follows [22]:
˜
A =
x∈X
u∈[µ
˜
A
(x), ¯µ
˜
A
(x)]
1/u
x
. (3)
In this paper, we will use interval T2FSs to represent the
input and output variables as they are simple to use, and they
distribute the uncertainty evenly among all admissible primary
memberships [22]. Furthermore, the general type-2 FLS is com-
putationally intensive, and the computation simplifies a lot when
using interval T2FSs, which will enable us to design a type-2
FLC that operates in real time.
B. Embedded Fuzzy Sets
For discrete universes of discourse X and U , Mendel et al.
[22] have shown that an interval T2FS
˜
A can be represented as
follows:
˜
A =
n
j=1
˜
A
j
e
(4)
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 377
where
˜
A
j
e
is an embedded type-2 fuzzy set, which can be written
as [22] follows:
˜
A
j
e
=
N
d=1
[1/u
j
d
]
x
d
,u
j
d
∈ J
x
d
⊆ U =[0, 1]. (5)
Here,
˜
A
j
e
has N elements, as it contains exactly one el-
ement from J
x1
,J
x2
,...,J
xN
, namely, u
1
,u
2
,...,u
N
, each
with its associated secondary grade of 1, as we are using inter-
val T2FSs [22].
˜
A
j
e
is embedded in
˜
A, and there is a total of n =
N
d=1
M
d
˜
A
j
e
[20], where M
d
is the discretization levels of u
j
d
at each x
d
. For discrete universes of discourse X and U,anem-
bedded type-1 set A
j
e
has N elements, as it contains exactly one
element from J
x1
,J
x2
,...,J
xN
, namely, u
1
,u
2
,...,u
N
[19],
i.e., A
j
e
can be represented as follows:
A
j
e
=
N
d=1
u
j
d
x
d
,u
j
d
∈ J
xd
⊆ U =[0, 1]. (6)
There is a total of
N
d=1
M
d
A
e
[19]. For continuous universes
of discourse X and U, there is an uncountable number of A
j
e
and
˜
A
j
e
[19], [20]. After reviewing the definition of the T2FSs and
their associated terminologies, we can realize that using T2FSs
to represent the knowledge of inputs and outputs of FLC has
many advantages when compared with the T1FSs as follows (as
has been shown in the various type-2 FLC applications [18],
[19], [23]–[25]).
1) As the T2FSs MFs are fuzzy and contain an FOU, then
they can model and handle the linguistic and numerical
uncertainties associated with the inputs and outputs of the
FLC. Therefore, FLCs that are based on T2FSs will have
the potential to produce a better performance than the
type-1 FLCs when dealing with uncertainties [19], [25].
2) Using T2FSs to represent the FLC inputs and outputs will
result in the reduction of the FLC rule base when compared
with using T1FSs, as the uncertainty represented in the
FOU in T2FSs lets us cover the same range as T1FSs with
a smaller number of labels, and the rule reduction will be
greater when the number of the FLC inputs increases [19],
[25].
3) Each input and output will be represented by a large num-
ber of T1FSs, which are embedded in the T2FSs. The use
of such a large number of T1FSs to describe the input and
output variables allows for a detailed description of the an-
alytical control surface as the addition of the extra levels
of classification give a much smoother control surface and
response. In addition, according to Karnik and Mendel,
the type-2 FLC can be thought of as a collection of many
different embedded type-1 FLCs [19], [25].
4) It has been shown in [26] that the extra degrees of freedom
provided by the FOU enables a type-2 FLS to produce
outputs that cannot be achieved by type-1 FLSs with the
same number of MFs. It has been shown that a T2FS may
give rise to an equivalent type-1 membership grade that is
negative or larger than unity. Thus, a type-2 FLC is able
to model more complex input–output relationships than
Fig. 2. Trapezoidal T2FS
˜
T .
its type-1 counterpart and, thus, can give a better control
response.
It should also be mentioned that T2FSs have some disad-
vantages as they are perceived to be more complex to use and
design than T1FSs. In addition, till recently, it was envisaged
that type-2 fuzzy systems are computationally more demand-
ing, and hence, they are slower than their type-1 counterparts
for real-world applications. However, recent advances in inter-
val type-2 FLSs have resulted in computational algorithms that
avoided the computational bottlenecks of type-2 FLSs, which
enabled its applications in several real-world applications [18],
[23]–[25].
III. T
YPE-2 FUZZY ONTOLOGY
This paper presents a novel T2FO based on T2FSs to de-
scribe the fuzzy concepts and fuzzy relations. The proposed
T2FO stores T2FSs and is an extended version of the fuzzy on-
tology [3], which was proposed by our previous research works.
As described previously, T2FSs provide us with more design
degrees of freedom than T1FSs; therefore, using T2FSs has
the potential to outperform the system using T1FSs, especially
when dealing with an environment with high interuser uncer-
tainty levels, such as diabetes handling, where we have several
experts and where each expert has a different opinion. In this
section, the structure of T2FO, T2FSs for personal knowledge
representation and embedding T2FSs to food ontology will be
described.
A. Structure of Type-2 Fuzzy Ontology
In this section, we will introduce the definition of the T2FO,
and some other detailed definitions are also presented.
Definition 1 (Trapezoidal T2FS
˜
T ): A trapezoidal T2FS
˜
T is a T2FS, which is shown in Fig. 2, with the up-
per bound of FOU(
˜
T ), which is called T
U
, and the lower
bound of FOU(
˜
T ), which is called T
L
.
˜
T is represented
by the following parameters on the x-axis {
˜
l, ˜m
l
, ˜m
r
, ˜r} =
{[l
U
,l
L
], [m
l
U
,m
l
L
], [m
r
L
,m
r
U
], [r
L
,r
U
]}. T
U
and T
L
are de-
fined in (7) and (8), respectively.
