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Introduction to Innovative Design Thinking. CDI. Lecture 4. Concept of Fuzzy Logic Lateral thinking Six Thinking Hats Problem Identification. Fuzzy Logic. Fuzzy logic is a notion introduced by Lotfi Zadeh, a Russian professor in 1964. Fuzzy Logic.

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lecture 4
Lecture 4
  • Concept of Fuzzy Logic
  • Lateral thinking
  • Six Thinking Hats
  • Problem Identification
fuzzy logic
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







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Fuzzy Logic



Proficiency of Languages





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Fuzzy Logic










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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.,


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:






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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.

lateral thinking
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


Logical Thinking is a vertical thinking method started from the problem towards the solution in step by step approach.


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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


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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What if X








Lateral Thinking

U-shape thinking model


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




We can also set up the anti-design 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
  • 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 ?

  • Lateral Thinking, Edward de Bono, 1985
six thinking hats
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

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







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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.

  • Six thinking hats, Edward De Bono, 1988
problem identification
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, i.e. 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
  • Logical thinking
  • Linguistic analysis
  • Mind map and concept map
  • Questioning
  • Interpretation
  • Semiotic ……………..
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Problem Identification


Is there any problem you would like me trying to identify?