Re: Fuzzy Arithmetic

From: Phil Diamond (pmd@maths.uq.edu.au)
Date: Mon Jan 08 2001 - 12:27:02 MET

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    In comp.ai.fuzzy you write:

    But zero is contained in the support of B, so the support of A/B is
    an infinite interval, and so A/B is not a fuzzy number. (If I understand
    your notation correctly).

    Cordially, Phil Diamond

    >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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