Definition 2 (Triangular T2FS
˜
T
∆
): In this paper, the
employed triangular T2FS
˜
T
∆
(as shown in Fig. 3) is a
378 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
Fig. 3. Triangular T2FS
˜
T
∆
.
special case of the T2FS
˜
T with two properties: 1) m
l
U
=
m
l
L
= m
r
L
= m
r
U
= m, and 2) β =1.
˜
T
∆
is represented
by the following parameters on the x-axis {
˜
l, ˜m, ˜m, ˜r} =
{[l
U
,l
L
], [m, m], [m, m], [r
L
,r
U
]}:
T
U
(x)=[l
U
,m
l
U
,m
r
U
,r
U
]=
0,x<l
U
x −l
U
m
l
U
−l
U
,l
U
≤x ≤m
l
U
1,m
l
U
≤x<m
r
U
r
U
−x
r
U
−m
r
U
,m
r
U
≤x ≤r
U
0,x>r
U
(7)
T
L
(x)=[l
L
,m
l
L
,m
r
L
,r
L
]=
0,x<l
L
β(x −l
L
)
m
l
L
−l
L
,l
L
≤x ≤m
l
L
β, m
l
L
≤x<m
r
L
β(r
L
−x)
r
L
−m
r
L
,m
r
L
≤x ≤r
L
0,x>r
L
.
(8)
We will employ the hierarchical visualization of fuzzy sys-
tems in several parts of this paper (see Figs. 4, 5, 8, and 9). Other
works have employed the tree-oriented representation of fuzzy
systems as in [12]–[14], [38], and [39].
Definition 3 (Type-2 fuzzy ontology): A T2FO is a knowledge-
representation model to describe the domain knowledge with
uncertainty. It is an extension of the domain ontology [3], [28]
and contains six layers, including a domain layer,acategory
layer,afuzzy-concept layer,afuzzy-variable layer,aT1FS layer,
and a T2FS layer.TheT2FO has three relationships, namely,
“generalization,” “aggregation,” and “association.”
The meanings of three relations are expressed as follows.
1) The “generalization” is a relationship between a domain
and its corresponding category, which means the “is-kind-
of ” relationship.
2) The “aggregation” relationship is a relationship, which
denotes the “is-part-of" relationship.
3) The “association” relationship represents a semantic re-
lationship between concepts either “generalization”or
“aggregation.”
The concepts and relations of the T2FO are constructed by
fuzzy variables, fuzzy sets, and T2FSs, i.e., a fuzzy variable,
including some fuzzy sets, is used to represent a fuzzy concept.
The T1FS layer and the T2FS layer are constructed by some
fuzzy sets and T2FSs. The main differences between the T1FS
layer and the T2FS layer are the property of the concepts in these
two layers. The T2FS layer is an extension of the T1FS layer.
The concepts in the T1FS layer are T1FSs and the concepts in
the T2FS layer are T2FSs aggregated from the T1FSs in the
T1FS layer. The relation between the two layers represents an
association. The meanings, relations, and utility of the six layers
of the T2FO are clearly explained as follows.
1) Domain layer: This represents the domain name of an
ontology and comprises various categories defined by do-
main experts. The relationship between the domain layer
and the category layer is the “generalization.”
2) Category layer: This defines several categories, namely,
“Category 1,” “Category 2,” ..., “Category k.” The rela-
tionship between each category in the category layer and
its corresponding concepts in the fuzzy-concept layer is
the “aggregation.”
3) Fuzzy-concept layer: The fuzzy concepts, “fuzzy concept
1,” “fuzzy concept 2,” ..., “fuzzy concept i,” exist in this
layer. The relationship between the fuzzy-concept layer
and the fuzzy-variable layer is the “aggregation.” There
are many fuzzy variablesin the fuzzy-variable layer, which
are defined for the fuzzy concept in the fuzzy-concept
layer.
4) Fuzzy-variable layer: There are two kinds of relationships,
“aggregation” and “association,” in the fuzzy-variable
layer. The relationship between the fuzzy-variable layer
and the T1FS layer is “aggregation.” The “association”
relationship also exists between two fuzzy variables in the
fuzzy-variable layer.
5) T1FS layer: The concepts in this layer are T1FSs.The
“association” relationship also exists between the T1FS
layer and the T2FS layer.
6) T2FS layer: T2FS layer is an extension of the T1FS layer,
and the concepts in this layer are T2FSs aggregated from
the T1FS layer.
The structure of the six-layer T2FO is shown in Fig. 4. There
are i fuzzy concepts in the fuzzy-concept layer. Each fuzzy con-
cept has some fuzzy variables in the fuzzy-variable layer. There
are m
i
fuzzy variables FV
i1
, ..., FV
im
i
, which are defined for
the fuzzy concept i. The fuzzy sets FS
in
i
1
, ..., FS
in
i
q
ni
are
defined in the fuzzy variable FV
im
i
, where q
n
i
denotes the num-
ber of fuzzy sets for fuzzy variable FV
im
i
.IntheT2FS layer,
there are some T2FSs generated by combining some T1FSs in
the T1FS layer. For example, the “T 2FS
11
" is generated by
combining two T1FSs, i.e., FS
11 1
and FS
1n
1
1
. In the real
world, the “is-kind-of” relation is very important for the ontol-
ogy. However, there are many different kinds of relations still
existing in the real-world applications, for example, “aggre-
gation” relation, “greater-than” relation, “less-than” relation,
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 379
Fig. 4. Structure of the T2FO.
Fig. 5. Structure of the type-2 FPPO.
380 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
Fig. 6. Triangular T2FS for fuzzy variable Weight.
“belong-to” relation, “inclusive” relation, “exclusive” relation,
etc. In fact, we consider that the relationships are very complex
in the real world, and therefore, the “generalization” relation,
“aggregation” relation, and “association” relation are adopted
to simplify the relationships of the T2FO in this paper.
