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CDI
MING
Introduction to
Innovative Design
Thinking
Lecture 4
1.
2.
3.
4.
Concept of Fuzzy Logic
Lateral thinking
Six Thinking Hats
Problem Identification
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Fuzzy Logic
Fuzzy logic is a notion
introduced by Lotfi Zadeh, a
Russian professor in 1964.
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Fuzzy Logic
It is a notion of uncertainty.
Unlike logical thinking in a
dialectic deduction or
induction pattern, fuzzy
logic aims at investigating
the Class – categories.
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Fuzzy Logic
Fuzzy logic is a superset of
conventional (Boolean) logic
that has been extended to
handle the concept of partial
truth -- truth values
between"completely true"
and "completely false".
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Fuzzy Logic
The process of “fuzzification” as a
methodology to generalize ANY
specific theory from a crisp
(discrete) to a continuous(fuzzy)
form. Thus recently researchers have
also introduced "fuzzy calculus",
"fuzzy differential equations",and so
on .
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Fuzzy Logic
Fuzzy logic depends on the
degree of “truth”. The issue
studying can be categorized into
mathematical calculation and
classify the in-between
differences in the degree of
“truth” and “fact”.
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Fuzzy Logic
New
Perception
Perception
Concept
Idea
Heritage
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Fuzzy Logic
New
Perception
Perception
Proficiency of
Languages
Concept
Idea
Heritage
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Fuzzy Logic
New
Perception
Superordinates
Perception
Concept
Idea
Ordinates
Subordinates
Heritage
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Fuzzy Logic
In classical set theory, a
subset U of a set S can be
defined as a mapping from
the elements of S to the
elements of the set {0,1},
U: S --> {0, 1}
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Fuzzy Logic
This mapping may be represented as
a set of ordered pairs, with exactly
one ordered pair present for each
element of S. The first element of the
ordered pair is an element of the set
S, and the second element is an
element of the set {0, 1}.
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Fuzzy Logic
The value zero is used to represent
non-membership, and the value one
is used to represent membership.
The truth or falsity of the statement x
is in U is determined by finding the
ordered pair whose first element is x.
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Fuzzy Logic
The statement is true if the
second element of the
ordered pair is 1, and the
statement is false if it is 0.
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Fuzzy Logic
Similarly, a fuzzy subset F of a
set S can be defined as a set of
ordered pairs, each with the first
element from S, and the second
element from the interval [0,1],
with exactly one ordered pair
present for each element of S
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Fuzzy Logic
This defines a mapping between elements
of the set S and values in the interval
[0,1]. The value zero is used to represent
complete non-membership, the value one
is used to represent complete
membership, and values in between are
used to represent intermediate DEGREES
OF MEMBERSHIP.
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Fuzzy Logic
The set S is referred to as the
UNIVERSE OF DISCOURSE for the
fuzzy subset F. Frequently, the mapping
is described as a function, the
MEMBERSHIP FUNCTION of F. The
degree to which the statement x is in F is
true is determined by finding the ordered
pair whose first element is x.
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Fuzzy Logic
The DEGREE OF TRUTH of the
statement is the second element
of the ordered pair. In practice,
the terms "membership function"
and fuzzy subset get used
interchangeably.
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Fuzzy Logic
Let's talk about people and
"tallness". In this case the set S
(the universe of discourse) is the
set of people. Let's define a
fuzzy subset TALL, which will
answer the question "to what
degree is person x tall?"
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Fuzzy Logic
TALL as a LINGUISTIC
VARIABLE, which represents
our cognitive category of
"tallness". To each person in the
universe of discourse, we have to
assign a degree of membership in
the fuzzy subset TALL.
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Fuzzy Logic
The easiest way to do this is with a
membership function based on the
person's height.
Tall(x) = { 0, if height(x) < 5 ft.,
(height(x)-5ft.)/2ft.,
if 5 ft. <= height (x) <= 7 ft.,
1, if height(x) > 7 ft. }
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Fuzzy Logic
We can draw a graph like this:
1.0
0.5
0.0
5.0
7.0
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Fuzzy Logic
Given this definition, here are some example
values:
Person Height degree of tallness
Billy
3' 2"
0.00 [I think]
Yoke 5' 5"
0.21
Drew
5' 9"
0.38
Erik
5' 10"
0.42
Mark
6' 1"
0.54
Kareem 7' 2"
1.00
[depends on who you ask]
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Fuzzy Logic
Expressions like "A is X" can be
interpreted as degrees of truth,
e.g., "Drew is TALL" = 0.38.
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Fuzzy Logic
The standard definitions in fuzzy
logic are:
truth (not x) = 1.0 - truth (x)
truth (x and y) = minimum (truth(x),
truth(y))
truth (x or y) = maximum (truth(x),
truth(y))
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Fuzzy Logic
This is a very commonly used
mathematical calculation in
developing artificial intelligence.
The power of fuzzy logic
depends on the ambiguity of the
language.
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Fuzzy Logic
Hence, beyond profound
calculation, we can make use
of the concept to build up a
fuzzy map, helping us to see
the vague argument more
clearly and thoroughly.
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Lateral Thinking
My true story:
When I was studying design
……
If you were me, what would
you do in order to get back
the pen???
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Lateral Thinking
As you can see, logical
thinking sometimes does
not help in problem
solving. You have to find
another way out.
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Lateral Thinking
Lateral thinking is a
method introduced by
Dr. Edward De Bono.
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Lateral Thinking
It is also known as
Horizontal thinking. This
method is totally different
from the traditional
logical thinking – Vertical
thinking.
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Lateral Thinking
Problem
Logical Thinking is a
vertical thinking
method started from
the problem towards
the solution in step by
step approach.
