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.

    Thanks for your input
    Clifton

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