B. Type-2 Fuzzy Sets for Personal Profile
Knowledge Representation
Definition 4 (Type-2 fuzzy personal profile ontology): A type-
2 fuzzy-personal-profile ontology (type-2 FPPO) contains some
important fuzzy concepts to represent the knowledge of a per-
sonal profile with uncertainty in real-world applications, for
example, “People,” “Size,” “Behavior,” “Eating Habit,” etc. In
this paper, we can consider that there are two fuzzy variables,
i.e., “Age” and “Sex” in the concept “People.” The fuzzy vari-
ables “Height” and “Weight” are defined in the type-2 FPPO
for the concept “Size.” The fuzzy sets “Young,” “Middle,” and
“Old” are defined in the fuzzy variable “Age.” The fuzzy sets
“Heavy,” “Proper,” and “Light” are defined in fuzzy variable
“Weight.” The fuzzy sets “Tall,” “Medium,” and “Short”are
defined in the fuzzy variable “Height.” In addition, the T2FSs
“Extra Large,” “Big,” “Medium,” “Small,” and “Extra Slim”are
defined for the fuzzy concept “Size.” The T2FSs “Boy,” “Girl,”
“Man,” “Woman,” “Old Man,” and “Old Woman” are defined in
the fuzzy concept “People.” In addition, we also can define other
important personal profile with uncertainty in some application
domains for type-2 FPPO.
Next, we briefly describe how to construct the T2FO.The
process of constructing the fuzzy ontology follows the descrip-
tion of the [41]. We consider Fig. 5 for an example to depict the
construction process, which includes the following.
1) The domain and scope of the ontology (“Type-2 Fuzzy-
Personal Profile”) is determined.
2) Enumerate important fuzzy concepts, fuzzy variables,
fuzzy sets, and T2FSs of the constructed fuzzy ontology
such as personal appearance (people and size). People can
be illustrated by age and sex. Age can be young, middle,
and old. Sex can be male and female. Height can be short,
medium, and tall. Weight can be light, proper, and heavy.
3) Define the fuzzy concepts and the concept hierarchy.
Herein, a top-down development process is adopted. The
most general fuzzy concepts (“People” and “Size”) are
started for the constructed fuzzy ontology. Then, the fuzzy
variables “Age” and “Sex” are specialized for the fuzzy
concept “People.” Fuzzy variable “Age” defines “Young,”
“Middle,” and “Old” as its fuzzy sets. Fuzzy sets “Male”
and “Female” are the ones of the fuzzy concept “Sex.” Fi-
nally, T2FS “Boy” is composed of the fuzzy sets “Young”
and “Male.”
4) Define the properties of the fuzzy concepts. For example,
the parameters of the MF of the T2FS “Boy” are defined.
5) Define the nonhierarchical relations in the fuzzy ontology.
For example, there are two fuzzy variables “Age” and
“Sex” in the fuzzy concept “People,” and therefore, there
is an “aggregation” relation between the fuzzy variable
“Age” and the fuzzy concept “People.”
Briefly, the construction of the fuzzy ontology is built from
the top down. The domain name is first decided, and then, some
categories are determined. Next, fuzzy concepts, fuzzy vari-
ables, and fuzzy sets are chosen. Finally, any two fuzzy sets are
composed to build a new T2FS by domain experts.
Fig. 5 shows the constructed structure of the type-2 FPPO.In
the category layer, there are six categories, including “Africa,”
“Asia,” “Europe,” “Latin America,” “Northern America,” and
“Oceania” to describe different personal profiles for different
continental areas. The proposed type-2 FPPO is composed of
two fuzzy concepts, “People” and “Size.” For example, “Young
Female,” “Middle Female,” and “Old Female,” represent “Girl,”
“Woman,” and “Old Woman,” respectively. Figs. 6 and 7 show
the fuzzy variable “Weight” with T2FSs = {
˜
T
Light
,
˜
T
Proper
,
˜
T
Heavy
}, and “Age” with T2FSs = {
˜
T
Young
,
˜
T
M iddle
,
˜
T
Old
},
respectively.
C. Embedding Type-2 Fuzzy Set to Personal Food Ontology
Different people eat different types of food. However, no
matter what they eat, food items are divided into six major
groups, including the grains and starches group, the vegetables
group, the fruits group, the milk group, the meats and proteins
group, and the fats group. Each portion of food contains some
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 381
Fig. 7. Triangular T2FS for fuzzy variable Age.
Fig. 8. Structure of the type-2 FFO.
information, such as servings of six food groups, nutrition facts,
and contained calories that can be calculated by the domain ex-
perts in a scientific manner. If there is such an ontology existing
to represent the aforementioned information, then people can
easily know the calories of each food item as high, medium, or
low for an adult or a child. This way, for those who want to lose
weight, they will easily know what kind of food is with high
calories and should stay away from it. Moreover, with the help
of the ontology, it will be much more convenient for diabetics
to choose the proper food to eat to avoid complications. Based
on such ideas, as shown in Fig. 8, we provide an illustrative
example of the type-2 FFO.
The domain layer represents the domain name of the on-
tology “type-2 FFO” in Fig. 8. The categories in the category
layer include “Grains and Starches,” “Vegetables,” “Fruits,”
“Milk,” “Meats and Proteins,” and “Fats.” A type-2 FFO con-
tains four concepts, i.e., “Servings of Six Food Groups each
Portion,” “Nutrition Facts each Portion,” “Contained Calories
of each Serving of Six Food Groups,” and “Contained Calories
of Nutrition each Gram.” The fuzzy variables, i.e., “Servings
of Grains and Starches,” “Servings of Vegetables,” “Servings of
Fruits,” “Servings of Milk,” “Servings of Meats and Proteins,”
and “Servings of Fats,” are defined in the fuzzy concept “Serv-
ings of Six Food Groups each Portion.” The fuzzy set “Low,”
“Medium,” and “High” are defined in fuzzy variables “Servings
of Grains and Starches,” “Servings of Vegetables,” “Servings of
Fruits,” “Servings of Milk,” “Servings of Meats and Proteins,”
and “Servings of Fats.” In T2FS layer, there are three T2FSs,
382 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
Fig. 9. Structure of the type-2 FPFO.
including “Calories each Portion Low,” “Calories each Portion
Medium,” and “Calories each Portion High,” which are defined
to describe the linguistic meaning of calories of the food item.
