# Fuzzy Arithmetic

From: Clifton Black (cblack1212@yahoo.com)
Date: Sat Jan 06 2001 - 12:42:35 MET

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Hello:

I would like an input from anyone who is familiar with fuzzy
arithmetic.

The problem is regarding the division of two trapezoidal fuzzy
numbers. In some cases I have got incorrect results.
The formula for the division of two trapezoidal fuzzy numbers (m & n)
is based on 4 cases:
1. m > 0 & n > 0; 2. m <0 & n>0; 3. m >0 & n <0; 4. m <0 & n < 0.
Consider the fuzzy numbers A & B:
Let A = [0.11 0.2 0.4 0.6] & B=[-0.4 0.2 0.4 0.6]
The two cases that seem to apply are case 1 and case 3
Using case 1(m > 0 & n > 0)
A/B = [0.18 0.5 2.0 -1.5]

Using case 3(m > 0 & n < 0)
A/B = [1.0 1.0 1.0 -0.275]

These are both incorrect. It also raises the question, how does one
determine if a trapezoidal fuzzy number is negative. Do you think
finding the crisp average through defuzzification is accurate?

Cases 2 and 4 (obviously did not apply) also yielded incorrect
results.

Clifton

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