Question

Question:
What is the Bandwidth of fuzzy set A which is given as follows: A = (10, 0.1), (15, 0.2), (20, 0.5), (25,
0.4), (30, 0.4), (35, 0.5), (40,0.2), (45, 0.1)​

Answer 1

Answer: 15

Explanation:

For a fuzzy set , bandwidth is defined as the distance between 2 unique crossover points.

:-> Bandwidth (A) = | x1 - x2 |

Taking x1 = 10

and x2 = 25

Bandwidth = | 10 - 25 | =  15.

Answer 2

The bandwidth of fuzzy set A = (10, 0.1), (15, 0.2), (20, 1/2), (25,0.4), (30, 0.4), (35, 0.5), (40,0.2), (45, 0.1)​ is 15.

Given

A fuzzy set A = (10, 0.1), (15, 0.2), (20, 1/2), (25,0.4), (30, 0.4), (35, 0.5), (40,0.2), (45, 0.1)​

To Find:

The bandwidth of the fuzzy set A

Solution:

The crossover points are seen in μₐ(x) = 0.5

The distance between two unique crossover points gives the bandwidth of the fuzzy set.'

In the given fuzzy set,

A = (10, 0.1), (15, 0.2), (20, 1/2), (25,0.4), (30, 0.4), (35, 0.5), (40,0.2), (45, 0.1)​

For (20,0.5), x₁ = 20

For (35,0.5), x₂ = 35

To find the bandwidth,

BW(A) = | x₁ - x₂ |

BW(A) = | 20 - 35 |

BW(A) = | 15 |

Therefore, the bandwidth of the given set A is 15.

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