The ideas behind the construction of the type-2 FPFO are as
follows. There are different kinds of people all over the world,
and each kind of person has their own eating habits. Even for
those who are with the same kind of people, each person still
has his/her own eating habits. Hence, a unique diet planning is
definite for a different person. According to such ideas, a type-2
FPFO is constructed in Fig. 9.
The domain name is “type-2 FPFO”inFig.9.Thereare
two categories, i.e., “Planned Healthy Diet Goal” and “Actual
Diet”inthecategory layer, which are defined in this ontology.
In additions, the type-2 FPFO also referred to type-2 FPPO
and type-2 FFO. Type-2 FPFO contains six fuzzy concepts,
including “Planned Servings of Daily Calories from Six Food
Group,” “Planned Daily Calories Needs,” “Planned Percent-
age of Daily Calories from Nutrition,” “Actual Eaten Items at
Breakfast,” “Actual Eaten Items at Lunch,” and “Actual Eaten
items at Dinner.” The fuzzy variables “Planned Percentage of
Carbohydrate,” “Planned Percentage of Protein,” and “Planned
Percentage of Fat,” are defined in the type-2 FFO for the con-
cept “Planned Percentage of Daily Calories from Nutrition.”
The fuzzy sets “Low,” “Balanced,” and “High” are defined in
the fuzzy variable “Recommended Dinner Servings of Six Food
Groups.” The T2FSs “Eat Little,” “Eat Balanced,” and “Eat
Much” are defined in the fuzzy concepts of the type-2 FPFO,
i.e., if “Recommended Dinner Servings of Six Food Group”is
“Low” and “Recommended Dinner Menu Calories”is“Low,”
then it means that this volunteer is recommended to “Eat Little”
at dinner.
IV. T
YPE-2-FUZZY-SET-BASED INTELLIGENT
DIET-RECOMMENDATION AGENT
Each person has different eating habits and diet that intro-
duces high uncertainty levels, which makes it more appropriate
to present the diet using the concept of the T2FSs. Therefore,
this section presents a T2FS-based intelligent agent for diabetic-
diet recommendation based on T2FO. The system is composed
of an only one agent whose intelligence is realized by exploit-
ing, in a joint way, the T2FSs and ontologies. The structure
contains an ontology-creating mechanism, a diet goal-planning
mechanism,afood-item-creating mechanism,aT2FO, and a
T2FS-based IDRA. We will start first by briefly introducing
the system structure followed by the details of the proposed
agent.
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 383
Fig. 10. System structure for T2FS-based IDRA based on T2FO.
A. System Structure
Fig. 10 shows the system structure for T2FS-based IDRA,
which is based on T2FO. First, the nutrition facts for some pop-
ular food eaten in Taiwan and unique daily calorie goals for
each involved diabetic are defined by domain experts through
the food-item-creating mechanism and the diet goal-planning
mechanism, respectively. The information about each food’s
nutrition facts contains the amount of various nutrients, calo-
ries, portion size, and servings of six food groups. Addition-
ally, the involved diabetics’ brief personal profiles, including
height, weight, age, and sex, are also built. Second, the in-
volved diabetics are routinely requested to input eaten items
each day. Third, the ontology-creating mechanism constructs
the type-2 FPPO and type-2 FFO based on the obtained per-
sonal profiles and built nutrition facts of common Taiwanese
food. Afterwards, the proposed T2FS-based IDRA operates as
follows.
1) The T2FS construction builds T2FSs for each food item
and the individual daily calorie requirement.
2) The T2FS-based personal ontology filter then carries out
the individualization to build the type-2 FPFO based on
acquired diet goal and meal records.
3) The T2FS-based fuzzy inference mechanism implements
type-2 fuzzy operations to recommend a dinner allowance
based on obtained calories at breakfast and lunch.
4) The T2FS-based diet-planning mechanism then suggests
the number of servings of six food groups according to the
recommended dinner allowance and predefined T2FO.
5) With the suggested servings of six food groups, the T2FS-
based menu-recommendation mechanism plans some bal-
anced dinner menus for the involved diabetes based on the
predefined T2FO.
6) The T2FS-based semantic-description mechanism
presents the knowledge for the suggested diet in the
TABLE I
H
ARRIS–BENEDICT EQUATIONS
form of the human readable language for the involved
diabetics.
Finally, the personal recommended meal plan is validated by
the domain experts to evaluate the performance of the proposed
approach.
B. Diet Goal-Planning Mechanism and Food-Item-Creating
Mechanism
People’s eating habits vary by the individual, and may be
influenced by original nationality, personal preference, social
status, economic position, and region. Therefore, the domain
experts, such as the medical or health experts, would plan the
unique diet goal for each person to meet a balanced diet. The
Harris–Benedict equation [29], which is listed in Table I, is
commonly used to figure out the energy requirements based
on each person’s sex, height, weight, and age. Therefore, first,
the domain experts plan how many calories each patient needs
per day according to the Harris–Benedict equation. Then, the
domain experts multiply by a factor between 1.2 and 1.5 to
account for extra calories according to the patient’s physical
activity. The suggested percentages of the daily intake for car-
bohydrate, protein, and fat are 55%–65%, 10%–20%, and 25%–
35%, respectively. Table II shows the well-balanced diet for an
adult Taiwanese. With the suggested values, the domain ex-
perts set the percentage of calories from each nutrient and how
many servings of each food group should be needed for each
384 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
TABLE II
W
ELL-BALANCED DIET FOR AN ADULT TAIWANESE
Fig. 11. Generation of a T2FS from the various T1FSs that represent the experts’ individual opinions.
