science

Fuzzy relation

Fuzzy relation is a science 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 relation rather than just read about it. In short: A fuzzy relation is the cartesian product of mathematical fuzzy sets. Two fuzzy sets are taken as input, the fuzzy relation is then equal to the cross product of the sets which is created by vector multiplication.

Key takeaways

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

Reference excerpt

A fuzzy relation is the cartesian product of mathematical fuzzy sets. Two fuzzy sets are taken as input, the fuzzy relation is then equal to the cross product of the sets which is created by vector multiplication. Usually, a rule base is stored in a matrix notation which allows the fuzzy controller to update its internal values. From a historical perspective, the first fuzzy relation was mentioned in the year 1971 by Lotfi A. Zadeh. A practical approach to describe a fuzzy relation is based on a 2d table. At first, a table is created which consists of fuzzy values from 0..1. The next step is to apply the if-then-rules to the values. The resulting numbers are stored in the table as an array. Fuzzy relations can be utilized in fuzzy databases.

References

Illustrations

Worked examples

Example 1 — a first encounter with Fuzzy relation

Start with the simplest possible case. Write down what Fuzzy relation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 relation 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 relation 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 relation

In research: Fuzzy relation appears in science 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 relation 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 relation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fuzzy logic, so understanding it makes those chapters shorter.
In everyday life: Look for Fuzzy relation 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 relation in 20 minutes

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

Frequently asked questions

What is Fuzzy relation in simple terms?

Why does Fuzzy relation matter?

Because it connects several science 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 relation?

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 relation.