Fuzzy sets

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tags: 🌱 date: 03--Apr--2023

Fuzzy sets

A fuzzy set A in X is expressed as a set of ordered pairs

$$A = {(x,\mu_A(x))|x\in X}$$ Where

• A is fuzzy set
• X is the Universe or Universe of discourse
• mu(x) is the membership function
• x is the crisp input

Convexity of fuzzy set

For any $\lambda \in [0,1]$

Example

When X is discrete, then A would have be discrete as well. $\sum{\mu_A(x)|x}$

When X is Continuous distribution, then the function above must be used $\integrate{\mu(x)|x}$

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