TABLE III
F
IRST INVOLVED DIABETIC’S DIET GOALS AND ITS RELATIVE CONSTRUCTED T 2FSs
meal per person. Next, according to the Taiwanese food ingredi-
ents database from the Department of Health, Executive Yuan,
Taiwan [36], the domain experts construct common Taiwanese
foods’ basic information, including calories (in kilocalories),
carbohydrate (in grams), protein (in grams), fat (in grams), vita-
min (in milligrams), and mineral (in milligrams), each 100 g or
100 cm
3
, as well as portion size, and servings of each portion of
the six food groups, through the food-item-creating mechanism.
C. Ontology-Creating Mechanism and Type-2 Fuzzy
Set Construction
With the planned diet goals, constructed popular Taiwanese
foods’ ingredients, the collected involved diabetics’ meal
records, and the involved diabetics’ profiles, the ontology-
creating mechanism performs the construction of the type-2
FFO and type-2 FPPO. For the design of the T2FSs,weemploy
the method reported in [34] for the generation of T2FSs from the
type-1 fuzzy sets proposed by each domain expert. As shown in
Fig. 11, in this method, each expert provides the T1FS that repre-
sents each linguistic label from the domain expert point of view.
We then employ the method reported in [34], which generates a
T2FS whose FOU embeds the various T1FSs that represent each
domain expert individual opinion about a given linguistic label.
Hence, the generated T2FSs FOU will aggregate the different
domain experts’ opinions and handle the interexpert uncertain-
ties. The T2FS construction mechanism constructs the T2FS for
each food item, suggested percentage of calories from each nu-
trient, planned servings of six food groups for each meal, and the
individual daily caloric requirement. Tables III and IV list the
diet goals and planned servings of six food groups and relative
constructed T2FSs for the first involved diabetic, respectively.
Table V shows common foods’ diet and nutrition and its relative
constructed T2FS.
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 385
TABLE IV
F
IRST INVOLVED DIABETIC’S PLANNED SERVINGS OF SIX FOOD GROUPS AND ITS RELATIVE CONSTRUCTED T 2FSs
TABLE V
C
OMMON FOODS’DIET AND NUTRITION AND ITS RELATIVE CONSTRUCTED T 2FSs
TABLE VI
F
OOD PREFERENCES FOR VOLUNTEER NO.1
D. Type-2-Fuzzy-Set-Based Personal Ontology Filter and Type-
2-Fuzzy-Set-Based Fuzzy Inference Mechanism
The main task of the T2FS-based personal ontology filter
is to carry out the individualization to build the type-2 FPFO
based on the predefined type-2 FFO and type-2 FPPO.The
constructed type-2 FPFO would store the food preference for
each involved diabetic. Herein, the individual food preference is
chosen according to the collected meal records. For an example,
let us consider volunteer no. 1, who input his eaten items into
the constructed platform from July 14, 2007, to September 8,
2007. Then, the T2FS-based personal ontology filter processes
the eaten items statistics to find the four most popular foods for
each food group as volunteer no. 1’s food preference. Table VI
shows volunteer no. 1’s food preference.
According to the individual eating habits, planned diet goal,
and meal records stored in the T2FO,theT2FS-based fuzzy infer-
ence mechanism implements type-2 fuzzy operations to generate
the recommended dinner allowance. Next, we briefly describe
the T2FS-based fuzzy inference mechanism as follows. The in-
puts contain type-2 FFO, type-2 FPFO, the breakfast eaten sets,
and the lunch eaten set. The outputs contain the T2FSs for total
calories intake at the breakfast, lunch, and dinner allowance.
The process of this mechanism contains the following steps.
1) Retrieve the T2FSs for calories per 100 g or per 100 cm
3
of food eaten both at breakfast and at lunch from the
T2FO.
2) Retrieve the size of average portion of food eaten both at
breakfast and lunch from the T2FO.
386 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
TABLE VII
C
ALORIES AND NUMBER OF GRAMS OF NUTRIENTS FOR ONE SERVING OF SIX FOOD GROUPS
3) Calculate the T2FSs caloric intake both at breakfast and
at lunch.
4) Calculate the T2FSs caloric intake at breakfast and lunch,
respectively.
5) Calculate the T2FSs sum of the caloric intake at both
breakfast and lunch.
6) Retrieve the T2FSs daily caloric needs from the T2FO,
and then, calculate the T2FSs for dinner allowance.
E. Type-2-Fuzzy-Set-Based Diet-Planning Mechanism
Based on the recommended dinner allowance, the T2FS-
based diet-planning mechanism suggests how many servings
of each food group are needed at dinner to meet the balanced
and healthy menu. However, before planning a diet, first, the
T2FS-based diet-planning mechanism gets to know the planned
percentage of calories from nutrients. It then even knows that
each gram of carbohydrate, protein, and fat contains 4, 4, and
9 kcal, respectively [36]. In the last step of the T2FS-based
diet-planning mechanism, it is necessary to realize how many
grams of nutrients one serving of six food groups are contained
listed in Table VII. With all the necessary information stored in
the T2FO,theT2FS-based diet-planning mechanism can do a
balanced diet.
The T2FS-based diet-planning mechanism is described as
follows. The inputs contain 1) type-2FFO;2)type-2 FPFO; and
3) T2FS-planned dinner servings of the involved diabetic from
type-2 FPFO. The outputs are the recommended servings for
each food group. The process of the T2FS-based diet-planning
mechanism contains the following steps.
1) Retrieve the suggested percentage of calories from nutri-
ents and dinner servings of six food groups from type-2
FPFO.
2) Calculate the expected calories from nutrients.
3) Calculate the expected grams from nutrients according to
the fact that each gram of carbohydrate, protein, and fat
contains 4, 4, and 9 kcal, respectively.
