Re: number of membership functions?
Sat, 6 Jun 1998 19:30:40 +0200 (MET DST)


May I have a copy of
Discussion on soft computing at FLINS'96

A ftppable or electronic version is helpful.

Thanx in advance.


您在 <> 文章內提到:
: At 03:46 98-05-18 +0200, you wrote:
: >
: >
: >
: >My first question:
: >
: >I remember reading a passage about the number of
: >membership functions (MFs) that should be (or recommended)
: >used in a fuzzy system, in Constantin von Altrock's book.
: >The recommended number was about (if I'm not wrong) 7 for
: >each variable. The reason for using such a low number was
: >that humans can use only few linguistic terms simultaneously
: >during their reasoning or decision making processes.
: >
: >Wouldn't using more MFs increase the precision of the fuzzy
: >system? Suppose we are provided with sufficient amount of
: >(training) data to generate a rule-base that could cover
: >tens(or hundreds) of MFs. Then why limit ourselves with few MFs?

: Using more MFs will increase the precision of the fuzzy system to
: approximate a function. This has been proved by Bart Kosko. However, if you
: have some practical experience of making fuzzy controller, you will know the
: following fact. The degree of complexity (memory, computing time, etc.) of
: your system will also be increased exponentially if the number of MFs are
: increased. Will the precision be increased exponentially too? If yes, you
: are right, and we don't need to limit ourselves with few MFs. Unfortunately,
: when the number of MFs are big enough, the precision of the system will be
: increased much slower and slower. Therefore, a dilemma lies between the
: precision and the complexity. Normally, 7 MFs can provide good precision and
: proper complexity which both are acceptable by us.

: >
: >Second question:
: >
: >Fuzzy logic is always referred as the technique which can deal
: >with linguistic uncertainties. That's why the MFs are represented
: >by linguistic terms. This makes it easy to incorporate linguistic
: >rules obtained from a human expert.
: >
: >However, in cases where only numerical data is used to generate
: >rules, is it still necessary to label each MF by a linguistic term?
: >

: If you want to use fuzzy logic, I think so. Otherwise, you can use neural
: network which is good to process the numerical data.

: >What if a large number (say 50) of MFs is used? Wouldn't it
: >be inconvenient to use a separate linguistic term for each MF?
: >Could "numbers" instead of linguistic terms be used? In that case
: >a fuzzy rule would look like:
: >(x1,x2)-->(y):
: >If x1 is "13" and x2 is "35" then y is "46"

: Actually, a practical fuzzy controller is equivalent to a classical mapping.
: Therefore you can do the above crisp rules. The condition is that you must
: know exactly which point is mapping to which value. But please remember,
: fuzzy logic is supposed to be used in an environment with uncertainty in which
: it is not possible or too difficult to get all input-output data.

: Fuzzy logic, as well as other techniques of soft computing, provides us a
: way to solve the problem with a lower cost but a good enough solution.
: Purely pursuing high precision is not the purpose of fuzzy logic.

: For further understanding, please refer to

: "Discussion on soft computing at FLINS'96", by X. Li, D. Ruan, and A. J. van
: der Wal, International Journal of Intelligent Systems, Vol. 13, 287-300 (1998).

: Regards.

: Xiaozhong
: _____________________________________________________________________
: * Xiaozhong Li. PhD, Currently Young Scientific Researcher *
: * Belgian Nuclear Research Centre (SCK.CEN) *----------*
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