Fuzzy thinking

Natural language doesn’t fit neatly into logical or mathematical categories. That makes natural language processing difficult. But the problem is being addressed. Patrick Durusau cites an article[1] that suggests linguistic variables cannot be members of ordinary sets, that fuzzy sets may be a better way of handling linguistic terms.

What is a fuzzy set? In set theory, an entity is either a member of a set or it is not — a “binary” or discrete distinction, true or false. In fuzzy sets, an entity is more or less a member of a set, a continuous distinction. For example, if an object is a member of the fuzzy set red, then it can be more red or less red than another member. In normal sets, an object is either “1” or “0” as to its membership in a set. In fuzzy sets, an object can be “0.5” or “0.2” as to its membership.

But there are many linguistic terms that are discrete: singular-plural, male-female-neuter, past-present-future, perfect-imperfect and many others. The citation from the article in Durusau’s blog suggests the actual variable is the linguistic object itself: sentence, word, etc. The article says, “Linguistic terms are essentially subjective categories for a linguistic variable.” I don’t think so. Languages inflect for many categories, and that is hardly subjective.

I’ve got the article on order, so I will need to revisit this when I read it. Reality is a single perceptual unity. Humans divide up reality in different ways. And it does matter how you slice it!

[1] H. Aktaș and N. Çağman, “Soft sets and soft groups,” Information sciences, vol. 177, iss. 13, pp. 2726-2735, 2007.
[Bibtex]
@ARTICLE{Aktas:2007fk,
author = {Haci Aktaș and Naim {\c{C}}a\&\#287;man},
title = {Soft sets and soft groups},
journal = {Information Sciences},
year = {2007},
volume = {177},
pages = {2726-2735},
number = {13},
month = {July},
date-added = {2010-09-11 08:24:47 -0400},
date-modified = {2010-09-11 09:51:00 -0400},
keywords = {fuzzy sets}
}

Comments (2)

  • Kirk,

    I don’t think you should key so strongly on the use of the term “subjective.”

    The authors said: “Linguistic terms do not hold exact meaning, however, and may be understood differently by different people. The boundaries of a given term are rather subjective, and may also depend on the situation.”

    Nothing remarkable there and nothing inconsistent with your finding instances where traditional set theory would work.

    Nor does finding instances where traditional set theory would work mean that is applicable to all linguistic terms.

    Oh, btw, “linguistic term” was not being used as a label for terms used by linguists. Think names/labels in a natural language.

  • It’s what comes from commenting before reading the article (which will take awhile getting to me). :-(

    Does “linguistic term” mean “word in a language”, then? I’m having a hard time visualizing how that would be “fuzzy”.

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