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Fuzzy number

Fuzzy number is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Fuzzy number rather than just read about it. In short: A fuzzy number is a generalization of a regular real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. This weight is called the membership function.

Fuzzy number — main illustration
Fuzzy number — illustration

Key takeaways

  • Fuzzy number belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Fuzzy number to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Fuzzy number from memory before moving on to harder problems.

Reference excerpt

A fuzzy number is a generalization of a regular real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. This weight is called the membership function. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. Just like fuzzy logic is an extension of Boolean logic (which uses absolute truth and falsehood only, and nothing in between), fuzzy numbers are an extension of real numbers. Calculations with fuzzy numbers allow the incorporation of uncertainty on parameters, properties, geometry, initial conditions, etc. The arithmetic calculations on fuzzy numbers are implemented using fuzzy arithmetic operations, which can be done by two different approaches: (1) interval arithmetic approach; and (2) the extension principle approach. A fuzzy number is equal to a fuzzy interval. The degree of fuzziness is determined by the a-cut which is also called the fuzzy spread.

See also Fuzzy set Uncertainty Interval arithmetic Random variable

References

External links Fuzzy Logic Tutorial

Illustrations

Fuzzy number: Fuzzy arithmetic
Fuzzy arithmetic

Worked examples

Example 1 — a first encounter with Fuzzy number

Start with the simplest possible case. Write down what Fuzzy number claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Fuzzy number before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Fuzzy number ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Fuzzy number

In research
Fuzzy number appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Fuzzy number in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Fuzzy number is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fuzzy logic, Real numbers, so understanding it makes those chapters shorter.
In everyday life
Look for Fuzzy number outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Fuzzy number in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Fuzzy number means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Fuzzy number out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Fuzzy number in simple terms?

A fuzzy number is a generalization of a regular real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. This weight is called the membership function.

Why does Fuzzy number matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Fuzzy number?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Fuzzy number.

Tags

  • Fuzzy logic
  • Real numbers

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