Solution
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Lateral Thinking
Unlike Logical
thinking, lateral
thinking encourage
people to think all
possible alternatives.
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Lateral Thinking
By lateral thinking, we are trying
to propose as many “crazy” ideas
as we can, without applying
logic or knowledge.
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Lateral Thinking
If blue is the best
proposal, we then
started to build up
the logic to study
how the idea can
be executed.
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Lateral Thinking
A
If H?
In lateral thinking, we only
ask WHAT IF, and keep all
nonsense as treasure. Do not,
and never criticize in the
lateral thinking process.
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Lateral Thinking
What if X
A
U-shape
thinking
model
CX
BX
CDX
EX
Solution
DEX
Sometimes,
we cannot depend
on linear logical
thinking. Using the
U-shape model can
help us keep on
examining the
problem.
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Lateral Thinking
A
X
X’
We can also set
up the antidesign statement
for the problem
so as to create
more ideas.
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Lateral Thinking
There are no fixed rules
in lateral thinking. Hence,
there are some points to
note to arouse creativity.
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Lateral Thinking
1.
2.
3.
4.
5.
Encourage intuition.
Allows crazy ideas.
Simple is the best.
Make use of possibilities.
Treasure coincident.
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Lateral Thinking
An interesting question
before you go:
Why 7 + 6 equal to 10 ?
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References
Lateral Thinking, Edward
de Bono, 1985
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Six Thinking Hats
This is a thinking method
introduced by Dr. Edward
De Bono. It depends highly
on role-playing technique.
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Six Thinking Hats
There are six different
coloured thinking hats,
which are White, Red,
Black, Yellow, Green and
Blue.
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Six Thinking Hats
PROBLEM
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Six Thinking Hats
White Hat:
 Collecting Data and
Facts
 No interpretation and
no personal opinion
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Six Thinking Hats
Red Hat:
 Expression of one’s
emotion and feeling.
 No need to elaborate
the reasons behind.
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Six Thinking Hats
Black Hat:
 Collecting all negative
comments.
 It helps to build up the
negative design criteria.
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Six Thinking Hats
Yellow Hat:
 Optimistic opinions
with reasons.
 Constructive ideas with
logical thinking
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Six Thinking Hats
Green Hat:
 Creative ideas under
lateral thinking.
 Select the appropriate
solution and skill.
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Six Thinking Hats
Blue Hat:
 Drafting of design
statement and criteria.
 Control and monitor the
creative thinking process.
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Six Thinking Hats
It is very important that you
know the role of each hat. When
conducting six thinking hats
method in lesson, students can
require others to wear or change
their hats during the discussion.
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Six Thinking Hats
It is also important that
throughout the discussion,
students ( and teachers )
should understand thoroughly
the use of each hat and its
limitation.
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Six Thinking Hats
Teacher can require student
to wear specific hat when
discussing an issue. For
example, let us all wear Red
hats to discuss this problem.
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Six Thinking Hats
Participants can require
others to change specific hat
when discussing an issue. For
example, let us all change the
Red hats to Black hats to
further discuss this problem.
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Six Thinking Hats
Despite the fact that it looks
childish for participants to
wear hats when discussing, it
helps them to build up their
mind set in the role play
within an argument.
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Six Thinking Hats
In order to make students feel
more “comfortable” in using
the six hats thinking method,
I designed a hexagonal model
for such activities.
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Six Thinking Hats
Criteria
Fact
Creative
Problem
Emotion
Positive
Negative
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Six Thinking Hats
After sorted out all the possibilities,
we have to map out all of them and
select the best solutions. It relies on
the deduction of concept map to see
the relationship between each
proposal, and logic to execute the
ideas.
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Six Thinking Hats
Are you ready?
Remember, play the role when
you wear specific hat!!!
Let us try this out. Any subject
matter you would like to study
or solve?
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Six Thinking Hats
As you may see in the
activities, the six thinking hats
depends on the participation of
role playing and it may works
out lots of possibilities out of
your imagination.
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Six Thinking Hats
It can be a very powerful tool
when you encounter a specific
problems and can pretended to
be an outsider to scrutinize the
subject matter that you are
working at.
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Six Thinking Hats
That is why lateral thinking and
Six hats thinking method are also
known as “Serious thinking”
methodology. For further study,
here is a CDROM designed by one
of my friend Miss Leung Ching
Yee.
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References
Six thinking hats, Edwaed
De Bono, 1988
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Problem Identification
Words can help us to think,
question, criticize and
analysis a problem.
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Problem Identification
Brief for HKCE D&T design
project 2001:
A restaurant menu holder can
help promote food item.
To design a restaurant menu
holder for a selected restaurant.
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Problem Identification
How can you guide students
to build up their own mind
set in designing the product
under such “smartly”
drafted design brief?
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Problem Identification
Mind mapping, concept
map, linguistic analysis and
logic can help them to
identify a problem and set
up new design criteria.
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Problem Identification
The way to identify a
problem is first of all
understand your position, ie.
What is your role play.
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Problem Identification
You have to decipher the
problem(s) behind the
stated problem instead of
the mentioned statement
itself.
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Problem Identification
Under careful examination,
the problem can be
elaborated by various
means.
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Problem Identification
1.
2.
3.
4.
5.
6.
Logical thinking
Linguistic analysis
Mind map and concept map
Questioning
Interpretation
Semiotic ……………..
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Problem Identification
Demonstration:
Is there any problem you
would like me trying to
identify?
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Next Week
Lecture 5
1. Brain Storming
2. The power of group project
3. Questioning
4. Importance of presentation
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Next Week
Lecture 6
1. Interpretation
2. Semiotics
3. Imagery versus Languages
4. Free association
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Ming
Thank You