4) Calculate the recommended servings of six food groups
at dinner according to how many grams of nutrients are
contained in one serving of six food groups listed in Ta-
ble VII.
F. Type-2-Fuzzy-Set-Based Menu-Recommendation
Mechanism
Based on the recommended servings of six food groups and
the type-2 FPFO,theT2FS-based menu-recommendation mech-
anism generates some dinner menus recommended for diabetics
to choose from. The detailed algorithm is listed in Table VIII.
The T2FS-based menu-recommendation mechanism adopts the
depth-first search approach to find the volunteer’s food prefer-
ence of six food groups as the recommended menu, i.e., the top
four favorite foods of each food group will be the vertex, and
the depth-first search is then implemented to find the possible
menu path. Finally, the extracted menu path is generated.
G. Type-2-Fuzzy-Set-Based Semantic-Description Mechanism
After the above processes, the T2FS-based semantic-
description mechanism uses human readable languages to
present the knowledge of recommended servings of the six food
groups and menus. Meanwhile, the personal recommended meal
plan is also given to domain experts to confirm if they meet a
balanced and healthy diet. Table IX lists the detailed algorithm
for the T2FS-based semantic-description mechanism.
Fig. 12 shows a 3-D view of the semantic description for
T2FS, and it indicates that there are five parameters (l
U
, l
L
, m,
r
L
, and r
U
)fortheT2FS
˜
T
Actual Calories Intake
and one output fuzzy
variable “Planned Calories Intake” with three linguistic terms,
including “Little,” “Balanced,” and “Much.” Each parameter
of the T2FS
˜
T
Actual Calories Intake
will be applied to the term
set {“Little,” “Balanced,” “Much”}. Take parameter m as an
example. When parameter m is applied to the term set {“Little,”
“Balanced,” “Much”} in Fig. 12, the membership degrees
µ
Planned Calories Intake Little
(m),µ
Planned Calories Intake Balanced
(m), and
µ
Planned Calories Intake Much
(m) belonging to the T
Planned Calories Intake
Little
,T
Planned Calories Intake Balanced
, and T
Planned Calories Intake Much
,
respectively, can be obtained. The MAX operator is then
adopted to find the mapped semantic output of parameter
m, namely, “Much,” as shown in Fig. 12. For example, the
volunteer no. 1 ate about 180 kcal at breakfast on July 19, 2007.
Because of this,
˜
T
Actual Calories Intake
is represented by the fol-
lowing parameters on the x-axis: {[130,150], [180, 180], [180,
180], [210, 240]}. Nevertheless, he should get about 570 kcal
for his breakfast on this date according to his planned diet goal.
Therefore, T
Planned Calories Intake Little
, T
Planned Calories Intake Balanced
,
and T
Planned Calories Intake Much
could be represented by [0, 0,
370, 570], [370, 570, 570, 770], and [570, 770, 970, 970],
respectively. After defuzzification, the semantic descriptions of
the µ
T
Planned Calories Intake
Little
, µ
T
Planned Calories Intake
Balanced
, and
µ
T
Planned Calories Intake
Much
for all parameters on the x-axis of
˜
T
Actual Calories Intake
is “Little.” Eventually, the output semantic
description of this case is “The calories eaten at breakfast are
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 387
TABLE VIII
T 2FS−
Based Semantic-Description Mechanism
ALGORITHM
Little (about 180 kcal: {[130, 150], [180, 180], [180, 180],
[210, 240]}). The result of the semantic-description mechanism
is listed in Table X.
V. E
XPERIMENTAL RESULTS
The T2FS-based IDRA, which is based on T2FO,wasim-
plemented with the Borland C++ Builder programming lan-
guage. The research presented in this paper was a research
project involving the National University of Tainan (NUTN),
Taiwan, and University of Essex, U.K. With the support of
the domain experts of the Changhua Christian Hospital, the
proposed method was applied to the diabetes domain. There
were eight diabetics involved in this project. The eight volun-
teers were responsible for routinely recording their meals. The
T2FS-based IDRA recommended their diet based on the built
T2FO, and the domain experts evaluated the proposed agent’s
performance. For most involveddiabetics, the meal records were
collected for five months from July 2007 to November 2007.
The involved diabetics’ profiles with “T2FS Size” and “T2FS
People” semantic meanings are given in Table XI and stored
into the type-2 FPPO. In this paper, we adopt T2FSs to test
our proposed approach. Table XII shows some of the T2FSs,
which are adopted in this paper. Fig. 13(a) shows the shapes
of the T2FSs of {ExtraSlim, Small, Medium, Big, ExtraLarge}
for the fuzzy concept Size. Fig. 13(b) shows the shapes of the
T2FSs {EatLittle, EatBalanced, EatMuch}for the fuzzy concept
PlannedDailyCaloriesNeeds.
The usage of T2FO to represent personal profile is a good
way because the same weight and height may have different
meanings in different countries. For example, a man who is
173 cm tall and weighs 60 kg in Taiwan is a medium size, while
in America, he may be considered small. In addition, if there is
a 31-year-old man who is 168 cm tall and weighs 61 kg, then
388 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
TABLE IX
T 2FS−
Based Menu-Recommended Mechanism
ALGORITHM
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 389
Fig. 12. Three-dimensional view of the semantic description for T2FS.
TABLE X
R
ESULT OF THE SEMANTIC-DESCRIPTION MECHANISM
fuzzy variables “Age” is “Young,” “Sex” is “Male,” “Height” is
“Medium,” and “Weight” is “Light,” then the T2FS representa-
tion can be denoted as the “Boy” with “Small” Size. Another
example in Table XI is as follows: If there is a 39-year-old
man who is 169 cm tall and weighs 87 kg, then fuzzy variables
“Age” is “Medium,” “Sex” is “Male,” “Height” is “Medium,”
and “Weight” is “Heavy,” then the T2FS representation can be
denoted as the “Man” with “Big” Size.
