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.
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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