**Subject: **Re: does fuzzy bound probability?

*WSiler@aol.com*

**Date: **Tue Nov 21 2000 - 15:55:30 MET

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Jaime B. Zamora S.: "Fuzzy logic and EMG pattern recognition."**Previous message:**Nadine Gisler: "no title"**Maybe in reply to:**Scott Ferson: "does fuzzy bound probability?"**Next in thread:**Scott Ferson: "Re: does fuzzy bound probability?"**Maybe reply:**WSiler@aol.com: "Re: does fuzzy bound probability?"

In a message dated 11/21/00 5:10:46 AM Central Standard Time, scott@ramas.com

writes:

<< Because (standard) fuzzy arithmetic makes no assumptions about the

* > dependence or independence among quantities, it has been suggested
*

* > that fuzzy arithmetic might be able to provide bounds on probability
*

* > distributions in cases where the dependence among input variables
*

* > cannot be specified empirically.
*

*>>
*

I'm not sure what basis was offered for the statement that fuzzy logic makes

no assumptions about independence, but I'm afraid that the statement is not

true. Standard Zadehian min-max fuzzy logic assumes implicitly that the

operands of the logical operations AND and OR are positively associated as

much as possible, just as the probabilistic AND (a*b) and OR (a + b - a*b)

assumes independence (zero association) and the bounded sum and difference

logic AND (max(0, a + b - 1)) and OR (min(a +b - 1)) assume maximum negative

association. Jim Buckley and I have a paper or two in FS&S which discuss this

point and present a family of multivalued logic parameterized in terms of the

correlation coefficient between the operands, based either on neccessity (a

AND NOT a) or past history.

Consequently, any manipulations which employ fuzzy logical operations (such

as the extension principle) implicitly make an assumption about the

independence of the operands. That would seem to include fuzzy arithmetic.

William Siler

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