Based on the collected data, we extend our previous method,
i.e., Personal Food Recommendation Agent (PFRA), which is
published in [37], to this one, i.e., T2FS-based IDRA (T2FS-
based IDRA), which is based on T2FO in this paper. The dif-
ference between PFRA and T2FS-based IDRA is in the fuzzy
sets. PFRA uses T1FSs to implement the research performance,
while the T2FS-based IDRA uses T2FSs. In the first experiment,
a subjective experiment on evaluating the user’s satisfaction de-
gree for the performance of the PFRA and T2FS-based IDRA is
done by the eight volunteers, respectively, i.e., the volunteer is
asked to make a self-evaluation for his/her own recommended
menu generated by the system and then gives a satisfaction de-
gree. Fig. 14(a) shows the self-evaluated results done by each
volunteer. Herein, the unit of evaluating the user’s satisfaction
degree is the percentage whose range is from 0% to 100%,
where “100%” means that the user has the highest satisfaction,
while “0%” means the lowest one. Hence, each volunteer (V1,
V2, ..., and V8) evaluates his/her own recommended menu and
then gives a feedback of the satisfaction degree, including “very
dissatisfied (0%–20%),” “dissatisfied (20%–40%),” “more-or-
less satisfied (40%–60%),” “satisfied (60%–80%),” and “very
satisfied (80%–100%).” For example, in Fig. 14(a), the first eval-
uated result (i.e., “V1/V1”) means that the first volunteer (V1)
gives a “satisfied (70%)” degree and “very satisfied (85%)” de-
gree for his own recommended menu generated by the PFRA
and the T2FS-based IDRA, respectively. In other words, vol-
unteer no. 1 considers that the performance of the T2FS-based
IDRA is better than one of the PFRA for his own recommended
menu.
The second experiment is to make an objective experiment,
i.e., the satisfaction degrees of PFRA and T2FS-based IDRA
are provided by the three domain experts. The satisfaction de-
gree also contains “very dissatisfied (0%–20%),” “dissatisfied
(20%–40%),” “more-or-less satisfied (40%–60%),” “satisfied
(60%–80%),” and “very satisfied (80%–100%).” The three do-
main experts (i.e., DE1, DE2, and DE3) also do an evaluation
of the eight volunteers’ recommended menus and then give
feedback for the degree of satisfaction. The evaluation results
from the viewpoint of the first, the second, and the third do-
main expert view of points are shown in Fig. 14(b), (c), and
(d), respectively. For an example, see Fig. 14(b). The first re-
sult (i.e., “V1/DE1”) means that the first domain expert gives
390 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
TABLE XI
I
NVOLVED DIABETICS’PROFILES
TABLE XII
S
OME T 2FSsADOPTED IN THIS PAPER
Fig. 13. T2FS of fuzzy concepts (a) Size and (b) PlannedDailyCaloriesNeeds.
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 391
Fig. 14. User’s satisfaction degree evaluated by (a) each volunteer, (b) domain expert no. 1, (c) domain expert no. 2, and (d) domain expert no. 3.
TABLE XIII
B
REAKFAST AND LUNCH INTAKE FOR THE SECOND VOLUNTEER ON OCTOBER 9, 2007
“satisfied (75%)” degree and “very satisfied (90%)” degree for
the volunteer no. 1’s recommended menus generated by the
PFRA and the T2FS-based IDRA, respectively. The other results
of Fig. 14(b), such as “V2/DE1,” “V3/DE1,” ..., and “V8/DE1,”
mean the first domain expert’s (DE1) satisfaction degrees of the
system-generated recommended menus for the volunteer nos. 2
(V2), 3 (V3), ..., and 8 (V8), respectively. Fig. 14(c) and (d)
shows the second and third domain experts’ degrees of satis-
faction of the menus for each volunteer, respectively. Fig. 14
indicates that the T2FS-based IDRA has higher user’s satisfac-
tion performance than the PFRA because the representation of
T2FS-based IDRA is much related to human thinking and regular
behavior. Therefore, the performance-evaluation index used in
comparing the proposed method (i.e., T2FS-based IDRA) with
the existing one (i.e., PFRA) is that both the domain experts and
involved people consider that the proposed method has higher
satisfaction.
Finally, some experimental results are displayed. For exam-
ple, the collected meal records for volunteer no. 2 on October
9, 2007, are listed in Table XIII, i.e., 1) He ate three fourths of
392 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
TABLE XIV
S
EMANTIC DESCRIPTIONS OF THE FOOD INTAKE ON OCTOBER 9, 2007, OF VOLUNTEER NO.2
TABLE XV
O
VERVIEW EXAMPLE OF RECOMMENDED RESULT FOR THE SIMPLIFIED USE OF THE PUBLIC USER
TABLE XVI
R
ECOMMENDED DIET ON JULY 17, 2007, FOR VOLUNTEER NO.1
LEE et al.: TYPE-2 FUZZY ONTOLOGY AND ITS APPLICATION TO PERSONAL DIABETIC-DIET RECOMMENDATION 393
Fig. 15. Recommended servings of six food groups.
Fig. 16. Recommended diet menu.
a bowl of rice, four fifths of a bowl of bamboo shoots, and one
tofu sheet. 2) For lunch, he ate three fourths of a piece of an
oriental pear and one dish of fried rice. Based on the portion
size of each food listed in Table XIII, the acquired total intake
of calories at breakfast and lunch are about 290 and 210 kcal,
respectively. Table XIV lists the semantic descriptions of the
food intake on October 9, 2007, of volunteer no. 2. It indi-
cates that the planned diet goal for volunteer 2, on this date, is
about 1800 kcal so that the recommended calories at dinner are
about 1300 kcal. Based on the recommended calories at dinner,
the recommended menu for volunteer no. 2 is finally inferred.
Table XV shows an overview example of recommended result
394 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 18, NO. 2, APRIL 2010
for the simplified use of the public user. Table XVI shows the
recommended diet provided by the T2FS-based IDRA on July
17, 2007, for volunteer no. 1. Figs. 15 and 16 show parts of the
screen shot of the recommended servings of six food groups and
the recommended diet menu for volunteer no. 2 on October 9,
2007, respectively.
VI. C
ONCLUSION AND DISCUSSIONS
This paper proposes a T2FO based on T2FSs. This ontol-
ogy is composed of a type-2 FPPO,atype-2 FFO, and some
type-2 FPFOs. Additionally, based on T2FO, this paper fur-
ther proposes a T2FS-based IDRA to apply to the balanced-diet
recommendation for diabetes domain, which includes the fol-
lowing:
1) T2FS construction;
2) a T2FS-based personal ontology filter;
3) a T2FS-based fuzzy inference mechanism;
4) a T2FS-based diet-planning mechanism;
5) a T2FS-based menu-recommendation mechanism;
6) a T2FS-based semantic-description mechanism.
For the design of the T2FSs, each expert provides the T1FS
that represents each linguistic label from the expert point of
view. Then, the generated T2FSs FOU will aggregate the differ-
ent experts’ opinions and handle the interexpert uncertainties.
The experimental results show that the proposed agent is able
to recommend an individual balanced menu, even offer a per-
sonal semantic description for the dinner intake. In addition, the
proposed T2FO-based agent achieves better user’s satisfaction
degree (compared with the T1FO system) as the type-2 based
system can better handle the faced uncertainties in the diabetes
domain, which result in a system that is closer to the human’s
thinking and regular behavior than the T1FO-based system.
On the current implementation, the performance-evaluation
index is more subjective due to the employment of the human
opinion of the domain experts and the diabetic patients. How-
ever, in the future, the performance-evaluation indexused should
be objective rather than subjective; however, for this, we will
need more hardware (which we are currently implementing) to
measure the wellbeing of the involved patients as a result of
the proposed system. Additionally, we will aim to provide auto-
matic learning of the ontology learning, as well as the automatic
construction of the food ontology. Furthermore, the proposed
agent will be applied to other areas’ diet and other related do-
mains, such as losing weight to enhance the performance and
the ability of the IDRA.
A
CKNOWLEDGMENT
The authors would like to thank the Institute for Information
Industry and the experts from the Diabetes Education Center,
Changhua Christian Hospital, Changhua, Taiwan, for their con-
structive and useful comments.
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Chang-Shing Lee (SM’09) received the Ph.D. de-
gree in computer science and information engi-
neering from the National Cheng Kung University,
Tainan, Taiwan, in 1998.
He is currently a Professor with the Department
of Computer Science and Information Engineering,
National University of Tainan, where he is the Direc-
tor of the Computer Center. He is also an Associate
EditoroftheJournal of Ambient Intelligence and Hu-
manized Computing. He is a member of the Editorial
Board for Applied Intelligence,theJournal of Ad-
vanced Computational Intelligence and Intelligent Informatics,andtheOpen
Cybernetics and Systemics Journal. He is a Guest Editor for the Applied Intelli-
gence Journal,theInternational Journal of Intelligent System,theInternational
Journal of Fuzzy Systems,andtheJournal of Internet Technology. His current
research interests include ontology applications, knowledge management, capa-
bility maturity model integration, meeting scheduling, and artificial intelligence,
and he is also interested in intelligent agents, web services, fuzzy theory and
applications, genetic algorithms, and image processing. He also holds several
patents on ontology engineering, document classification, image filtering, and
healthcare.
Dr. Lee has been the Emergent Technologies Technical Committee (ETTC)
Chair of the IEEE Computational Intelligence Society (CIS) since 2009. During
2008, he was the ETTC Vice Chair of the IEEE CIS. He is a Committee Member
of the IEEE CIS International Task Force on Intelligent Agents and on Emerg-
ing Technologies for Computer Go . He is also a member of the IEEE Systems,
Man, and Cybernetics Technical Committee on Intelligent Internet Systems.
He is an Associate Editor and a Guest Editor of the IEEE T
RANSACTIONS ON
COMPUTATIONAL INTELLIGENCE AND AI IN GAMES. He is also a member of
the Program Committees of more than 40 conferences. He is a member of the
Taiwanese Association for Artificial Intelligence and the Software Engineering
Association Taiwan.
Mei-Hui Wang received the B.S. degree in biomedi-
cal engineering from the Chung Yuan Christian Uni-
versity, Chung-Li, Taiwan, in 1993 and the M.S. de-
gree in electrical engineering from the Yuan Ze Uni-
versity, Chung-Li, in 1995.
She is currently a Researcher with the Ontology
Application and Software Engineering Laboratory,
Department of Computer Science and Information
Engineering, National University of Tainan, Tainan,
Taiwan. From July 1995 to June 2005, she was a Se-
nior Firmware Engineer with Delta Electronics, Inc.,
Chung-Li. Her research interests include intelligent agents, ontology engineer-
ing, and image processing.
Hani Hagras (M’03–SM’05) received the B.Sc.
and M.Sc. degrees in electric engineering from
Alexandria University, Alexandria, Egypt, and the
Ph.D. degree in computer science from the Univer-
sity of Essex, Colchester, U.K.
He is currently a Professor with the School of
Computer Science and Electronic Engineering, Uni-
versity of Essex, where he is also the Director of
the Computational Intelligence Center and the Head
of the Fuzzy Systems Research Group. His research
interests include computational intelligence, notably
type-2 fuzzy systems, fuzzy logic, neural networks, genetic algorithms, and
evolutionary computation. He has authored or coauthored more than 150 papers
in international journals, conferences, and books.
Prof. Hagras has won numerous prestigious international awards, including
the IEEE Computational Intelligence Society IEEE T
RANSACTIONS ON FUZZY
SYSTEMS Outstanding Paper Award for his work on type-2 fuzzy controllers.
